**2.5.2 Gearbox casing model – Component mode synthesis method**

Lumped parameter modelling (LPM) is an efficient means to express the internal dynamics of transmission systems; masses and inertias of key components such as gears, shafts and bearings can be lumped at appropriate locations to construct a model. The advantage of the LPM is that it provides a method to construct an effective dynamic model with relatively small number of degrees-of-freedoms (DOF), which facilitates computationally economical method to study the behaviour of gears and bearings in the presence of nonlinearities and geometrical faults [32, 33, 34, 35].

One of the limitations of the LPM method is that it does not account for the interaction between the shaft and the supporting structure; i.e. casing flexibility, which can be an important consideration in light weight gearboxes, that are common aircraft applications. Not having to include the appropriate effect of transmission path also results in poor comparison between the simulated and measured vibration signals.

Finite Element Analysis (FEA) is an efficient and well accepted technique to characterize a dynamic response of a structure such as gearbox casings. However, the use of FEA results in a large number of DOF, which could cause some challenges when attempt to solve a vibrodynamic model of a combined casing and the LMP of gearbox internal components. Solving a large number of DOFs is time consuming even with the powerful computers available today and it could cause a number of computational problems, especially when attempting to simulate a dynamic response of gear and bearing faults which involves nonlinearities.

To overcome this shortcoming, a number of reduction techniques [36, 37] have been proposed to reduce the size of mass and stiffness matrix of FEA models. The simplified gearbox casing model derived from the reduction technique is used to capture the key characteristics of dynamic response of the casing structure and can be combined with the LPM models of gears and REBs.

The Craig-Bampton method [37] is a dynamic reduction method for reducing the size of the finite element models. In this method, the motion of the whole structure is represented as a combination of boundary points (so called master degree of freedom) and the modes of the structure, assuming the master degrees of freedom are held fixed. Unlike the Guyan reduction [38], which only deals with the reduction of stiffness matrix, the Craig-Bumpton

Gearbox Simulation Models with Gears and Bearings Faults 31

By applying this transformation, the number of DOFs of the component will be reduced. The new reduced mass and stiffness matrices can be extracted using Equations 2.5.11 &

*t*

0

0 0

Thus Equation-2.5.7 can be re-written in the new reduced form using the reduced mass and

Where *Mbb* is the boundary mass matrix i.e. total mass properties translated to the boundary points. *bb k* is the interface stiffness matrix, i.e. stiffness associated with displacing one boundary DOF while the others are held fixed. The *Mbq* is the component matrix ( *Mqb*

\ 0

0 \ *kqq i*

\ 0

0 \

0 0 0

Finally the dynamic equation of motion (including damping) using the Craig-Bampton

*M M u u uF k*

*bb bq m m bb m m*

 = fraction of critical damping) For more detailed explanation of the techniques related to the modelling of rolling element bearings and the application of component mode synthesis (CMS) techniques, refer to the

*qb*

works by Sawalhi, Deshpande and Randall [41].

= modal damping (

*M M u uF k*

*reduced reduced reduced M k F bb bq m bb m m*

*qb qq qq*

If the mode shapes have been mass normalized (typically they are) then:

*ii i i k m*/

, and,

*i* is the eigenvalues; 2

stiffness matrices as well as the modal coordinates as follows:

*t Mreduced T MT* (2.5.11)

*reduced k T kT* (2.5.12)

*M I qq* (2.5.15)

2

0 2 0 0

*MIq q q* (2.5.16)

(2.5.14)

*MM q k q* (2.5.13)

2.5.12 respectively:

is the transpose of *Mbq* ).

where

where 2

transform can be written as:

and

method accounts for both the mass and the stiffness. Furthermore, it enables defining the frequency range of interest by identifying the modes of interest and including these as a part of the transformation matrix. The decomposition of the model into both physical DOFs (master DOFs) and modal coordinates allows the flexibility of connecting the finite elements to other substructures, while achieving a reasonably good result within a required frequency range. The Craig-Bumpton method is a very convenient method for modelling a geared transmission system as the input (excitation) to the system is not defined as forces, but as geometric mismatches at the connection points (i.e. gear transmission error and bearing geometric error). The following summary of the Craig-Bampton method is given based on the references [39-41].

In the Craig-Bampton reduction method, the equation of motion (dynamic equilibrium) of each superelement (substructure), without considering the effect of damping, can be expressed as in Equation-2.5.6:

$$[M]\{\ddot{u}\} + [k]\{u\} = \{F\} \tag{2.5.6}$$

Where [ ] *M* is the mass matrix, [ ] *k* is the stiffness matrix, *F* is the nodal forces, *u* and *u* are the nodal displacements and accelerations respectively. The key to reducing the substructure is to split the degrees of freedom into masters *um* (at the connecting nodes) and slaves *us* (at the internal nodes). The mass, the stiffness and the force matrices are rearranged accordingly as follows:

$$
\begin{aligned}
\overbrace{\begin{bmatrix}
\boldsymbol{M}\_{mm} & \boldsymbol{M}\_{ms} \\
\boldsymbol{M}\_{sm} & \boldsymbol{M}\_{ss}
\end{bmatrix}}
\end{aligned}
\begin{aligned}
\begin{bmatrix}
\ddot{\boldsymbol{u}}\_{m} \\
\ddot{\boldsymbol{u}}\_{s}
\end{bmatrix}
\end{aligned}
\begin{aligned}
\begin{aligned}
\boldsymbol{\underline{k}}\_{m} \\
\boldsymbol{\underline{k}}\_{s}
\end{aligned}
\end{aligned}
\begin{aligned}
\begin{aligned}
\boldsymbol{\underline{k}}\_{m} \\
\boldsymbol{\underline{k}}\_{m} \\
\boldsymbol{\underline{k}}\_{s}
\end{aligned}
\end{aligned}
\begin{aligned}
\begin{aligned}
\boldsymbol{\underline{k}}\_{m} \\
\boldsymbol{\underline{k}}\_{m} \\
\boldsymbol{\underline{k}}\_{s}
\end{aligned}
\end{aligned}
\begin{aligned}
\boldsymbol{\underline{k}}\_{m} \\
\boldsymbol{\underline{k}}\_{m} \\
\boldsymbol{\underline{k}}\_{s}
\end{aligned}
\end{aligned}
\begin{aligned}
\boldsymbol{\underline{k}}\_{m} \\
\boldsymbol{\underline{k}}\_{m} \\
\boldsymbol{\underline{k}}\_{s}
\end{aligned}
\end{aligned}
\begin{aligned}
\boldsymbol{\underline{k}}\_{m} \\
\boldsymbol{\underline{k}}\_{m} \\
\boldsymbol{\underline{k}}\_{s}
\end{aligned}
\end{aligned}
\begin{aligned}
\boldsymbol{\underline{k}}\_{m} = \begin{bmatrix}
\boldsymbol{F}\_{m} \\
\boldsymbol{\underline{k}}\_{m} \\
\boldsymbol{\underline{k}}\_{m} \\
\boldsymbol{\underline{k}}\_{m} \\
\boldsymbol{\underline{k}}\_{m} \\
\boldsymbol{\underline{k}}\_{m} \\
\boldsymbol{\underline{k}}\_{m} \\
\boldsymbol{\underline{k}}\_{m} \\
\boldsymbol{\underline{k}}\_{m} \\
\boldsymbol{\underline{k}}\_{m} \\
\boldsymbol{\underline{k}}\_{m} \\
\boldsymbol{\underline{k}}\_{m} \\
\end{aligned}}
\end{aligned}$$

The subscript *m* denotes master, *s* denotes slave. Furthermore, the slave degrees of freedom (internals) can be written by using generalized coordinates (modal coordinates by ( *q* ) using the fixed interface method, i.e. using the mode shapes of the superelement by fixing the master degrees of freedom nodes (connecting/ boundary nodes). The transformation matrix (*T* ) is the one that achieves the following:

$$
\begin{Bmatrix} \mu\_m\\ \mu\_s \end{Bmatrix} = T \begin{Bmatrix} \mu\_m\\ q \end{Bmatrix} \tag{2.5.8}
$$

For the fixed interface method, the transformation matrix (*T* ) can be expressed as shown in Equation-2.5.9:

$$T = \begin{bmatrix} I & \mathbf{0} \\ G\_{\text{sur}} & \phi\_s \end{bmatrix} \tag{2.5.9}$$

where,

$$\mathbf{G}\_{sm} = -k\_{ss}^{-1} k\_{sm} \tag{2.5.10}$$

and *s* is the modal matrix of the internal DOF with the interfaces fixed. By applying this transformation, the number of DOFs of the component will be reduced. The new reduced mass and stiffness matrices can be extracted using Equations 2.5.11 & 2.5.12 respectively:

$$M\_{reduced} = \mathbf{T}^t \mathbf{M} \mathbf{T} \tag{2.5.11}$$

and

30 Mechanical Engineering

method accounts for both the mass and the stiffness. Furthermore, it enables defining the frequency range of interest by identifying the modes of interest and including these as a part of the transformation matrix. The decomposition of the model into both physical DOFs (master DOFs) and modal coordinates allows the flexibility of connecting the finite elements to other substructures, while achieving a reasonably good result within a required frequency range. The Craig-Bumpton method is a very convenient method for modelling a geared transmission system as the input (excitation) to the system is not defined as forces, but as geometric mismatches at the connection points (i.e. gear transmission error and bearing geometric error). The following summary of the Craig-Bampton method is given

In the Craig-Bampton reduction method, the equation of motion (dynamic equilibrium) of each superelement (substructure), without considering the effect of damping, can be

Where [ ] *M* is the mass matrix, [ ] *k* is the stiffness matrix, *F* is the nodal forces, *u* and *u* are the nodal displacements and accelerations respectively. The key to reducing the substructure is to split the degrees of freedom into masters *um* (at the connecting nodes) and slaves *us* (at the internal nodes). The mass, the stiffness and the force matrices are re-

>

The subscript *m* denotes master, *s* denotes slave. Furthermore, the slave degrees of freedom (internals) can be written by using generalized coordinates (modal coordinates by ( *q* ) using the fixed interface method, i.e. using the mode shapes of the superelement by fixing the master degrees of freedom nodes (connecting/ boundary nodes). The transformation matrix

> *m m*

For the fixed interface method, the transformation matrix (*T* ) can be expressed as shown in

 0 *sm s*

*I*

*u u T*

*s*

*T*

*s* is the modal matrix of the internal DOF with the interfaces fixed.

*M M u kk u F*

*sm ss s sm ss s*

*mm ms m mm ms m m*

*M k*

[ ] [] *M u ku F* (2.5.6)

0

*u q* (2.5.8)

*G* (2.5.9)

1 *G kk sm ss sm* (2.5.10)

*MM u kk u* (2.5.7)

based on the references [39-41].

expressed as in Equation-2.5.6:

arranged accordingly as follows:

(*T* ) is the one that achieves the following:

Equation-2.5.9:

where,

and

$$k\_{reduced} = T^{\ddagger} k T \tag{2.5.12}$$

Thus Equation-2.5.7 can be re-written in the new reduced form using the reduced mass and stiffness matrices as well as the modal coordinates as follows:

$$
\begin{aligned}
\overbrace{\begin{bmatrix}
\boldsymbol{M}\_{bb} & \boldsymbol{M}\_{hq} \\
\boldsymbol{M}\_{qb} & \boldsymbol{M}\_{qq}
\end{bmatrix}}
\begin{Bmatrix}
\ddot{\boldsymbol{u}}\_{m} \\
\ddot{\boldsymbol{q}}
\end{Bmatrix}+
\begin{Bmatrix}
\boldsymbol{k}\_{radw} \\
\boldsymbol{0}
\end{Bmatrix}
\begin{Bmatrix}
\boldsymbol{u}\_{m} \\
\boldsymbol{q}
\end{Bmatrix}
\end{aligned}
\begin{aligned}
\begin{aligned}
\boldsymbol{\tilde{\boldsymbol{u}}}\_{radw} \\
\boldsymbol{\tilde{\boldsymbol{\eta}}}
\end{aligned}
\end{aligned}
\begin{aligned}
\boldsymbol{\tilde{\boldsymbol{\eta}}}\_{radw} \\
\boldsymbol{\tilde{\boldsymbol{\eta}}}
\end{aligned}
\begin{aligned}
\boldsymbol{\tilde{\boldsymbol{\eta}}}\_{radw} \\
\boldsymbol{\tilde{\boldsymbol{\eta}}}
\end{aligned}
\tag{2.5.13}
\end{aligned}
\tag{2.5.13}
\end{aligned}$$

Where *Mbb* is the boundary mass matrix i.e. total mass properties translated to the boundary points. *bb k* is the interface stiffness matrix, i.e. stiffness associated with displacing one boundary DOF while the others are held fixed. The *Mbq* is the component matrix ( *Mqb* is the transpose of *Mbq* ).

If the mode shapes have been mass normalized (typically they are) then:

$$\mathcal{A}\_{qq} = \begin{bmatrix} \ & & 0 \\ & \mathcal{A}\_i & \\ 0 & & \ \end{bmatrix} \tag{2.5.14}$$

where *i* is the eigenvalues; 2 *ii i i k m*/ , and,

$$\mathcal{M}\_{q\eta} = \begin{bmatrix} \ & & \ & \\ & I & & \\ 0 & & \ & \end{bmatrix} \tag{2.5.15}$$

Finally the dynamic equation of motion (including damping) using the Craig-Bampton transform can be written as:

$$
\begin{bmatrix} M\_{bb} & M\_{bq} \\ M\_{qb} & I \end{bmatrix} \begin{bmatrix} \ddot{u}\_m \\ \ddot{q} \end{bmatrix} + \begin{bmatrix} 0 & 0 \\ 0 & 2\zeta a \end{bmatrix} \begin{bmatrix} \dot{u}\_m \\ \dot{q} \end{bmatrix} + \begin{bmatrix} k\_{bb} & 0 \\ 0 & a^2 \end{bmatrix} \begin{bmatrix} u\_m \\ q \end{bmatrix} = \begin{bmatrix} F\_m \\ 0 \end{bmatrix} \tag{2.5.16}
$$

where 2 = modal damping ( = fraction of critical damping)

For more detailed explanation of the techniques related to the modelling of rolling element bearings and the application of component mode synthesis (CMS) techniques, refer to the works by Sawalhi, Deshpande and Randall [41].

Gearbox Simulation Models with Gears and Bearings Faults 33

Discontinuities

Stiffness

Fig. 2.6.2. Non-linearity due to contact loss in meshing gears; a) Force vs. Displacement, b)

order terms above the 1st derivative are ignored for linearization, which leaves the following expression (Equation-2.6.3). The differential term '*J'* is called the Jacobian matrix (or Jacobian in short). The problems involving gear contact losses are "Stiff" problems because of the discontinuity in system derivatives (Jacobians). For a more detailed discussion on this

The study of gear faults has long been an important topic of research for the development of gear diagnostic techniques based on vibration signal analysis. Understanding how different types of gear tooth faults affect the dynamics of gears is useful to characterise and predict the symptoms of the damage appearing in vibration signals [44, 45]. The strong link between the TE and the vibration of the gears was explained earlier. The effect of different types of gear tooth faults on TE can be studied by using the static simulation models. The result of static simulation can be then used to determine how different types of gear faults can be

Gears can fail for a broad range of reasons. Finding a root cause of damage is an important part of developing a preventative measure to stop the fault from recurring. Analysis of gear failure involves a lot of detective works to link the failed gear and the cause of the damage. Comprehensive guidelines for gear failure analysis can be found in Alban [46], DeLange [47] and DANA [48]. AGMA (American Gear Manufacturers Association) recognizes four types of gear failure mode and a fifth category which includes everything else: Wear, Surface

0 0 , , *x*

0

*d f f xt f x t x x dx* (2.6.2)

*f xt f x t J x x* , , 0 0 (2.6.3)

, *dx f xt dt* (2.6.1)

Displacement

derivative of former, i.e. Stiffness vs. Displacement

Backlash tolerance

(a) (b)

Displacement

Force

topic refer to the work presented by Singh [42].

**3. Modelling gearbox faults**

modelled into the dynamic simulation.

Fatigue, Plastic Flow, Breakage and associated gear failures [49].


These results extend the prior results of Lawrence and Kacmar [38], who found emotional exhaustion as a mediator in the relationship between job insecurity and unethical behavior. This is by highlighting the role of emotional exhaustion that derived from family financial pressures and motivation. Complementing prior research, family financial pressures [25,46] and motivations [9,55] were found to reduce self-regulatory resources and motivate unethical behaviors in the name of the family. The results indicated that participants who suffered high job instability in their workplace experienced higher levels of family pressures and were more prone to practice UOB to benefit their relatives. In support, Zhang et al. [46] articulated that when employees encounter substantial financial difficulties in their families, they are more likely to focus on obtaining financial benefits from their employer. In addition, this study provides empirical support for the argument of Hillebrandt and Barclay [4] that anxiety elicited by COVID-19 may focus employees' attention on their self-related interest and encourage cheating and other unethical behaviors.

### *5.1. Implications to Theory*

The result of this study has a three-fold contribution to theory. First, it extends the discussion of previous studies on conditions that shape unethical practices in workplaces. Most previous studies have identified that perceived job insecurity results in UOB that are either for benefiting the organization or self-serving. While this study adds empirical evidence on the important effect of family-related pressures, financial or motivational, on UOB, with particular attention of the influence of these factors when accompanied with job insecurity. Second, this study tries to answer the calls of prior researchers [3,4,22,25,66] to further examine the influence of environmental factors (e.g., COVID-19 outbreak) on UOB. The results add to explaining the reasons of the widespread unethical behaviors in organizations encountered during the COVID-19 pandemic. In particular, the current study adds to the understanding of the psychological process that employees may go through in making unethical decisions when faced by job insecurity. It is also the first study to discuss the mediating role of family motivation and financial pressure in the relationship between perceived job insecurity and UOB.

Third, this study answers calls to examine the employee's family as a source of motivation to possible UOB [25,46]. Despite previous warnings of its possible strong influence on unethical workplace behavior [46], family motivation has received little empirical and theoretical attention. Instead, most studies have regarded family motivation as a driver of

work effectiveness (e.g., [47]). Therefore, by demonstrating the role of family motivation in triggering unethical workplace behavior, this study extends research knowledge about possible psychological aspects that fuel UOB. At the same time, it gives insights to the possible dual role of family motivation as a source of desirable (work effectiveness, for more information see [47]) and undesirable organizational actions (UOB).

### *5.2. Implications to Practice*

The tourism industry was the most affected during the COVID-19 pandemic. The large seen shutdowns and layoffs during the pandemic and their effect on employee's psychology and behavior would have a long-lasting difficult influence on tourism workplaces and hospitality industry if not well understood and dealt with by decision-makers. Although the influence of COVID-19 on job loss and job insecurity has received much attention in recent tourism and hospitality research, a more comprehensive picture of the detrimental effect of job stress and anxiety on employee's behavior still needs to be explored to better inform tourism decision-makers [9,23]. In this regard, this study contributes to the understanding of why the COVID-19 pandemic has induced UOB in the tourism industry and highlights the role of job insecurity and family pressures and motivation in increasing UOB in the name of the family. This would inform tourism decision-makers and managers toward preventing unethical behavior and the possible damaging consequences on financial performance and reputation. Decision-makers should strive to advocate social messages and enact policies that reduce employees' perceived job insecurity, since this is a gateway to UOB.

In addition, based on the concept of bounded ethicality, the current study asserted that ambiguous circumstances (e.g., job insecurity) may veil the ethical aspects of employee's decisions, as people lean to self-justification of their immoral actions in the workplace [17,18,67]. Therefore, pressures of job loss may drive even honest employees to engage in minor dishonesty and simultaneously stay ignorant (ethically blind) of the ethical repercussions of their acts [18,68]. Thus, with this in mind, organizational managers need to carefully observe the actions of all employees and regularly provide moral reminders, which can be a useful tool to reduce or prevent UOB. Organizations also should assess the ethical development of employees, promote moral actions and punish for unethical behavior.

### **6. Conclusions, Limitations, and Further Research**

The prevalent and costly unethical practices in workplaces and their different types have attracted recent research attention, especially during the COVID-19 crises. This study investigated a neglected yet important form of UOB: unethical organizational practices in the name of the family. It proposed a model that may assist academics and practitioners in better understanding of how perceived job insecurity influences UOB through the mediating effect of family financial pressure and family motivation. The results revealed that perceived risk of job insecurity predicts employees' engagement in UOB, while intentions of unethical behaviors increase by high family motivation and financial pressures.

However, this study has some limitations that offers opportunities for future research papers. The current results of the analyzed data showed that family motivation and financial pressure partially mediated the impact of job insecurity and unethical workplace behavior. To further our understanding on the relationship between job insecurity and UOB, future research papers can investigate more mediating variables (e.g., work intensification, trust in management, feeling of guilt, and job embeddedness) that can affect the relationship between job insecurity and unethical workplace behavior in the name of the family. Moreover, future studies should investigate possible boundary conditions such as moral identities and religious commitment, since previous studies, for example, revealed that moral identity undermines the strong influence of the self-control depletion on dishonesty and unethical practices [69].

Although this study ensured the confidentiality and anonymity of the questionnaire for the participants, the self-reported survey used in this study may encourage participants to biases their answers, since questions were about unethical actions to benefit the

family. Thus, future studies can allow peer evaluation through colleagues or supervisors for more objectivity. In addition, future research can address the practices of decision makers to diminish UOB for family benefit and suggest methods that can be followed to control unethical practices. Furthermore, the collected data were cross-sectional; therefore, causal association between latent variables cannot be completely confirmed, and it is recommended for future investigations to collect longitudinal objective data or a different data source to validate the study model. Finally, a multigroup analysis approach can be conducted in future studies to validate and compare the results of the current study with data collected from different context (industry/country) [70]. Finally, it is important to highlight that the current study explores the relationship between family pressure and unethical workplace behavior under job insecurity. Accordingly, the UOB examined is not general but rather related to the benefit of the family. Future research would need to study general and other specific unethical behaviors that prevail in times of crisis (e.g., under job insecurity) and apply them to different contexts to understand how prevalent UOB is and how to mitigate its undesired consequences.

**Author Contributions:** Conceptualization, I.A.E. and M.G.; methodology, I.A.E., M.G. and A.M.S.A.; software, I.A.E. and M.G.; validation, I.A.E., A.M.S.A. and M.G.; formal analysis, I.A.E. and A.M.S.A.; investigation, I.A.E., M.G. and A.M.S.A.; resources, I.A.E.; data curation, I.A.E.; writing—original draft preparation, M.G., I.A.E. and A.M.S.A.; writing—review and editing, I.A.E. and M.G; visualization, I.A.E.; supervision, I.A.E.; project administration, I.A.E., M.G. and A.M.S.A.; funding acquisition, I.A.E. and A.M.S.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported through the Annual Funding track by the Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia [GRANT466].

**Institutional Review Board Statement:** The study was conducted according to the guidelines of the Declaration of Helsinki and approved by the deanship of scientific research ethical committee, King Faisal University (project number: GRANT466, date of approval: 11 January 2022).

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.

**Data Availability Statement:** Data are available upon request from researchers who meet the eligibility criteria. Kindly contact the first author privately through e-mail.

**Conflicts of Interest:** The authors declare no conflict of interest.

### **References**

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ISBN 978-3-0365-5574-4


**1. Introduction**

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Throughout history the function and the original role of the textile changed very little. One could only think of only few generations of textiles that would bear significant differences when compared one to another. Textiles were to provide the necessary shielding against climatic conditions and only later on in history the shear design of it became more importance. Nowadays, textile engineers and technologists like to think there is a new generation of textiles emerging. This thinking is supported by new functionalities being added onto textiles in the last few several decades. For this to happen, it was necessary to combine state of the art electronics and newly synthesized organic molecules which would bring the functionality of the textile to another level. Scientists of various research branches working together, looking at issues and solving problems applying multisciplinary approaches was the right angle of looking at things. Results of this can be seen daily, as textiles are emerging into a new era in which "know how" and "state of the art" have to be combined to give products of highly added values. Producing "highly added value" products can give the leverage to companies of the western world in an ongoing "battle" against massively produced, low quality textiles of mainly eastern origin.

Although, the way to commercialization of many of the ideas of how to upgrade the functionalities of the textile is long, the results may be far greater than the challenges encountered. Often, the answer on how to do it lies in using technologies and knowledge that have been around for centuries. Therefore, this paper will deal with the phenomenon of photochromics, which has first been noticed in 19th century and so far not exploited nearly enough within the realm of textiles (Hepworth et al., 1999). It will cover the historical overview, division of photochromic systems and their synthesis, principals and triggering mechanisms, various fastness property issues and applicability to fibres of different origin (Shuiping et al., 2010). Application methods and state of the art shall be described thoroughly, providing scientific and technological achievements from the relevant literature references (Durr & Bouas-Laurent, 1990).

Group of authors addresses the combination of photochromism phenomenon and textile in general as newly derived system, bearing all the qualities of a sensory material. Within it, molecule of photochromic dye may be observed as "smart", as it is triggered by a specific and quantifiable physical value. Properly applied, this "smart dye" and adequate textile fibre form a textile sensor capable of sensing and reacting to a particular impulse in a predictable manner (Czarnik, 1995; Van Langehove, 2007).

From Murex Purpura to Sensory Photochromic Textiles 59

for compounds of redox active localities, such as metal ions and metal radicals - Solavtochromism – change in colour of a compound is caused by solvent polarity. Most

Over the past ten years, investigations on thermochromic pigments have gained popularity. These are aimed at obtaining new effects on dyed textile materials. Using a conventional technique of textile printing in combination with thermochromic pigment an intelligent textile is obtained. Intelligence is defined by the ability of the printed textile to change colour in accordance to the presence of an outside stimulus. In this case temperature changes ocurring within the close environment of the textile (Karlessi, et al. 2009; Kulčar et

As far as quality of the chromic materials goes, it will depend on several parameters:

The phenomenon of photochromism is an analogue to all chromic processes. The change in colour is influenced by light in a reversible way (Fig. 1) (Cheng, 2007). Uncoloured material doesn't absorb light and may only be activated by energetically rich photons of the near UV electromagnetic spectra. Many of the inorganic materials such as copper, mercury, various metal oxides and some minerals exhibit the photochromic phenomenon (Van Gemert, 1999a, b). However, their use is considered inappropriate for textile materials and substrates. Organic molecules such as spiropyrans, spirooxazines and fulgides are suitable for use on

of the solvatochromic compounds are metallic complexes - Ionochromism – change in colour of a compound is ion induced

agents i.e. toxic gasses, detergents etc.

form of chromism

moisture

al., 2010; Maeda, S. 1999).

**3. Photochromism**

textiles (Bouas-Laurent & Dürr 2001).

Described as such, the system bears all the necessary qualities of a smart textile. It is capable of alerting and protecting the wearer from the very specific threat as it has been specifically designed, calibrated and optimized.

From the textile engineer's, namely dyer's point of viewing things, not much has changed. Only the concept of "colour all the time" has changed to "colour at the right time" principle, which may be observed as one of the options of giving leverage to textile companies in search of means and ends of once again reclaiming the leader status on the worldwide market.


**2. Conventional catalytic approach to convert methane to oxygenates**

### **2.1 Gas phase reaction based on homogeneous radical mechanism**

This reaction is a free radical conducted under high temperature and pressure. The thermodynamic and kinetics studies identified the partial oxidation of methane as the rate limiting step due to the formation of methyl radical [7, 11]. Many studies with different oxidants have been conducted in this route. Babero et al. studied the partial oxidation of methane at 500 C temperature using nitrogen oxide as an oxidant [12]. Another study compared between oxygen and nitrogen oxide for the partial oxidation of methane in the gas phase [13]. The effect of adding small quantities of hydrocarbons such as ethane was investigated to promote the activation of methane and increase the selectivity of methanol [14]. Pressure is one of the most important factors which has a pronounced effect on the selectivity of methane oxidation. Dozens of studies have been performed in attempts to promote the selectivity toward oxygenates using high pressures and temperatures [8, 9, 15]. The results of these studies show that a conversion of 5–10% and a methanol yield of 30–40% can be achieved at a temperature of 723–773 K and pressures of 30–60 bar in the gas phase reaction. There are several works that investigated the reactor design and modifications. Zhang et al. designed a new tubular reactor based on quartz-line and stainless-steel line. The reaction was conducted at a temperature of 430–470°C and 5.0 Mpa pressure, and a high yield of methanol was obtained [9].

*Advances in Selective Oxidation of Methane DOI: http://dx.doi.org/10.5772/intechopen.86642*

The methane conversion to methanol was also conducted in the absence of catalysts at high reaction conditions. Methanol yields as high as 7–8% are obtained in the absence of catalysts operating at 350–500°C and 50 bar [10, 11, 16]. As reactor inertness is essential for obtaining good selectivity to methanol, the feed gas should be isolated from the metal wall by using quartz and Pyrex glass-lined reactors [17]. A typical experimental conversion-selectivity plot for the gas-phase partial oxidation of methane is shown in **Figure 1** [18]. This plot ably demonstrates that any improvement in the direct conversion of methane to methanol must come from the enhancement of selectivity without reducing the conversion per pass. The Huels process uses cold-flame burners operating at 60 bar, with a selectivity of 71% to methanol and 14% to formaldehyde, and a recycle ratio of 200 to 1 [8].

The suggested mechanism for the direct conversion of methane to methanol via homogeneous gas phase reactions is shown in **Figure 2** [19].


*Article* **Variation Characteristics of Multi-Channel Differential Code Biases from New BDS-3 Signal Observations**

**Qiqi Shi 1,2 and Shuanggen Jin 1,3,4,\***

**Abstract:** A multi-frequency Global Navigation Satellite System (GNSS) provides greater opportunities for positioning and navigation applications, particularly the BeiDou Global Navigation Satellite System (BDS-3) satellites. However, multi-frequency signals import more pseudorange channels, which introduce more multi-channel Differential Code Biases (DCBs). The satellite and receiver DCBs from the new BDS-3 signals are not clear. In this study, 9 DCB types of the new BDS-3 signals from 30-days Multi-GNSS Experiment (MGEX) observations are estimated and investigated. Compared with the DCB values provided by the Chinese Academy of Science (CAS) products, the mean bias and root mean squares (RMS) error of new BDS-3 satellite DCBs are within ±0.20 and 0.30 ns, respectively. The satellite DCBs are mostly within ±0.40 ns with respect to the product of the Deutsches Zentrum für Luft- und Raumfahrt (DLR). The four sets of constructed closure errors and their mean values are within ±0.30 ns and ±0.15 ns, respectively. The mean standard deviation (STD) of the estimated satellite DCBs is less than 0.10 ns. In particular, our estimated satellite DCBs are more stable than DCB products provided by CAS and DLR. Unlike satellite DCBs, the receiver DCBs have poor compliance and show an obvious relationship with the geographic latitude when compared to the CAS products. The STDs of our estimated receiver DCBs are less than 1.00 ns. According to different types of receiver DCBs, the distribution of STDs indicates that the coefficient of the ionospheric correction has an influence on the stability of the receiver DCBs under the ionosphere with the same accuracy level. In addition, the type of receiver shows no regular effects on the stability of receiver DCBs.

**Keywords:** BeiDou Global Navigation Satellite System (BDS-3); Differential Code Biases (DCBs); multi-channel; ionospheric correction

#### **1. Introduction**

The Global Navigation Satellite System (GNSS) has been widely used in geosciences and life [1,2]. In particular, China's BeiDou Global Navigation Satellite System (BDS-3) was officially operated for global users on July 31, 2020 [3]. As the first hybrid constellation of navigation satellite systems in the world, BDS-3 has been developing rapidly and providing global services, and can provide positioning, navigation, and timing (PNT) services [4]. BDS-3 transmits other new signals of multiple frequency bands, which is compatible with signals of B1 and B3 provided by the BeiDou regional navigation satellite system (BDS-2). Multi-frequency signals provide plentiful observations for satellite applications but also introduce new errors in the positioning process [5,6]. For example, the difference of hardware delay between the signals of double-frequency bands is designated as the differential code bias (DCB), which affects the accuracies of the ionospheric modeling and GNSS precise positioning [7,8]. There are multiple channels for BDS observations on the same frequency, which are summarized in Table 1 from the Receiver Independent Exchange

**Citation:** Shi, Q.; Jin, S. Variation Characteristics of Multi-Channel Differential Code Biases from New BDS-3 Signal Observations. *Remote Sens.* **2022**, *14*, 594. https://doi.org/ 10.3390/rs14030594

Academic Editor: José Fernández

Received: 11 December 2021 Accepted: 25 January 2022 Published: 26 January 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

(RINEX) format (https://files.igs.org/pub/data/format/rinex305.pdf). Therefore, the multiple DCBs caused by multi-channel signals of BDS-3 should be estimated and analyzed accurately.

**Table 1.** The pseudorange channels of BDS multi-frequency signals.

Generally, the ionospheric total electron content (TEC) and DCB need to be considered simultaneously during the estimation process. Carrier-to-code leveling (CCL) is a common estimation method to extract ionospheric TEC and DCB. It exhibits suitable accuracy and simple implementation with the dual-frequency geometry-free (GF) observation combination [9,10]. Moreover, the method of undifferenced and uncombined precise point positioning (PPP) shows higher estimation accuracy when compared with the CCL [11]. However, the PPP approach introduces external constraints on the receiver coordinates, orbits, and clock errors [12,13]. The above-mentioned methods are only used to extract the ionospheric observations, while DCB estimation should be further considered. Ionospheric correction generally includes two components: external ionospheric models and simultaneous estimation [14]. The empirical ionospheric models and the global ionospheric map (GIM) can be used as external ionospheric models to correct the ionosphere. The empirical ionospheric models mainly include the Klobuchar model, NeQuick model, and BeiDou Global Ionospheric delay correction Model (BDGIM) [15–17]. Since the Ionosphere Working Group (IWG) was created by IGS in 1998, many Ionosphere Associate Analysis Centers (IAACs) continue to generate GIMs with high-precision for GNSS users [18]. To achieve simultaneous estimation, the ionospheric modeling is performed, including the global spherical harmonics (SH) and regional generalized trigonometric series function (GTSF) [19,20]. The Multi-GNSS Experiment (MGEX) network of the International GNSS Service (IGS) has been developed [21] so that more and more stations can track multifrequency new BDS-3 signals. However, the number of these stations is insufficient for global ionospheric modeling and DCB estimation of BDS-3 signals.

Recently, the ionosphere and DCB of BDS-2/3 have been analyzed and discussed. Xue et al. [22] analyzed the stability of BDS-2 B1I-B2I and B1I-B3I DCBs by using multi-GNSS observations. Zhu et al. [23] verified and analyzed satellite and receiver DCB by employing the BDGIM. MGEX observations are utilized to analyze the stability and systematic bias of BDS-2 and BDS-3 DCBs [24,25]. Deng et al. [26] also estimated multiple satellite DCBs of BDS-3 and compared with the Chinese Academy of Sciences (CAS) and the Deutsches Zentrum für Luft- und Raumfahrt (DLR) products. However, most studies have focused on the DCBs estimation and analysis of BDS B1 and B3 frequency, or between B1/B3 and other frequencies. It has a lack of variation characteristics of satellite and receiver DCBs from new BDS-3 signal observations.

This paper aims to estimate and analyze the satellite and receiver DCBs of the new BDS-3 signals (B1C/B2a/B2b/B2(a+b)). The method of DCB estimation and data are introduced in Section 2. Results are presented in Section 3. Nine DCB types from the MGEX network are estimated and compared with DCB products provided by the CAS/DLR. Besides, four sets of closure errors of satellite DCBs are analyzed in detail, including the distribution and the mean values of closure errors. The accuracy and stability of the BDS-3 receiver DCBs are analyzed. Finally, some discussion and conclusions are given in Sections 4 and 5.

#### **2. Methods and Data**

#### *2.1. Ionospheric Estimation Equation*

Observations obtained from the files of RINEX format generally include pseudorange and carrier-phase observations. Considering multiple errors, the general observation equations can be expressed as follows [27]:

$$\begin{cases} \begin{aligned} P^s\_{i,j} &= \rho^s\_i + dt\_i - dt^s + d^s\_{tro,i} + \mu\_j \cdot d^s\_{ion,j,1} + d\_{i,j} - d^s\_{,j} + \varepsilon\_P \\ \Phi^s\_{i,j} &= \rho^s\_i + dt\_i - dt^s + d^s\_{tro,i} - \mu\_j \cdot d^s\_{ion,j,1} + b\_{i,j} - b^s\_{,j} + N^s\_{i,j} + \varepsilon\_\Phi \\ \mu\_j &= f^2\_1 / f^2\_j \end{aligned} \end{cases} \tag{1}$$

where *P* and Φ are the pseudorange and carrier-phase observations, respectively; *i* and *j* refer to the receiver and the frequency index, respectively; *s* denotes the BDS satellite; *ρ* is the geometric range between the receiver and satellite; *dti* and *dts* are the receiver and satellite clock offsets, respectively; *dtro* and *dion* are the slant tropospheric and ionospheric delays, respectively; *μj* denotes the frequency-dependent multiplier factor; *di*,*j* and *ds* ,*j* are the receiver and satellite pseudorange instrumental delays at *fj* frequency, respectively; *bi*,*j* and *bs* ,*j* are the receiver and satellite the carrier-phase hardware delays at *fj* frequency, respectively; *N* denotes the integer ambiguity; and *εP* and *ε*Φ are the noises of pseudorange and carrier-phase observations, including multipath, respectively.

For any dual-frequency observations of BDS-3, ionospheric observable can be obtained from GF combined observations, which can be expressed as [28]:

$$\begin{cases} P\_4 = P\_{i,1}^s - P\_{i,2}^s &= \left(\mu\_1 \cdot d\_{im,i1} - \mu\_2 \cdot d\_{im,i1}\right) + \left(d\_{i,1} - d\_{i,2}\right) - \left(d\_{j,1}^s - d\_{j,2}^s\right) + \varepsilon\_{P,4} \\ &= \left(\mu\_1 \cdot d\_{im,i1} - \mu\_2 \cdot d\_{im,i1}\right) + DCB\_i - DCB^s + \varepsilon\_{P,4} \\ \Phi\_4 = \Phi\_{i,1}^s - \Phi\_{i,2}^s = \ -\left(\mu\_1 \cdot d\_{im,i1} - \mu\_2 \cdot d\_{im,i1}\right) + \left(b\_{i,1} - b\_{i,2}\right) - \left(b\_{i,1}^s - b\_{i,2}^s\right) + \left(N\_{i,1}^s - N\_{i,2}^s\right) + \varepsilon\_{\Phi,4} \end{cases} \tag{2}$$

where *P*4 and Φ4 are the GF pseudorange and carrier-phase observations, respectively; *DCBi* and *DCBs* are the corresponding receiver and satellite *DCB*, respectively; and *εP*,4 and *ε*Φ,4 are the noises of GF pseudorange and carrier-phase observations, respectively.

To eliminate the large noise of pseudorange observations *P*4 [29], the CCL approach is adopted during one observation arc with no cycle slips. The pseudorange instrumental delay and integer ambiguity remain the same constant in such arcs, so the ionospheric observables after smoothing can be expressed as [14]:

$$P\_s = \Phi\_4(t\_i) - \frac{1}{n} \sum\_{n=t\_1}^{t\_0} \left[ P\_4(t\_i) + \Phi\_4(t\_i) \right] = -(\mu\_1 - \mu\_2) \cdot d\_{ion,i,1}^s - D \subset \mathbb{B}\_i + D \subset \mathbb{B}^s \tag{3}$$

where *n* refers to the number of measurements during one observation arc.

#### *2.2. Ionospheric Correction Based on GIM*

Due to the insufficient distribution of BDS-3 stations, the external ionospheric correction is introduced from GIM provided by the Center for Orbit Determination in Europe (CODE). Then, the single-layer mapping function is used for converting slant TEC (STEC) to VTEC. It can be expressed as follows [30]:

$$\begin{cases} \begin{array}{l} d\_{ion,i1}^{s} = \frac{40,30}{f\_1^2} \text{STEC}\_i^s\\ \text{STEC}\_i^s = \text{MF} \cdot \text{VTEC}\_i^s\\ \text{MF} = \frac{1}{\cos\left[\arcsin\left(\frac{R}{R+H}\sin(a\cdot\mathbb{E})\right)\right]} \end{array} \tag{4}$$

where MF denotes the mapping function, *R* is the average radius (6371 km) of the Earth, *H* is the assumed height (450 km) of the single layer ionosphere, *α* refers to the model coefficient (0.9782), and E is the satellite elevation angle. VTEC can be obtained by linear

interpolation based on GIM, involving interpolations of two-dimensional space and time series [31].

#### *2.3. DCB Separation and Estimation*

After correcting the ionosphere, Equation (3) contains only satellite and receiver DCB. For one-day observation, the DCBs of each satellite and receiver are estimated as one constant, respectively. To solve the singular problem of the equation, the zero-mean condition is adopted to separate the DCBs of satellites and receivers. Namely the sum of the DCBs of all satellites is zero on one day, so Equation (3) can reach full rank [32]. Under this constraint condition, the DCB variations are not affected [33]. The zero-mean condition for BDS-3 satellites can be expressed as:

$$\sum\_{s=1}^{N} D \! \! CB^s = 0 \tag{5}$$

where *N* denotes to the total number of BDS-3 satellites observed per day. When the satellites observed are different per day, the zero-mean condition will be inconsistent. In that case, the conversion method needs to be implemented for unified zero-mean condition [25].

Based on Equations (3)–(5), the DCB estimation by employing CODE's GIM can be rewritten as:

$$\begin{cases} \begin{aligned} P\_s - \frac{40.30 \left(f\_1^2 - f\_2^2\right)}{f\_1^2 f\_2^2} \cdot \text{MF} \cdot \text{VTEC}\_i^s = -DCB\_i + DCB^s \\ \sum\_{s=1}^N DCB^s = 0 \end{aligned} \tag{6} $$

Finally, the cut-off elevation angle is set to 15◦ to reduce the impact of multipath noise and mapping function errors [10]. To get an arc without cycle slips, the MW (Melbourne– Wübbena combination) and ionospheric residual observations are used to process the sequence of GF observations [28].

#### *2.4. Experimental Data*

With the development and updating of MGEX stations, increasingly more stations can track the BDS-3 new signals. Eighty-eight stations of the MGEX network collected from a period of 30 days, corresponding to the day of year (DOY) 060-089 in 2021, were processed to estimate DCBs of BDS-3. Figure 1 shows the distribution of the MGEX stations with tracking the BDS-3. It can be seen from Figure 1 that the distribution of the stations tracking the BDS-3 new signals is inadequate and uneven, so a single BDS-3 system cannot implement the global ionospheric modeling yet. According to the multi-channel type of BDS-3 in the observation file, we estimate 9 DCB types of BDS-3 new signals. The channel type depends on the type of station receiver. Table 2 shows pseudorange observation channels and corresponding frequency bands used to estimate 9 DCB types in our study. As we can see from Table 2, the number of stations with receiving new BDS-3 signals is still less than GPS stations in the hundreds. In particular, the C7Z-C8X combination has only 19 stations that can be used for DCB estimation.

**Figure 1.** Distribution of MGEX stations with tracking the new BDS-3 signals.

#### **3. Results and Analysis**

*3.1. Quality Analysis of New BDS-3 Signal*

To assess the quality of the new BDS-3 signals, we analyze the multipath (MP) combination of multi-channel signals. Figure 2 shows MP values of BDS-3 C19, C37, C38, and C45 satellites during the DOY 60–89, 2021, which are observed at stations PTGG and FFMJ. The digits represent the root mean squares (RMS) of MP. As shown, the MP values vary within ±2 m. The signal quality of C1P/C5P/C7D channels is not significantly different. The RMS of C1X(B1C) MP is significantly larger than the other three channels. Nevertheless, MP of the C8X (B2) channel has satisfying signal performance. Thus, it can be seen the signal quality of B1C frequency is the worst and that of B2(a+b) frequency is the best.

**Figure 2.** MP of the BDS-3 C19, C37, C38, and C45 satellites at stations PTGG (**a**) and FFMJ (**b**) during a period of 30 days.

#### *3.2. Validation of Satellite DCBs*

CAS and DLR analysis centers (ACs) provide DCB products for BDS-3 signals but do not include all DCB types. To validate the accuracy of DCBs within the 30 days estimated in this paper, we analyzed statistics of the DCBs, including mean bias and RMS, with CAS and DLR products. Figure 3 depicts the statistical results of 4 DCB types with the direct value provided by CAS products. The mean bias and RMS of satellite DCBs vary within ±0.20 ns and 0.30 ns, respectively. The results show our estimated DCBs have better consistency with the direct DCB value provided by CAS products. Owing to the DLR only provides DCB types between C2I and other channels, we calculated the conversion value of DCBs between the channels of BDS-3 new signal by using DLR products. The mean bias and RMS of 6 satellite DCB types are shown in Figure 4. The results of comparison with DLR products are inferior to the previous result with CAS and are mostly within ±0.40 ns. According to the error propagation principle, the cumulative error of the converted value can lead to a larger deviation of the result. In particular, C45 and C46 are obviously difference. Compared with CAS products and our estimated results, it is found that the values of DLR products deviate. This may be related to corresponding satellite stability and observation

quality. Finally, the time series of C1P-C5P of DCB and the differences with respect to CAS products are shown in Figure 5. The estimated DCB of C1P-C5P varies between the −79.00 and 23.00 ns, and the differences vary within ±0.30 ns. It can be seen that the time series DCB of C1P-C5P are stable and consistent with the DCB provided by CAS products.

**Figure 3.** The mean bias and RMS of our estimated C1P-C5P, C1X-C5X, C1X-C7Z, and C1X-C8X, of BDS-3 satellite DCBs, with respect to the direct values provided by CAS products.

**Figure 4.** The mean bias and RMS of our estimated C1X-C5X, C1X-C7Z, C1X-C8X, C5X-C7Z, C5X-C8X, and C7Z-C8X, of BDS-3 satellite DCBs, with respect to the conversion values provided by DLR products.

**Figure 5.** DCB time series of BDS-3 C1P-C5P during a period of 30 days, and the differences time series with respect to CAS products.

The stability of satellites during long time series is an important index to evaluate the accuracy of DCBs. Figure 6 shows the distribution of deviation between 9 DCB types of BDS-3 satellites and the corresponding mean values. The deviations of 9 DCB types vary within ±0.30 ns for the whole distribution. The optimal deviation is less than 0.10 ns, particularly for the C5P-C7D and C7Z-C8X. Table 3 summarizes the mean values of the standard deviation (STD) of BDS-3 DCBs of DLR, CAS, and our results. Our results are consistent with the stability of DCBs provided by CAS products. The conversion values of DCB provided by CAS and DLR products are less stable than our estimated DCBs. DCBs provided by DLR products related to C1X and C5X channels exhibit instability in C45 and C37 satellites. Our estimated DCBs of C37 satellites show instability in the C1X channel. This indicates that the stability levels of our estimated DCB and CAS are the same, but the conversion values of DCB provided by DLR products are slightly less stable.

**Figure 6.** Distribution of deviations between nine DCB types of BDS-3 satellites and the corresponding mean values.

**Table 3.** Mean STD of BDS-3 DCBs of DLR, CAS, and our results, showing the corresponding satellite psuedo random noise (PRN); the bold types are the direct values provided by CAS products.

#### *3.3. Internal Coincidence of Satellite DCB*

According to the nine estimated DCB types, four sets of closure errors can be constructed, including C1P-C5P-C7D, C1X-C5X-C7Z, C1X-C5X-C8X, and C1X-C7Z-C8X. Figure 7 shows the distribution of four sets of closure errors for all BDS-3 satellites. The fluctuation in closure error is within ±0.30 ns. The closure errors of C1P-C5P-C7D are less than 0.10 ns by using more stations. From the normal distribution curve, the distribution of BDS-3 satellites closure error conforms to the condition under the influence of random noise. Moreover, the corresponding mean closure error is also depicted in Figure 8. The mean closure errors of all DCB types are less than 0.15 ns. Echoing the conclusion above, the C1P-C5P-C7D set has the smallest closure error, which relates to the use of more stations. The closure errors of the C37 satellite related to the C1X channel are larger, indicating its poor stability.

**Figure 7.** Distribution of BDS-3 satellites C1P-C5P-C7D (**a**), C1X-C5X-C7Z (**b**), C1X-C5X-C8X (**c**), and C1X-C7Z-C8X (**d**) closure errors. The red line denotes the fitted normal distribution curve.

**Figure 8.** Mean closure error of BDS-3 satellites C1P-C5P-C7D, C1X-C5X-C7Z, C1X-C5X-C8X, and C1X-C7Z-C8X.

#### *3.4. Validation and Variation of Receiver DCBs*

To evaluate variation characteristics of receiver DCBs, we classify experimental stations in terms of receiver types, which are summarized in Table 4. According to the receiver tracking the channel types of BDS-3 new signals, the observation channels consist of two sets, i.e., C1P/C5P/C7D and C1X/C5X/C7Z/C8X. The former receiver types belong to Septentrio (SEPT), and the latter receiver types belong to TRIMBLE and JAVAD (https: //files.igs.org/pub/station/general/IGSNetwork.csv) [21]. The corresponding station names are also given. As a matter of common knowledge, the stability of receiver DCBs is not as good as satellite DCBs, and it is susceptible to receiver hardware and changes in the external environment. Besides, receiver DCBs provided by CAS tracking BDS-3 new signals are not continuous for 30 days. Thus, we only compare our estimated receiver DCBs with their corresponding values provided by CAS products during 30 days.

**Table 4.** Station and receiver information for BDS-3 DCB estimation.

When the estimated results of satellite DCBs are relatively stable, the estimation of receiver DCBs is also directly subject to ionospheric delay estimation or correction. The accuracy of the ionospheric modeling is also closely related to geographic latitude. Hence, the geographic latitude is taken as the horizontal axis to analyze receiver DCBs. Figure 9 shows the RMS of four receiver DCB types, including C1P-C5P, C1X-C5X, C1X-C7Z, and C1X-C8X, which are dotted in different colors. Overall, the RMS of receiver DCBs vary within 2.50 ns. The RMS show an obvious relationship with the geographic latitude. The RMS mostly exceed 1.00 ns at low latitudes between −30◦ and 30◦. However, higher consistency exists between our estimated receiver DCBs and CAS products in middle and high latitudes. Statistics for RMS of four receiver DCB types are depicted in Figure 10, including the maximum, minimum, and mean for each DCB type. The RMS of our estimated receiver DCBs is mostly less than 1.50 ns with respect to CAS. There is an equivalent accuracy among C1X-C5X, C1X-C7Z, and C1X-C8X DCBs. Because there are more low-latitude stations used to estimate C1P-C5P, the RMS values are relatively large. Finally, we calculate the mean value for RMS of our estimated receiver DCBs, which is about 0.68 ns. Considering the previous satellite DCB analysis, this phenomenon is caused by higher ionospheric activity at lower latitudes and the different ionospheric modeling strategies from CODE and CAS.

**Figure 9.** RMS error of the estimated BDS-3 receiver DCBs with respect to the products provided by CAS during the period of DOY 60–89 in 2021.

**Figure 10.** Statistics for RMS error of the estimated BDS-3 receiver DCBs with respect to the products provided by CAS during the period of DOY 60–89 in 2021.

Figure 11 shows the STDs for all BDS-3 receiver DCB types in our study. Most STD values are less than 0.50 ns, and all of them are less than 1.00 ns. This indicates the receiver DCBs have poor stability compared with satellite DCBs. In addition, it can be seen that the receiver DCB types associated with the B1C(C1P/C1X) frequency are less stable than other types. As shown by the digitals in this figure, the absolute values of coefficient for ionospheric correction term increase due to the use of the dual-frequency observation with a larger frequency difference. The accuracy of ionospheric products provided by CODE is 2-8 TEC Unit (TECU) [34]. Coefficients with large absolute values can amplify the ionospheric errors under the ionospheric corrections with the same accuracy level, thus leading to the unstable estimated receiver DCBs. In terms of different colored dots, there is not a significant regularity. Thus, it can be explained that the type of receiver has no critical determinant for its stability.

(**b**) Receivers of C1X/C5X/C7Z/C8X channels.

**Figure 11.** Distribution of STDs for all BDS-3 receiver DCB types of C1P/C5P/C7D channels (**a**) and C1X/C5X/C7Z/C8X channels (**b**) during the period of DOY 60–89 in 2021. Receiver index is arranged according to the classification and order in Table 4. The digitals represent coefficients of the ionospheric correction with corresponding DCB types.

#### **4. Discussion**

The satellite and receiver DCBs of new BDS-3 signals are estimated and analyzed in this paper. The MP values of BDS-3 new signals show that the B1C signal quality is slightly worse at the highest frequency, which is significantly affected by MP and other noises. Comparing our estimated results with CAS and DLR products, the DCB values with respect to the C45 and C46 satellites in DLR products have a deviation. When fewer available stations are used to estimate DCB products, the quantity and quality of observables have

a large impact on the stability of satellite DCB estimates. Satellite DCB estimates are susceptible to poor quality observations and thus result in systematical bias and instability.

The receiver DCBs of the new BDS-3 signals exhibit an obvious relationship with the geographic latitude. The latitudinal dependence of receiver DCB estimates is consistent with Li et al. [24] and Wang et al [25]. Different ionospheric coefficients have a significant influence on the stability of receiver DCBs. Under the ionospheric corrections with the same accuracy level, the ionospheric coefficient with a larger absolute value will amplify the errors in the process of error propagation. Although the STDs of receiver DCBs show no obvious relationship between the type of receiver and its stability, this relationship also needs to be further analyzed and validated for latitude, temperature, and other influencing factors [22,35].

Because there are only a few MGEX stations with tracking such channel codes of observation, the DCB estimation does not cover all the channel codes, such as C1X-C7D and C5X-C7D. The DCB types can be further estimated and analyzed when more stations are established by tracking the relevant channel codes of observation in the future.

#### **5. Conclusions**

As the main error source of multi-frequency BDS signal applications, the DCBs of new BDS-3 signals (B1C/B2a/B2b/B2(a+b)) are estimated and analyzed systematically in this paper. The nine sets of DCB types are constructed using the 88 stations from the MGEX network for 30 days. The main conclusions are summarized as follows:

Although the BDS-2/3 system has been fully built, the number of stations with tracking new BDS-3 signals is far less than GPS. To promote precise applications of multi-frequency BDS-3, more stations with tracking full frequencies of BDS-3 signals need to be established, which will contribute to ionospheric modeling and DCBs estimation.

**Author Contributions:** Conceptualization of the Manuscript Idea: S.J. and Q.S. Methodology and Software: Q.S.; Supervision and Funding Acquisition: S.J.; Q.S. wrote the original draft preparation; S.J. reviewed and edited this paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China (NSFC) Project, grant number 12073012.

**Data Availability Statement:** The BDS observation data from IGS MGEX networks can be obtained https://cddis.nasa.gov/archive/gps/data/daily/. The precise orbit products from GFZ are available at https://www.gfzpotsdam.de/GNSS/products/mgex/. The GIM products from CODE are

available at https://cddis.nasa.gov/archive/gnss/products/ionex/. The DCB products provided by CAS and DLR can be obtained at https://cddis.nasa.gov/archive/gnss/products/bias/.

**Acknowledgments:** The authors thank IGS for providing the BDS observation data of MGEX networks, DLR/CAS for providing the DCB products, CODE for providing the GIM products, and GFZ for providing precise orbit products, as well as Ke Su and Zhenchuan Huang for their help with the English-language aspects of writing this paper.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**2. Tectonic setting**

Gathering of geologic, tectonic, seismologic and geodetic data through the last decades has led to a better understanding of the Caribbean plate, its margins and adjacent regions, progressively bringing in more complexity to the once drawn "drawer-like" Caribbean plate model [17]. In fact, the Caribbean plate borders are actually "plate boundary zones", PBZ, in the sense of [18], "wide deformation zones" in the sense of [19], particularly transpressional along the southern Caribbean PBZ, or "wide plate margins" in the sense of [10]. These margins amalgamate tectonic blocks of diverse size, composition, origin and geometry (**Figure 1**), somehow surrounding the Caribbean Sea, cored by the Caribbean Large Igneous Province (CLIP) or plateau.

Caribbean plate. Stable GPS stations inside the Caribbean, such as on San Andrés

*Tectonic frame. Tectonic blocks: PB (Panama B.), CB (Chocó B.), NAB (North Andean B.),TMB (Triangular Maracaibo B.), BB (Bonaire B.). Other features: CAVA (Central America Volcanic Arc); CCRDB (Central Costa Rica Deformed Belt), EPGFZ (Enriquillo-Plantain Garden Fault Zone), LAS (Leeward Antilles Subduction), MP (Mona Passage), MPFS (Motagua-Polochic Fault System), NHDB (North Hispaniola*

*GNSS Networks for Geodynamics in the Caribbean, Northwestern South America, and Central…*

*DOI: http://dx.doi.org/10.5772/intechopen.97215*

(Venezuela), will provide a reliable answer as to the relative motion between the Caribbean and surrounding plates. In addition, longer time span comparisons between these internal sites to the plate should confirm any internal deformation or

Besides, strain partitioning at different scales is common to the four Caribbean plate PBZs (**Figure 1**). In Central America, a coastal sliver, bounded by the Central America trench on the southwest and the active Central America volcanic arc (CAVA) on the northeast, escapes to the north-west (NW), taking advantage of the weakening of the continental crust by the CAVA volcanic activity [21–24]. A similar situation is reported in the northern Lesser Antilles arc, where the forearc in this region, limited by the active arc on the west-southwest (WSW) and the Atlantic trench on the north-northeast (ENE), moves northward with respect to the arc [25, 26]. Along the northern Caribbean PBZ, the northernmost sliver of the Hispaniola Island, bounded by North Hispaniola and Septentrional faults on the north and south respectively, displaces west faster than most of the island. In the southern Caribbean PBZ, the Bonaire block as well as the block containing the Caribbean nappes overriden onto South America along northern Venezuela (outcropping in the Coastal and Interior ranges), accommodate shortening while slipping dextrally along the large west–east (W-E) trending Oca-Ancón, San Sebastián and El Pilar

and Providencia islands and Serranilla Cay (Colombia), and Aves Island

fragmentation of the Caribbean plate itself, as proposed by [13].

*Deformed Belt), NLAF (Northern Lesser Antilles Forearc). Modified from [13].*

fault system (**Figure 1**).

**145**

**Figure 1.**

The recognition of such tectonic blocks started first along the southern Caribbean margin and northwestern South America corner, because being poorly defined by a disperse infrequent and moderate-in-magnitude (instrumental) seismicity, as well as by a poor surface/sea-bottom expression of the active tectonic features in comparison with the other Caribbean PBZs (**Figure 2**).

The study of this very complex but subtly expressed southern PBZ was enhanced by the fact that a large portion of the features are on land (**Figure 1**). Conversely, the northern Caribbean plate boundary became a natural laboratory for numerous space geodesy studies due to its apparent structural simplicity, although the first of all GPS studies worldwide, GPS CASA (Central And South America) Project was carried out in the complex southern Caribbean PBZ between 1988 and 1998 [10, 20]. Not as expected, GPS networks have not fully resolved the posed kinematic questions along this northern Caribbean PBZ, since the networks are mostly installed in rather small islands that are within the plate margin themselves that also resulted to be a complex PBZ with several active features lying offshore (**Figure 3**). As a matter of fact, the larger islands, such as Jamaica and Hispaniola, exist as a proof of such PBZ compressional or transpressional processes. A similar situation happens along the eastern border of the Caribbean plate, where the Atlantic plate subducts beneath an arc of active volcanic islands sitting on the

*GNSS Networks for Geodynamics in the Caribbean, Northwestern South America, and Central… DOI: http://dx.doi.org/10.5772/intechopen.97215*

#### **Figure 1.**

results obtained from the geodetic networks, initially composed of field stations of data gathering under episodic campaigns type, and later by continuously operating reference stations (cGPS). Several authors have pointed out the extensive applications of space geodesy for scientific purposes, e.g. [14–16], among others. In the study area, despite the restrictions due to the limited coverage of the national GNSS/GPS networks, its impact is already being observed in studies of the Earth dynamics. The data from the stations have allowed the generation of high precision products such as geodetic time series, velocity fields and estimation of tectonic plate motion rates, seismic cycle analysis, estimation of the magnitude and spatial variability of the plate coupling, among other aspects. In addition to tectonic studies, its use has been extended to the volcano deformation monitoring in several countries (Colombia, Costa Rica, Ecuador, Nicaragua), subsidence studies; the use of data for ionosphere and troposphere studies as well as its inclusion, still in its initial state, in tsunami warning systems. Progress has also been made in the conception of multiparameter stations, based on the joint installation in the same site of diverse equipment such as geodetic, seismological, strong motion and meteorological instruments, among others. It is also important to note that there is a good data

*Geodetic Sciences - Theory, Applications and Recent Developments*

availability, although not from all stations due to particular restrictions, that allows its use for various scientific purposes. However, in some cases, through agreements

Gathering of geologic, tectonic, seismologic and geodetic data through the last decades has led to a better understanding of the Caribbean plate, its margins and adjacent regions, progressively bringing in more complexity to the once drawn "drawer-like" Caribbean plate model [17]. In fact, the Caribbean plate borders are actually "plate boundary zones", PBZ, in the sense of [18], "wide deformation zones" in the sense of [19], particularly transpressional along the southern Caribbean PBZ, or "wide plate margins" in the sense of [10]. These margins amalgamate tectonic blocks of diverse size, composition, origin and geometry (**Figure 1**), somehow surrounding the Caribbean Sea, cored by the Caribbean Large

The recognition of such tectonic blocks started first along the southern Caribbean margin and northwestern South America corner, because being poorly defined by a disperse infrequent and moderate-in-magnitude (instrumental) seismicity, as well as by a poor surface/sea-bottom expression of the active tectonic

The study of this very complex but subtly expressed southern PBZ was enhanced by the fact that a large portion of the features are on land (**Figure 1**). Conversely, the northern Caribbean plate boundary became a natural laboratory for numerous space geodesy studies due to its apparent structural simplicity, although the first of all GPS studies worldwide, GPS CASA (Central And South America) Project was carried out in the complex southern Caribbean PBZ between 1988 and 1998 [10, 20]. Not as expected, GPS networks have not fully resolved the posed kinematic questions along this northern Caribbean PBZ, since the networks are mostly installed in rather small islands that are within the plate margin themselves that also resulted to be a complex PBZ with several active features lying offshore (**Figure 3**). As a matter of fact, the larger islands, such as Jamaica and Hispaniola, exist as a proof of such PBZ compressional or transpressional processes. A similar situation happens along the eastern border of the Caribbean plate, where the Atlantic plate subducts beneath an arc of active volcanic islands sitting on the

features in comparison with the other Caribbean PBZs (**Figure 2**).

or by formal request of data to national institutions, these can be obtained.

**2. Tectonic setting**

**144**

Igneous Province (CLIP) or plateau.

*Tectonic frame. Tectonic blocks: PB (Panama B.), CB (Chocó B.), NAB (North Andean B.),TMB (Triangular Maracaibo B.), BB (Bonaire B.). Other features: CAVA (Central America Volcanic Arc); CCRDB (Central Costa Rica Deformed Belt), EPGFZ (Enriquillo-Plantain Garden Fault Zone), LAS (Leeward Antilles Subduction), MP (Mona Passage), MPFS (Motagua-Polochic Fault System), NHDB (North Hispaniola Deformed Belt), NLAF (Northern Lesser Antilles Forearc). Modified from [13].*

Caribbean plate. Stable GPS stations inside the Caribbean, such as on San Andrés and Providencia islands and Serranilla Cay (Colombia), and Aves Island (Venezuela), will provide a reliable answer as to the relative motion between the Caribbean and surrounding plates. In addition, longer time span comparisons between these internal sites to the plate should confirm any internal deformation or fragmentation of the Caribbean plate itself, as proposed by [13].

Besides, strain partitioning at different scales is common to the four Caribbean plate PBZs (**Figure 1**). In Central America, a coastal sliver, bounded by the Central America trench on the southwest and the active Central America volcanic arc (CAVA) on the northeast, escapes to the north-west (NW), taking advantage of the weakening of the continental crust by the CAVA volcanic activity [21–24]. A similar situation is reported in the northern Lesser Antilles arc, where the forearc in this region, limited by the active arc on the west-southwest (WSW) and the Atlantic trench on the north-northeast (ENE), moves northward with respect to the arc [25, 26]. Along the northern Caribbean PBZ, the northernmost sliver of the Hispaniola Island, bounded by North Hispaniola and Septentrional faults on the north and south respectively, displaces west faster than most of the island. In the southern Caribbean PBZ, the Bonaire block as well as the block containing the Caribbean nappes overriden onto South America along northern Venezuela (outcropping in the Coastal and Interior ranges), accommodate shortening while slipping dextrally along the large west–east (W-E) trending Oca-Ancón, San Sebastián and El Pilar fault system (**Figure 1**).

#### **Figure 2.**

*Seismicity. Earthquake epicenters larger than 3 of magnitude recorded in the study area by the National Earthquake Information Center (NEIC) of the USGS and the National Seismic Network operated by the Geological Survey of Colombia for the period of time 2000–2020.*

(e.g., [12, 36]), with a tectonic paroxysm in the Pliocene (last 5–3 Ma, [21]), when most of the Eastern Cordillera of Colombia [37] and Mérida Andes of Venezuela [12] have actually started elevating to their present heights. A significant fraction of the time delay for the effective coupling (suturing) of the Chocó block against South America, besides the obliquity between the confronting plates, may be explained by the low rigidity exhibited by the Panamá arc at the latitudes of Panamá, which is intensely deformed internally by oroclinal bending and NW-SE trending en-echelon left-lateral faulting (e.g. [13, 24, 38]). The effective collision/ accretion of the Chocó block drives the extrusion of NAB (in the sense of [3]), which in the sense of [39] already comprises several NE-escaping blocks, such as Chocó, Maracaibo and Bonaire and others; NAB for this author was already an amalgamation of tectonic blocks. The subduction along which Caribbean plateau floor disappeared into the mantle and drove this indentation-extrusion process, is today partly fossilized between the Chocó block and South America, in association with or running near to the Romeral fault system. This collision has surface expression down to latitude 4°N in Colombia, up to an ENE-WSW-trending alignment of surface tectonic features running across the three Colombian chains at the latitude of Santa Fé de Bogotá, such as Garrapatas, Río Verde and Ibagué faults, and the change of structural style of the front of the Llanos foothills of the Eastern Cordillera, where a dominant dextral strike-slip style on the south (e.g. Algeciras fault) shifts to a much more compressional style on the north (e.g. Guaicáramo, Cusiana and Yopal faults. [39]). Also, the latter author underlines that the Eastern Cordillera becomes much wider across, north of this imaginary line. [40] proposes a broken indenter model for the Panamá-Chocó arc, in which the Chocó arc has been recently accreted to the NAB, resulting in a rapid decrease in shortening in the Eastern Cordillera. At depth,

*GNSS Networks for Geodynamics in the Caribbean, Northwestern South America, and Central…*

*DOI: http://dx.doi.org/10.5772/intechopen.97215*

*cGPS stations located on the study zone. Table 1 lists the cGPS stations by country.*

**Figure 3.**

**147**

In addition, block indentation and extrusion, and occasional induced oceanic subduction processes at the opposite side of indenters, are also present and rather common to the Caribbean PBZs. Indentation (collision) by submarine relieves or ridges (e.g. Carnegie and Cocos), as engine of tectonic block escape, has been invoked along the Pacific border of South America against the Nazca plate, as for the Pacific coastal sliver of Central America extending between Costa Rica and Guatemala, respectively. In other cases, such strain partitioning has been attributed to the oblique convergence of the subducting plate beneath the overriding one, such as along the northern sector of the Lesser Antilles arc and northernmost block of Hispaniola Island. So has the Ecuadorian-Colombian trench at the southern tip of the North Andes Block –NAB- [27], in the sense of [3]. However, the best regional example of indentation-extrusion is the collision and latter northward-prograding suturing of the Chocó block (originally a constitutive piece of the Cenozoic Panamá arc) against the north–south trending western coast of South America. Some authors as early as early 90's, e.g. [28–30], propose that such collision and diachronic suturing process induces the NNE-directed tectonic escape of a large portion of northwestern South America, extending from the Guayaquil Gulf-Tumbes basin –GGTB- in SW Ecuador to the Dutch Leeward Antilles (Aruba, Bonaire, Curaçao islands lying north of Venezuela, in the southern Caribbean), and incorporating most of Ecuador territory, the 3 main mountain chains (Western, Central and Eastern) of Colombia and all western mountainous Venezuela. This escape takes place along a major plate boundary named as the Eastern Frontal Fault System –EFFS- by [3]. Much precision has been gathered through the years as to the geometry of that NAB southeastern boundary (e.g., [31–35], among many others). This tectonic escape is probably young in age, starting in the late Miocene

*GNSS Networks for Geodynamics in the Caribbean, Northwestern South America, and Central… DOI: http://dx.doi.org/10.5772/intechopen.97215*

**Figure 3.** *cGPS stations located on the study zone. Table 1 lists the cGPS stations by country.*

(e.g., [12, 36]), with a tectonic paroxysm in the Pliocene (last 5–3 Ma, [21]), when most of the Eastern Cordillera of Colombia [37] and Mérida Andes of Venezuela [12] have actually started elevating to their present heights. A significant fraction of the time delay for the effective coupling (suturing) of the Chocó block against South America, besides the obliquity between the confronting plates, may be explained by the low rigidity exhibited by the Panamá arc at the latitudes of Panamá, which is intensely deformed internally by oroclinal bending and NW-SE trending en-echelon left-lateral faulting (e.g. [13, 24, 38]). The effective collision/ accretion of the Chocó block drives the extrusion of NAB (in the sense of [3]), which in the sense of [39] already comprises several NE-escaping blocks, such as Chocó, Maracaibo and Bonaire and others; NAB for this author was already an amalgamation of tectonic blocks. The subduction along which Caribbean plateau floor disappeared into the mantle and drove this indentation-extrusion process, is today partly fossilized between the Chocó block and South America, in association with or running near to the Romeral fault system. This collision has surface expression down to latitude 4°N in Colombia, up to an ENE-WSW-trending alignment of surface tectonic features running across the three Colombian chains at the latitude of Santa Fé de Bogotá, such as Garrapatas, Río Verde and Ibagué faults, and the change of structural style of the front of the Llanos foothills of the Eastern Cordillera, where a dominant dextral strike-slip style on the south (e.g. Algeciras fault) shifts to a much more compressional style on the north (e.g. Guaicáramo, Cusiana and Yopal faults. [39]). Also, the latter author underlines that the Eastern Cordillera becomes much wider across, north of this imaginary line. [40] proposes a broken indenter model for the Panamá-Chocó arc, in which the Chocó arc has been recently accreted to the NAB, resulting in a rapid decrease in shortening in the Eastern Cordillera. At depth,

In addition, block indentation and extrusion, and occasional induced oceanic subduction processes at the opposite side of indenters, are also present and rather common to the Caribbean PBZs. Indentation (collision) by submarine relieves or ridges (e.g. Carnegie and Cocos), as engine of tectonic block escape, has been invoked along the Pacific border of South America against the Nazca plate, as for the Pacific coastal sliver of Central America extending between Costa Rica and Guatemala, respectively. In other cases, such strain partitioning has been attributed to the oblique convergence of the subducting plate beneath the overriding one, such as along the northern sector of the Lesser Antilles arc and northernmost block of Hispaniola Island. So has the Ecuadorian-Colombian trench at the southern tip of the North Andes Block –NAB- [27], in the sense of [3]. However, the best regional example of indentation-extrusion is the collision and latter northward-prograding suturing of the Chocó block (originally a constitutive piece of the Cenozoic Panamá arc) against the north–south trending western coast of South America. Some authors as early as early 90's, e.g. [28–30], propose that such collision and diachronic suturing process induces the NNE-directed tectonic escape of a large portion of northwestern South America, extending from the Guayaquil Gulf-Tumbes basin –GGTB- in SW Ecuador to the Dutch Leeward Antilles (Aruba, Bonaire, Curaçao islands lying north of Venezuela, in the southern Caribbean), and incorporating most of Ecuador territory, the 3 main mountain chains (Western, Central and Eastern) of Colombia and all western mountainous Venezuela. This escape takes place along a major plate boundary named as the Eastern Frontal Fault System –EFFS- by [3]. Much precision has been gathered through the years as to the geometry of that NAB southeastern boundary (e.g., [31–35], among many others).

*Seismicity. Earthquake epicenters larger than 3 of magnitude recorded in the study area by the National Earthquake Information Center (NEIC) of the USGS and the National Seismic Network operated by the*

*Geological Survey of Colombia for the period of time 2000–2020.*

*Geodetic Sciences - Theory, Applications and Recent Developments*

**Figure 2.**

**146**

This tectonic escape is probably young in age, starting in the late Miocene

such a change of structural style roughly coincides with the Caldas tear, as described by [41]. In fact, it is not a plate tear but the confrontation of two different oceanic slabs [13]. On the north, the oceanic-plateau-affinity Caribbean plate sinks to the ESE, as a flat slab lying under the Triangular Maracaibo block and Mérida Andes and reaching depths of almost 700 km further east. This subducted piece of Caribbean plate was the one carrying the Panamá arc on its trailing edge and its consumption into the mantle conducted to the collision of the Panamá arc against South America. Meanwhile on the south, the Nazca plate which is a typical oceanic plate at these latitude, subducts under western South America. [42] propose that buoyant Caribbean crust has been amagmatically subducting under the North Andes for 75 Ma.

coverage, and because some stations have experienced problems in their operation,

*GNSS Networks for Geodynamics in the Caribbean, Northwestern South America, and Central…*

the monitoring is carried out from three volcanological and seismological

In Ecuador, The Geophysical Institute of the National Polytechnical School of Quito began installing in 2006 a network of GPS stations on the edifices of the most active volcanoes in the country. At the end of 2008, it started to implement a country-wide CGPS network of 70 stations [49]. At present, RENGEO (Spanish acronym for *Red Nacional de Geodesia*) is a geodetic network composed of 85 permanent stations, of which 30 are located in potentially active volcanoes [50]. The GPS receivers acquire data at different data tracking intervals, of 15 seconds and 1 second for volcanoes, and 30 seconds, 1 second and 0.2 seconds for tectonic studies, which are transmitted to the Monitoring Center in Quito through different ways such as radio links, internet, microwaves and satellite system. After the occurrence of the 2016 Pedernales earthquake, in order to improve the capacity of monitoring and generation of early warning information, especially due to tsunami hazards, a geodetic cGPS network in the province of Esmeraldas was implemented in real time. The data from this network are integrated with the seismic data to improve the rapid determination of the magnitudes and better characterize the

The deployment of the GPS geodetic network in Costa Rica has been the result of

actions carried out by institutions such as the OVSICORI, Spanish acronym for *Observatorio Vulcanológico y Sismológico de Costa Rica* (Volcanological and Seismological Observatory of Costa Rica), an institute that belongs to the Universidad Nacional, in coordination with foreign entities and researchers (UNAVCO, universities of South Florida, Central Washington, Georgia Tech, among others), as well as the contribution of National real estate institution. For geodynamic purposes, by the end of 2009, 19 cGPS stations had been established in the Nicoya Peninsula [51]. At present, the geodetic network of Costa Rica is composed of 55 cGPS stations [52]. In Venezuela, [53] points out that there are currently six cGPS stations that are part of COCONet (**Figure 3**), and two stations of the VENCREEP project funded by

In Colombia, the Geological Survey began in 2007 the development of GeoRED, a research and development project based on space geodesy technology that relied on a multifaceted approach to cataloging and defining the geodynamics of northwestern South America [47]. GeoRED is a Spanish acronym for *Geodesia: Red de Estudios de Deformación*. The general purpose of the GeoRED Project is to improve the technical, scientific and operational capabilities in Colombia for analysis, interpretation and policy formulation regarding phenomena related to crustal deformation in Colombia, using GNSS satellite technology. The GNSS GeoRED project is being executed under the operations framework of the Space Geodesy Research Group-SGRG of the Geohazards Directorate [48]. The current cGPS network has 153 stations installed as December 2020. Among these stations, 117 are GeoRED stations, 5 GNSS stations as part of the COCONet Project, and the Bogotá IGS GNSS station. Under a collaborative partnership with local Colombian institutions, thirteen stations have been installed with the Geographical Institute under a joint initiative named GNSS Colombia; eight with the Sugar Cane Research Institute (CENICAÑA); seven with the Bogota City Water Supply Company; and two stations installed with the Universidad Nacional and the Universidad Distrital, respectively. These stations have been fixed to the ground, following mainly UNAVCO's directions for the installation of permanent stations for the study of crustal deformation. Additionally, the Geological Survey of Colombia –GSC- has deployed another geodetic network composed of 70 permanent stations installed in three volcanic regions for the surveillance of the active volcanoes of the country, where

limiting the continuous availability of data.

*DOI: http://dx.doi.org/10.5772/intechopen.97215*

observatories.

source of the rupture.

**149**

Finally, the Caribbean plate itself can be considered as a single unit, at least at the current resolution level of the GPS results in the order of 2–3 mm/a [43]. However, the Hess escarpment is seismically active towards its southwestern end [13] and is moving left-laterally in that order of magnitude. In addition, this major submarine tectonic feature juxtaposes two very different Caribbean entities at naked eye. And it lies in the southern prolongation of an imaginary northeastsouthwest (NE–SW) striking line passing over the southern tip of the Bahamas platform, where transpression north of it is dominant, building up the Island of Hispaniola. This author proposes that such accident may have played a major role in the faster eastward migration of the Southern Caribbean, the one carrying the LIP or oceanic plateau, in the late and middle Miocene. This author further indicates that a modern reactivation could be starting in the recent geologic time, also with dominant sinistral and subordinate normal components, but this time related to the push of the floating Cocos ridge when being subducted.


**Abstract**

Arbuscular mycorrhizal fungi (AMF) are one of the essential components of the soil microbiome playing a crucial role in nutrients cycling and mediation of plant responses to different environmental stresses. They also play pivotal role in controlling soil erosion, enhancing phytoremediation, and eliminating other harmful microorganisms and then sustaining agroecosystem. Several studies have investigated the positive effects of mycorrhizal symbiosis as biofertilizers those are capable of reducing use of chemical fertilizer by 25–90% particularly NPK depending on crop species, soil type, and management practices, while increasing productivity in the range of 16–78%. Similarly, AMF can also act as bio-controllers and decrease the application rate and frequency of pesticides. This is directly translated to the primary role of AMF in the sustaining agriculture services. Thus, understanding the interaction between AMF-soil, and plant plays a vital role in benefitting societies and agro-industries. In this regard, this review attempted to explore how can AMF symbiosis reduce agro-chemicals and maintain sustainable human welfare. It also addresses impact of agrochemicals on crop production and the main factor influencing the success of AMF symbioses. Generally, if this is applied wisely it keeps the food safe, the soil healthy, the water clean, the climate stable, and the ecosystem flourishing.

**Keywords:** AMF symbioses, argo-chemical, biofertilizer, bio-controllers, agro-ecosystem


**5. Conclusions**

The findings suggest that high adherence to the DASH diet has a positive effect on reducing hypertension risk compared to low adherence. These data strengthen and are totally in line with all hypertension guidelines, i.e., European, American, and International, independent of the cut-off points used to define hypertension, pointing out that lifestyle modifications should start early before the establishment of hypertension, even in subjects with normal blood pressure levels.

**Supplementary Materials:** The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/nu15143261/s1, Supplementary Table S1. PRISMA 2020 checklist. Supplementary Table S2. MOOSE checklist. Supplementary Table S3. Search strategy for identifying studies on Pubmed. Supplementary Table S4. Quality assessment using the Newcastle-Ottawa scale for cross-sectional studies. Supplementary Table S5. Quality assessment using the Newcastle-Ottawa scale for cohort studies. Supplementary Table S6. Quality assessment using the JBI checklist for crosssectional studies. Supplementary Table S7. Quality assessment using the JBI checklist for cohort studies. Supplementary Figure S1. Subgroup analysis for the cohort studies based on hypertension diagnosis. Supplementary Figure S2. Sensitivity analysis by removing cohort studies with a NOS score < 7.

**Author Contributions:** Conceptualization, X.T. and A.T.; methodology, X.T.; formal analysis, X.T.; investigation, L.C., I.T. and V.C.; data curation, X.T. and L.C.; writing—original draft preparation, X.T. and L.C.; writing—review and editing, M.C., K.D., E.G. and A.T.; visualization, X.T.; supervision, M.C. and A.T. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available in the main text and Supplementary Materials.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

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**Meet the editor**

Alex Pappachen James received his PhD degree from the Queensland Micro- and Nanotechnology Centre, Griffith University, Brisbane, QLD, Australia. He is internationally known for his contributions on memristive networks, neuromorphic computing and image processing. Currently, he is chairing the Electrical Engineering Department at Nazarbayev University. He is a mentor to

several tech start-ups and co-founded companies in machine learning and computer vision hardware. He has been a founding chair for IEEE R10 Circuits and Systems Society Chapter and an executive board member of IET Vision and Imaging Network. He is the founding chair of IEEE Kazakhstan subsection, R8, and mentor to IEEE NU Student Branch. He was an editorial member of Information Fusion (2010–2015), Elsevier, and is an associate editor for HCIS (2015–present), Springer; IEEE Access (2017–present); IEEE Transactions on Emerging Topics in Computational Intelligence (2017– present); and IEEE Transactions on Circuits and Systems 1 (2018–present). He was a faculty senate chair of NU between 2016 and 2017. He received an award from the president of Kazakhstan for his services in the field of education in Kazakhstan in 2017. He is a senior member of IEEE, life member of ACM and senior fellow of HEA.

Contents

**Preface VII**

**Section 1 Memristor Devices 1**

**Memristor 41**

**Section 2 Memristor Modelling 113**

Morales-López

Chapter 1 **Physical Models for Resistive Switching Devices 3**

Chapter 3 **Emulator Circuits and Resistive Switching Parameters of**

Abdullah Yesil, Fatih Gül and Yunus Babacan

Chapter 4 **Nanoscale Switching and Degradation of Resistive Random**

Chapter 5 **Resistive Switching in Metal Oxide/Organic Semiconductor**

Chapter 6 **Memristor Emulator Circuit Design and Applications 115**

Chapter 7 **Simulating Memristive Networks in SystemC-AMS 147**

Dietmar Fey, Lukas Riedersberger and Marc Reichenbach

Geetika Khurana, Nitu Kumar, James F. Scott and Ram S. Katiyar

**Access Memory Studied by In Situ Electron Microscopy 63** Masashi Arita, Atsushi Tsurumaki-Fukuchi and Yasuo Takahashi

Henrique L. Gomes, Dago M. de Leeuw and Stefan C.J. Meskers

Carlos Sánchez-López, Illiani Carro-Pérez, Victor Hugo Carbajal-Gómez, Miguel Angel Carrasco-Aguilar and Francisco Epimenio

Luis‐Miguel Procel‐Moya

Chapter 2 **Graphene Oxide-Based Memristor 19**

**Nonvolatile Memories 93**