Citation

M. A. Shafiq, Z. Long, H. Di, and G. AlRegib, “A novel attention model for
salient structure detection in seismic volumes,” Applied Computing and
Intelligence, vol. 1, no. 1, pp. 31-45, Nov. 2021.

DOI

https://doi.org/10.3934/aci.2021002

Review

Date of publication: 22 November 2021

Data and Codes

https://ghassanalregib.info/

Bib

@article{shafiq2021aci,
title={A novel attention model for salient structure detection in seismic
volumes},
author={Shafiq, M. and Long, Z. and Di, H. and AlRegib, G.},
journal={Applied Computing and Intelligence},
volume={1},
number={1},
pages={31–45},
year={2021},
month={Nov.},
publisher={AIMS Press}}

Copyright

©2021 the Author(s), licensee AIMS Press. This is an open access article
distributed under the terms of the Creative Commons Attribution License
(http://creativecommons.org/licenses/by/4.0).

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Name of Editor

# A novel attention model for salient structure detection in seismic volumes

Muhammad Amir Shafiq  1  Zhiling Long  2,  Haibin Di and Ghassan AlRegib111M.
Shafiq, Z. Long, and H. Di were affiliated with the OLIVES Lab, directed by
Prof. Ghassan AlRegib, in the School of Electrical and Computer Engineering of
Georgia Institute of Technology (https://ghassanalregib.info/). 3  4,
11affiliationmark:  Apple Inc., Cupertino, CA, USA 22affiliationmark:  Mercer
University, Atlanta, GA, USA 33affiliationmark:  Schlumberger Ltd., Houston,
TX, USA 44affiliationmark:  Georgia Institute of Technology, Atlanta, GA, USA

###### Abstract

A new approach to seismic interpretation is proposed to leverage visual
perception and human visual system modeling. Specifically, a saliency
detection algorithm based on a novel attention model is proposed for
identifying subsurface structures within seismic data volumes. The algorithm
employs 3D-FFT and a multi-dimensional spectral projection, which decomposes
local spectra into three distinct components, each depicting variations along
different dimensions of the data. Subsequently, a novel directional center-
surround attention model is proposed to incorporate directional comparisons
around each voxel for saliency detection within each projected dimension.
Next, the resulting saliency maps along each dimension are combined adaptively
to yield a consolidated saliency map, which highlights various structures
characterized by subtle variations and relative motion with respect to their
neighboring sections. A priori information about the seismic data can be
either embedded into the proposed attention model in the directional
comparisons, or incorporated into the algorithm by specifying a template when
combining saliency maps adaptively. Experimental results on two real seismic
datasets from the North Sea, Netherlands and Great South Basin, New Zealand
demonstrate the effectiveness of the proposed algorithm for detecting salient
seismic structures of different natures and appearances in one shot, which
differs significantly from traditional seismic interpretation algorithms. The
results further demonstrate that the proposed method outperforms comparable
state-of-the-art saliency detection algorithms for natural images and videos,
which are inadequate for seismic imaging data.

###### keywords:

human visual system; attention model; saliency detection; seismic
interpretation

##  1 Introduction

One of the important steps in the exploration of hydrocarbons and reservoirs
of oil and gas is the detection of subsurface structures, such as faults and
salt domes. These structures span over several square kilometers and form
structural traps due to their distinct lithologic properties such as low
permeability. The detection of subsurface structures is accomplished through
seismic interpretation, a process in which a geophysicist explores the seismic
imaging data, both manually through visual inspection and with the assistance
of computer programs, to identify relevant structures. As summarized in a
recent survey [1], various computational algorithms for seismic interpretation
have been developed over the years. They focus on either detection or tracking
of subsurface structures such as faults, salt domes, gas chimneys, and
channels. They typically rely on analyzing characteristics observed in the
imaging data, such as correlations, changes in intensity or contrast, and
texture patterns, to name a few. Since seismic imaging data is represented in
the form of 2-dimensional sections or 3-dimensional volumes, and visual
inspection is utilized in a traditional interpretation by human interpreters,
image or video processing algorithms have been heavily adopted in
computational methods designed to assist seismic interpretation, which is
evident from the survey. However, saliency detection based on human visual
attention, although being studied extensively in the past two decades in the
image/video processing community, has rarely been applied to computational
seismic interpretation.

Saliency detection techniques aim to identify visually prominent areas or
objects within images and videos, which are salient areas or objects that most
likely draw the attention of the human visual system (HVS) [2]. When applied
to an image (or a video), a saliency detection algorithm will calculate a
saliency value for each pixel (or voxel), resulting in a saliency map, which
maps each pixel (or voxel) in the image (or video) to its associated saliency
value. Correspondingly, areas in the image (or video) with high saliency
values are identified as salient areas. Saliency detection mimics the
attention mechanism of HVS, which enables HVS to focus its processing
resources on elements conveying the most important information in a complex
surrounding environment. Such a mechanism is described computationally by an
attention model. The center-surround processing is commonly accepted as a
general framework for attention models [2]. According to the general concept
of center-surround processing, the level of saliency at a certain location is
determined by comparing that location against its surrounding neighbors in
terms of certain features. The higher is the center-surround difference, the
greater is the level of saliency. Based on the general center-surround model,
a specific saliency detection algorithm may have its own unique attention
model by customizing within the general framework. If an attention model
utilizes only low-level features extracted from the observed scene (such as
color, contrast, motion, etc.), it is a bottom-up model. If a model also
incorporates prior knowledge specific to a targeted application, it is a top-
down model.

Saliency detection has been studied extensively in the context of natural
images and videos [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]. For example, in
[3], saliency is determined using the self-information of visual features. In
[4], saliency is calculated using spectral residues obtained in the frequency
domain. In [5], a quaternion representation combining intensity, color, and
motion features is utilized for saliency detection. In [6], low-level features
such as color and luminance are combined with a frequency-tuned approach. In
[7], saliency in videos is detected by combining saliency in the space domain
and saliency in the time domain using a statistical uncertainty measure.
Saliency detection for videos was also studied in [8], where 3-dimensional
fast Fourier transform (3D-FFT) is performed locally, with the spectrum
decomposed into spatial and temporal components to yield spatial and temporal
saliency separately. In [15], an unsupervised approach was proposed to assess
the reliability of detected saliency. In the past several years, application
of deep learning techniques to saliency detection for natural images and
videos has also attracted increasing interest, for which a comprehensive
review can be found in [16].

Given that seismic interpretation is traditionally accomplished by human
interpreters through visual inspection, saliency detection algorithms, if
designed appropriately to imitate a human interpreter’s visual attention,
should be able to identify in seismic imaging data geological structures of
interest to an interpreter as salient areas. Such algorithms will provide a
brand new perspective to examine seismic imaging data. They have a potential
to become very useful computational tools to assist in seismic interpretation,
because they are capable of detecting various salient structures at the same
time, even though those structures may differ in nature and in appearance.
This will be drastically different from, and more efficient than most
currently available computational interpretation techniques, for which an
algorithm is typically designed to only detect structures of similar nature or
appearance.

Figure 1: A typical seismic image (that is, a 2D cross section of a 3D seismic
imaging data volume) with structures of interest for seismic interpretation
[17]. For illustration purpose, each structure has been annotated and colored
distinctively.

In the past, there were rarely research activities reported on saliency
detection for seismic imaging data. Among the very few pioneering
explorations, an approach was proposed in [18] for automated horizon picking
based on salient features detection. In [19], a study was carried out to gain
heuristic knowledge of experts while interpreting seismic imaging data.
Similarly, another study was reported in [20] of various saliency detection
algorithms for natural images to observe which algorithm closely mimics the
interpreter’s visual attention during the interpretation of gravity and
magnetic data, instead of seismic data. In our initial exploration on this
topic, we presented two novel algorithms applying visual saliency to the
detection and delineation of salt domes [21, 22]. These early studies applied
saliency detection algorithms originally designed for natural images and
videos directly to seismic imaging data. Although with some success for the
specific tasks, such an approach is inadequate in general for seismic
interpretation. Seismic imaging data is significantly different from natural
images and videos, not only because the appearance is atypical, but also most
structures are characterized by subtle changes in amplitude, texture, and
contrast. For example, as illustrated in Fig. 1, horizons are detected as
continuous smooth horizontal lines. Chaotic horizons are similar to horizons,
but with noisy fluctuations along the lines. A sigmoidal structure typically
appears as S-shapped downlapping character extending outward and upward, with
a fine texture. A salt dome is a mound of salt intruding upwards, typically
appearing as a textured area enclosed by strong reflective boundaries.
Finally, faults are identified when discontinuity is observed in any of the
structures. Furthermore, the contextual information in the form of object’s
surroundings and geology also plays an important role in seismic
interpretation. To detect salient structures in seismic imaging data, it is
imperative to incorporate such domain knowledge as prior information into the
attention model and the algorithm.

In this paper, we present a novel saliency detection algorithm for seismic
imaging data in the form of 3D data volumes, which incorporates domain
knowledge specific for seismic interpretation into the underlying attention
model. Following our previous study reported in [21, 22], we establish our new
algorithm on the basis of the same 3D-FFT-based saliency detection method. The
utilization of 3D-FFT helps capture energy variations within a seismic volume
both effectively and computationally efficiently, and the multi-dimensional
spectral projection tracks the variations along different dimensions reliably.
Our major innovation in this new saliency detection algorithm is with the
underlying attention model, in which we propose a unique directional center-
surround comparison to replace the non-directional comparison commonly
performed for natural images and videos. This directional operation is
adjustable for any orientation, and aims to better accommodate seismic
structures of directional nature, such as faults, gas chimneys, and horizons.
Additionally, we design an adaptive scheme to automatically combine saliency
values calculated from the multi-dimensional spectral projections into an
overall saliency value. For evaluation, we use two entirely different seismic
datasets under different geological settings to examine the effectiveness of
the proposed saliency detection algorithm. We demonstrate that our innovative
method outperforms comparable state-of-the-art algorithms in detecting salient
subsurface structures of interest in seismic interpretation. We note that,
although some of our preliminary results from this work were reported in [23,
24], the algorithm we present in this paper has been improved by incorporating
the adaptive scheme to obtain the final saliency map, and has been tested more
extensively.

##  2 Proposed algorithm

Our proposed saliency detection algorithm is illustrated in the block diagram
shown in Fig. 2. It starts with applying a localized 3D-FFT to the seismic
volume being examined. Afterwards, the multi-dimensional spectral projection
process decomposes a 3D-FFT spectrum to depict spatial variations along all
three dimensions within the 3D volume. Subsequently, the application of
directional center-surround (DCS) comparison highlights the salient variations
along relevant orientations within the projected space. In the last step, the
saliency maps generated from each projection are combined into the final
saliency map using adaptive weights. In the following step-by-step detailed
presentation of the algorithm, we assume a 3D seismic data volume
$\boldsymbol{V}$ of size $T\times X\times Y$, where $T$ represents time (when
reflection time is considered in imaging reconstruction) or depth (when actual
subsurface depth is considered in imaging reconstruction), $X$ represents
crosslines (direction perpendicular to the inlines), and $Y$ represents
inlines (direction along which seismic imaging data was acquired); and we
denote the computed saliency map as $\boldsymbol{S}$.

Figure 2: The block diagram of the proposed saliency detection algorithm.

In the first step, we compute 3D-FFT of $\boldsymbol{V}$ using a local cube,
with a sliding window having more than 50% overlap, to yield a volume
$\boldsymbol{F}$. In the second step, we perform decomposition of the spectral
cube as explained in Fig. 3. Within a 3D spectral cube in
$f_{t}$-$f_{x}$-$f_{y}$ coordinate system, if a spectral point is closer to
$f_{x}$-$f_{y}$-plane, then its projection on $f_{x}$-$f_{y}$-plane, i.e.,
along $f_{t}$-direction will depict variations more prominently as compared to
the projections on $f_{t}$-$f_{y}$ or $f_{t}$-$f_{x}$ planes. Therefore, we
decompose the 3D spectral cube by projecting the spectral point $F[i,j,k]$
along different dimensions as

$\boldsymbol{F}_{m}[i,j,k]=\boldsymbol{F}[i,j,k]\times\frac{\boldsymbol{P}_{m}[i,j,k]}{\sqrt{i^{2}+j^{2}+k^{2}}},\quad
m\in\\{t,x,y\\},$ (1)

where projections $\boldsymbol{P}_{m}$ along time, crossline, and inline
dimensions are represented by $\sqrt{j^{2}+k^{2}}$, $\sqrt{i^{2}+k^{2}}$, and
$\sqrt{i^{2}+j^{2}}$ respectively. $\boldsymbol{F}$ represents the multi-
dimensional FFT domain defined as
$\boldsymbol{F}=\mathcal{K}\oasterisk{C}_{n}$, where ${C}_{n}$ represents a
local cube of side length $n$ within volume $\boldsymbol{V}$, $\oasterisk$
represents tensor product, and $\mathcal{K}$ is the Kronecker matrix defined
as

$\mathcal{K}=D_{x}\otimes D_{y}\otimes D_{z},$ (2)

where $D_{x}$, $D_{y}$, and $D_{z}$ are transformation matrixes for the
discrete Fourier transform (DFT), and $\otimes$ represents the Kronecker
product. The spectral projections are not computed at the center of the local
cube, as it represents the zero Hertz component and does not reflect any
changes along the three planes.

(a) Spectral cube (b) Plane projections

Figure 3: The illustration of spectral cube, plane projections, and
decompositions. Figure 4: The illustration of DCS comparison along $t$, $x$,
and $t$-$x$ directions, respectively.

In the third step, we extract features also known as spectral energies,
$\boldsymbol{E}_{m}$, where $m\in\\{t,x,y\\}$, from spectral projections based
on the absolute mean of local cube. The process of feature extraction enhances
motion variations and provides pixel-level descriptions based on spectral
energies in the neighborhood of a voxel.

In the fourth step of the proposed method, we apply the DCS comparison to
construct the saliency maps $\boldsymbol{S_{m}}$ using $\boldsymbol{E_{m}}$ as

$\displaystyle\boldsymbol{S}_{m}[t,x,$ $\displaystyle
y]=\frac{1}{Q}\sum_{i_{0},j_{0},r_{0}}|\boldsymbol{E}_{m}[t,x,y]-$
$\displaystyle
w\cdot\boldsymbol{E}_{m}[t+i_{0},x+j_{0},y+r_{0}]|,~{}~{}m\in\\{t,x,y\\},$ (3)

where $Q$ represents the total number of points included in the summation and
$w$ represents Gaussian weights. $i_{0}$, $j_{0}$, $r_{0}$ are chosen such
that point $[t+i_{0},x+j_{0},y+r_{0}]$ is in the immediate neighborhood of
point $[t,x,y]$, such as within a directional window centered at $[t,x,y]$ as
depicted in Fig. 4. In order to incorporate a priori information, we can
either apply different directional filters pertaining to desired orientations,
sizes, or shapes in DCS comparison, or we can apply different weights to
various spectral projections to enhance any desired feature within seismic
volume. Alternatively, we can also combine both to yield optimum results. DCS
comparisons for selected orientations along $t$, $x$, and $t$-$x$ directions
are illustrated in Fig. 4, where level of brightness indicates the magnitude
of associated weights for each voxel, with darkest being the highest.
Similarly, we can create templates to embed desired orientation, size, or
shape information in DCS comparison.

Figure 5: Adaptive wights update.

Finally, the saliency map $\boldsymbol{S}$ is obtained via adaptive
combination of directional saliency maps along each dimension using a block
diagram shown in Fig. 5. $\boldsymbol{D}$ represents a desired map which can
be either manually labelled seismic volume that highlights desired structures
within the volume, or a saliency map selected from the directional saliency
maps $S_{m},m\in\\{t,x,y\\}$. For weights update, we implemented least mean
square (LMS), normalized least mean square (NLMS), and recursive least square
(RLS) algorithms. The saliency map $\boldsymbol{S}$, which is of the same size
as that of $\boldsymbol{V}$ is obtained by the dot product of weight vector
and individual saliency maps as

$\boldsymbol{S}=\begin{bmatrix}W_{t}&W_{x}&W_{y}\end{bmatrix}\cdot\begin{bmatrix}\boldsymbol{S}_{t}&\boldsymbol{S}_{x}&\boldsymbol{S}_{y}\end{bmatrix}^{T}$
(4)

where $W_{m},m\in\\{t,x,y\\}$ represents adaptive weights obtained via LMS,
NLMS, or RLS. Alternatively, the weights $W_{m}$ can be set either equally to
construct a saliency map with equal distribution of projections along each
axis or empirically to highlight certain features along any particular
dimension.

The adaptive combination of individual saliency maps along each dimension
provides a non-parametric way of computing $\boldsymbol{S}$ that can not only
be tuned to highlight specific structures, but can also be adapted to any
individual saliency map. The mean square error (MSE) of various adaptive
algorithms for adapting weights to a certain saliency map is shown in Fig. 6.
It can be observed that all algorithms converge to adapt the desired map, with
RLS requiring the least number of iterations. However, RLS is computationally
expensive because of matrix inversion; therefore, we have used NLMS for
adaptive combination of individual saliency maps in this paper. Finally, the
selection of desired map for weight adaption is left as an input by the
interpreter. For example, as in the case of interpreting normal and reverse
faults, which are usually oriented along time/depth dimension, an interpreter
can specify a labelled seismic section for faults adaption that will
automatically calculate the weights and yield an optimum saliency map without
any manual tuning or empirical weight selection. It is worth mentioning that
we do not have to adapt each seismic section for extracting desired features.
The weights are adapted to any individual saliency map or given desired map
only once for whole seismic volume and can be adapted again after every $N$
seismic sections, if required.

Figure 6: The mean square error of LMS, NLMS, and RLS algorithms for adapting
a saliency map along time dimension.

##  3 Experimental results

In this section, we present the results of the proposed saliency detection
algorithm on two real seismic datasets acquired from the Netherlands offshore
F3 block in the North Sea and Great South Basin (GSB), New Zealand,
respectively. Both datasets consist of standard 3D seismic imaging data
reconstructed from reflected vibration waves collected over an area of
interest. The datasets are available in the standard SEG-Y format. Detailed
information about the datasets can be found at [25, 26]. These datasets
comprise of different subsurface structures that are characterized by subtle
variations in intensity and texture, making them extremely challenging and
difficult to detect if regular saliency detection algorithms for natural
images and videos are used.

We note that visual inspection is the dominant method of evaluation in seismic
interpretation. Although attempts were made to propose quantitative methods of
evaluation in recent years [17, 21, 22, 27, 28, 29, 30], such methods are
limited in being tied to specific structures or tasks. They are still far from
being widely accepted in the community. As such, we follow the common practice
to evaluate our results in this paper. We show the saliency maps generated
from our proposed algorithm side by side with those from comparable state-of-
the-art saliency detection algorithms for a qualitative comparison. As a
general rule, a well-designed seismic interpretation algorithm should not only
resolve spatial variations along different directions within a seismic volume,
but also highlight geological structures that are hardly conspicuous with
respect to its surrounding environment.

###  3.1 F3 Block in the North Sea, Netherlands

A typical seismic time section (i.e., a cross section of the 3D data volume
along the t-direction, assuming an x-y-t coordinate system depicted in Fig. 2)
from the F3 block and its saliency map obtained using our proposed algorithm
in Fig. 2 are shown in Fig. 7a-b, respectively. It can be observed from the
saliency map that it effectively captures salt dome structures and, at the
same time, pleasantly highlights multiple faults as shown in the top left of
the saliency map.

(a) A typical seismic time slice

(b) Saliency map

Figure 7: A seismic time section within F3 block at 1600ms and its saliency
map generated using our proposed algorithm.

A seismic inline section (i.e., a cross section of the 3D data volume along
the y-direction) from the F3 dataset containing multiple seismic structures is
shown in Fig. 8a. The results of various comparable state-of-the-art image and
video saliency detection algorithms presented in [3], [4], [5], [6], [7], and
[8] are shown in Fig. 8b-g, respectively. The saliency map from the proposed
method with equal weights $W_{m},m\in\\{t,x,y\\}$ is shown in Fig. 8h, whereas
the saliency map adapted to highlight faults along the time direction (i.e.,
the vertical direction) is displayed in Fig. 8i.

(a) A typical seismic inline section.

(b) SUN [3]

(c) SR [4]

(d) PQFT [5]

(e) Achanta [6]

(f) Fang [7]

(g) Long [8]

(h) Proposed (Equal weights)

(i) Proposed (Adapted to highlight faults)

Figure 8: Comparison of the proposed algorithm against other algorithms on a
typical seismic section within F3 block. We note that the major structures (as
labeled in the original seismic image) have all been detected in the saliency
maps from the proposed algorithm.

(a) Original

(b) Fang [7]

(c) Long [8]

(d) EW

(e) AD

Figure 9: Comparison of saliency maps by zooming in on the major fault
extending along the vertical direction, visible in the middle of the original
seismic section within F3 block through the horizontal discontinuities. Here,
EW means the proposed with equal weights, and AD means the proposed being
adapted to highlight faults. It is obvious that the two zoom-in saliency maps
freom the proposed algorithm (EW and AD) are capable of highlighting the
fault, with the AD version presenting the best result, while the other two are
not.

As observed in the resulting saliency maps, the proposed algorithm effectively
highlights the salient structures from the seismic imaging data as compared to
other algorithms. Specifically, Fig. 8h shows horizons, chaotic regions, salt-
dome boundary, and faults in the given seismic inline section, all at once,
while most other algorithms can only highlight one or two structures,
typically with inferior visual appearance showing either more artifacts or
blurred boundaries. Figure 8i highlights not only a major fault in the middle
dissecting a salt dome but also a number of smaller faults at the bottom left
side of the seismic section. While majority of algorithms fail to detect even
the major fault in the center of the seismic section, the proposed algorithm
highlights such changes successfully because it accounts for the spectral
variations along all three dimensions of the seismic volume. In addition, the
proposed saliency detection algorithm accentuates a sigmoidal structure, which
is not distinctively detected by other algorithms.

###  3.2 GSB, New Zealand

The dataset from Great South Basin (GSB), New Zealand, comprises of complex
networks of faults inter-winded and dwindled together. While some faults can
be observed easily, others are very subtle and not easily discernible. To
examine the performance of our proposed algorithm on this challenging dataset,
first of all, we show the saliency maps $S_{m},m\in\\{t,x,y\\}$ obtained for a
typical seismic inline section (Fig. 12a) in Fig. 10a-c and a consolidated
saliency map obtained by combining these saliency maps using equal weights in
Fig. 10d. It can be observed clearly that each map depicts the spectral
variations and relative motion of structures along their respective
dimensions. Furthermore, the combined saliency map highlights all changes in a
unified manner without any manual tuning. Again, if needed, it can also be
adapted to highlight changes based on a priori information such as shape,
orientation or structures specified in a desired map. Second, we present a
time section from the GSB dataset and its saliency map in Fig. 11a-b,
respectively. As observed, the obtained saliency map effectively highlights
complex fault networks that are not evident in the original seismic section.
The subtle variations and overlapping faults can be easily recognized from the
saliency map.

(a) Saliency along time dimension, $\boldsymbol{S}_{t}$

(b) Saliency along crossline dimension, $\boldsymbol{S}_{x}$

(c) Saliency along inline dimension, $\boldsymbol{S}_{y}$

(d) Combined saliency map, $\boldsymbol{S}$

Figure 10: Example saliency maps obtained after spectral decomposition and DCS
comparisons, using the GSB dataset.

(a) A typical seismic time section

(b) Saliency map

Figure 11: A seismic time section within GSB dataset at 1556ms and its
saliency map, which clearly highlights the complex network of faults.

(a) A typical seismic inline section

(b) Ground Truth

(c) SUN [3]

(d) SR [4]

(e) PQFT [5]

(f) Achanta [6]

(g) Fang [7]

(h) Long [8]

(i) QSS [9]

(j) Seo [10]

(k) GTC [31]

(l) C-Cube[32]

(m) Proposed Method (Equal weights)

(n) Proposed Method (Larger $W_{t}$)

Figure 12: Comparison of the proposed algorithm against various saliency
detection algorithms, as well as non-saliency-based algorithms, on detecting a
complex network of faults in a typical seismic inline section within GSB
dataset. The proposed algorithm generated satisfactory results, while most
others failed to do the job.

For a comparative study, we examined a seismic inline section from GSB dataset
containing multiple faults, as shown in Fig. 12a. The ground truth for this
seismic section, with faults manually labelled by a geophysicist, is shown in
Fig. 12b. The results of comparable state-of-the-art saliency detection
algorithms presented in [3], [4], [5], [6], [7], [8], [9], and [10] are shown
in Fig. 12c-j, respectively. The detection results from two non-saliency-based
algorithms are also shown in Fig. 12k-l, respectively, of which one is based
on the generalized tensor coherence [31] and the other based on the coherence
cube [32]. The saliency map generated from the proposed algorithm with equal
weights $W_{m}$ is shown in Fig. 12m; whereas Fig. 12n displays the saliency
map from the proposed method adapted to highlight faults along the time
dimension.

From Fig. 12, it is clear that most available saliency-based algorithms in the
comparative study failed to detect any or vast majority of the faults. Only
two of them, that is, the ones from [8] and [10], were able to capture some of
the faults, but not with a distinct appearance. In contrast, from Fig. 12m-n
we observe that the proposed algorithm effectively highlighted all the major
faults present within the seismic section. Figure 12n demonstrates that, by
adapting to directional saliency along the time dimension, our proposed
algorithm not only tuned out clutters, but also presented the faults
distinctly with each fault easily distinguishable from others. As to the two
non-saliency-based detection results using [31] and [32], they contain too
much noise, not able to highlight the faults adequately.

From the studies above on the two real seismic datasets, it is evident that
the proposed algorithm can effectively detect subsurface structures of
diversified natures and appearances in one shot. It is also capable of
capturing subtle spatial variations characteristic of some structures such as
faults. The algorithm performs consistently across various structures and
different datasets, generating saliency maps of excellent qualities. The
amplitude of salient values detected by the proposed algorithm are
significantly higher for the structures of interest as compared to other
methods. In the mean time, the detected salient areas are more localized near
the structures of interest. Furthermore, the resolution of the results
generated from the proposed algorithm is typically much better than those from
the other algorithms, which makes it advantageous for applications requiring
not only fine perception but also efficient detection of subtle signatures.

##  4 Conclusion

In this paper, we presented a new approach to seismic interpretation
applications based on visual perception and modeling of human visual system.
We proposed a saliency detection algorithm based on a novel attention model
for identifying subsurface structures within seismic data volumes. The
proposed algorithm extracts features based on 3D-FFT local spectra and multi-
dimensional spectral projections. It utilizes a novel directional center-
surround attention model to compute saliency maps along different dimensions
within seismic volume, and then adaptively combines them to yield a
consolidated saliency map. Using the proposed algorithm, we can incorporate
seismic domain knowledge by specifying directional comparisons and adapting
the saliency map to desired characteristics that effectively highlight subtle
signatures and structures in a geologically complex setting. Experimental
results on two real seismic datasets from the North Sea, Netherlands and Great
South Basin, New Zealand demonstrated the effectiveness of the proposed
algorithm for detecting salient seismic structures of different natures and
appearances in one shot, which differs significantly from traditional seismic
interpretation algorithms. The results further demonstrated that the proposed
method outperforms comparable state-of-the-art saliency detection algorithms,
which are more suitable for natural images and videos, but not being adequate
for seismic imaging data.

## Conflict of interest

All authors declare no conflicts of interest in this paper.

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