# Multi-task multi-station earthquake monitoring: An all-in-one seismic Phase
picking, Location, and Association Network (PLAN)

Xu Si1, Xinming Wu1∗, Zefeng Li1∗, Shenghou Wang2 and Jun Zhu1
1School of Earth and Space Sciences, University of Science and Technology of
China,
Hefei, China.
2Key Laboratory of Tectonics and Petroleum Resources of Ministry of Education,
China University of Geosciences, Wuhan, China.

∗To whom correspondence should be addressed:
E-mail<EMAIL_ADDRESS>and<EMAIL_ADDRESS>
###### Abstract

Earthquake monitoring is vital for understanding the physics of earthquakes
and assessing seismic hazards. A standard monitoring workflow includes the
interrelated and interdependent tasks of phase picking, association, and
location. Although deep learning methods have been successfully applied to
earthquake monitoring, they mostly address the tasks separately and ignore the
geographic relationships among stations. Here, we propose a graph neural
network that operates directly on multi-station seismic data and achieves
simultaneous phase picking, association, and location. Particularly, the
inter-station and inter-task physical relationships are informed in the
network architecture to promote accuracy, interpretability, and physical
consistency among cross-station and cross-task predictions. When applied to
data from the Ridgecrest region and Japan regions, this method showed superior
performance over previous deep learning-based phase-picking and localization
methods. Overall, our study provides for the first time a prototype self-
consistent all-in-one system of simultaneous seismic phase picking,
association, and location, which has the potential for next-generation
autonomous earthquake monitoring.

## Introduction

Earthquake monitoring is one of the most fundamental operations in seismology.
A standard earthquake monitoring workflow involves a series of steps to detect
and characterize earthquakes, including phase picking, association, and event
location (Beroza et al., 2021; Mousavi and Beroza, 2022; Zhu et al., 2022c).
Phase picking, a conceptually simple task which is akin to detection problems
in computer vision, has recently been improved through deep learning (Zhu et
al., 2022c; Ross et al., 2018b, a; Zhu and Beroza, 2018; Mousavi et al., 2019;
Zhu et al., 2019; Pardo et al., 2019; Wang et al., 2019; Liu et al., 2020;
Mousavi et al., 2020; Yang et al., 2021; Yano et al., 2021; Zhu et al., 2022a;
Bilal et al., 2022; Feng et al., 2022; Münchmeyer et al., 2022), where
convolutional neural networks (CNNs) (Krizhevsky et al., 2017) are typically
used. After the phase picking, traditional (Arora et al., 2013; Gibbons et
al., 2016; Zhang et al., 2019; Zhu et al., 2022b) and deep-learning-based
(Ross et al., 2019; McBrearty et al., 2019a; Yu and Wang, 2022) phase
association algorithms have been used to link seismic phases at multiple
stations from the same events. Finally, location algorithms (Bakun and
Wentworth, 1997) utilize the associated phases to obtain the earthquake
hypocenters, although some deep-learning-based methods directly process raw
data to locate earthquakes (Zhang et al., 2014; DeVries et al., 2018; Perol et
al., 2018; Lomax et al., 2019; Mousavi and Beroza, 2019; Zhang et al., 2020;
Münchmeyer et al., 2021).

These three tasks (phase picking, association, and location) are closely
interdependent. The accuracy of multi-station phase picking affects the
accuracy of association and location. Conversely, association and location
impose constraints on multi-station phase picking. Additionally, phase picking
with multi-station data can further utilize the geographic relationships and
waveform similarities among multiple stations. To achieve more efficient and
accurate earthquake monitoring, a suitable earthquake monitoring workflow
should impose inter-task and inter-station constraints and preferrably perform
all three tasks simultaneously at all stations. However, most existing
earthquake monitoring methods perform phase picking, association, and
earthquake location separately. In addition, most of the current phase-picking
methods process seismic data on a station-by-station basis. While some recent
graph-based approaches (McBrearty et al., 2019b; van den Ende and Ampuero,
2020; McBrearty and Beroza, 2022b, 2023; Zhang et al., 2022) have demonstrated
the ability to handle irregularly spaced stations for phase association and
event location, it remains a challenging task to develop a method that
effectively leverages inter-task and inter-station constraints, and ideally
performs all three tasks simultaneously.

Here, we propose an all-in-one earthquake monitoring system called seismic
Phase picking, Location, and Association Network (PLAN) that achieves for the
first time the simultaneous implementation of the three tasks with multi-
station data and inter-task constraints. PLAN consists of four interdependent
neural network modules. Specifically, the first module of waveform feature
extraction utilizes an encorder-decoder architecture to extract relevant
features from multi-station seismic data. The second module of earthquake
location encodes station locations (i.e., longitude, latitude, and elevation)
and merges them with waveform features from the first module to predict the
earthquake depth and epicentral distance for each station. The third module of
phase association utilizes the predicted earthquake location information to
estimate the time shifts required to align multi-station waveform features.
Finally, the fourth module of phase picking aggregates the aligned features
for simultaneous multi-station phase picking. We applied PLAN in the
Ridgecrest and Japan regions and compared its efficiency and accuracy with
that of state-of-the-art phase-picking and event location methods,
demonstrating the merits of inter-station and inter-task constraints for
accurate earthquake monitoring.

## Results

### Network architecture

Figure 1:  The flowchart of the proposed multi-task and multi-station PLAN for
earthquake monitoring. The input data for the model comprise seismic waveforms
recorded by multiple stations and the locations of these stations. PLAN
consists of four sub-modules: waveform feature extraction encoder and decoder,
an earthquake location module, a multi-station association module and a
physics-informed multi-station phase-picking module. All of these sub-modules
are optimized simultaneously and constrained by each other during training to
improve performance in earthquake detection, association, and location.

The proposed multi-station multi-task PLAN (Fig. 1) employs a Graph neural
network (GNN) (Kipf and Welling, 2016) as the backbone to integrate the four
functional modules of waveform feature extraction, earthquake location, multi-
station association, and a physics-informed multi-station phase picking
(further details are provided in the Methods section). Compared with CNN, GNN
is naturally suited for handling seismic data acquired from irregularly spaced
stations whose quantity and location may vary (McBrearty and Beroza, 2023). In
constructing our GNN, we define the graph nodes with seismic stations and
define the feature vector for each node with the location and recoded seismic
signal of the corresponding station. All nodes (corresponding to the seismic
stations) are linked together and the linking weights are learnt during
training to infer the relationships among the stations. We construct the GNN
layers with TransformGConvs (Shi et al., 2020), which are designed based on an
attention mechanism (Vaswani et al., 2017) to learn the dynamically linking
weights among different stations. (details about TransformGConvs are provided
in the Methods section). In addition, the graph nodes are not fixed so that
the GNN could be adapted to variations in the station number and location.

Raw three-component seismic signals are input into the graph nodes. The front-
end waveform feature extraction module, constructed as an encoder-decoder CNN
and shared among the nodes, extracts their corresponding key features. The
station feature extraction block, constructed as two MLPs and shared among the
nodes, extract geographic features from the normalized input longitudes,
latitudes, and elevations of the stations. The earthquake location module then
concatenates the extracted waveform and geographic features and employs
multiple TransformGConvs to aggregate these features from multiple nodes to
predict the event depth and station-event offset. The predicted offsets and
depth are further used to determine the event location by a triangulation
algorithm (Yu and Segall, 1996). In the earthquake location module, we do not
directly predict the event location but the station-event offsets and depth
instead, because we will use them as input into a followed multi-station
association module to estimate the time shifts needed to align the P and S
arrivals.

This multi-station association module plays a key role in bridging the tasks
of earthquake location and multi-station phase picking and introduces physical
constraints between the two tasks. Prior to aggregating the waveform features
from different stations for multi-station phase picking, the features
corresponding to the same earthquake are required to be initially aligned or
associated; otherwise, aggregation of unaligned features could mutually
interfere and ultimately degrade the picking results. The multi-station phase-
picking module includes a non-trainable physical layer, implemented with the
Pytorch (Paszke et al., 2019) roll function, to shift and align the waveform
features (from the decoder of the waveform feature extraction module) using
the time shifts. Subsequently, multiple TransformGConvs in the phase-picking
module aggregate the aligned waveform features to enhance the phase-picking
features in the aligned space. Eventually, another physical layer unshifts the
aggregated features back to the original space, followed by two convolutional
layers to obtain the P/S-wave picks at all the stations.

Three regression loss functions are defined for the three modules of phase
picking, association, and earthquake location and then combined to jointly
train the entire network. Because all the modules are interconnected within
the entire network, the training process finds an optimal network that could
perform all the tasks both accurately and consistently. Moreover, after
training, the multi-station association module could be detached from the
network and utilized to calculate the S-P differential travel time with inputs
of offsets and event depth. Further details on this module are provided in the
section titled “Multi-station association module”.

### Data preparation

We tested the proposed PLAN in two regions of Ridgecrest and Japan. For the
Ridgecrest region (Fig. 2A), seismic recordings from 16 California Integrated
Seismic Network stations within an epicentral distance of < 80 km were
collected from July 4, 2019, to October 4, 2019, for a total of more than
71,000 M > 0 earthquakes. The data for Japan (Fig. 3A) included M > 2
earthquakes that occurred between January 1, 2011, and December 31, 2011,
including the Mw 9.1 Tohoku sequence. We collected the 3-component High
Sensitivity Seismograph Network (NIED Hi-net) (Obara et al., 2005; Aoi et al.,
2020) data from over 35,000 events. Subsequently, the data were randomly
divided into training, validation, and test sets (85%, 5%, and 10%,
respectively) in both regions.

The number of stations corresponding to each event in the training samples
varied, and the trained network can flexibly handle situations where the
number of stations changes in actual data. Further, the distributions of the
number of stations per event in the training and test sets were balanced. The
results for the test sets in the two regions are presented in Figs. 5 and 6,
respectively. To accommodate different range scales in the two study regions,
we used different window lengths in two regions (30.72 s for Ridgecrest and
61.44 s for Japan) with the same sampling frequency (100 Hz).

To ensure a fair comparison with the existing phase-picking methods, we
followed the same data preprocessing procedures used in previous studies (Zhu
and Beroza, 2018; Mousavi et al., 2020). This involved normalizing the data by
removing the mean and dividing by the standard deviation, and using a
Gaussian-shaped target function as training labels for the P/S-phase arrival
times. The use of Gaussian-shaped targets is effective in phase picking (Zhu
and Beroza, 2018; Mousavi et al., 2020), and in our study, the probabilities
of P wave and S wave arrival times were set to 1 at the first arrival time and
decreased to 0 within a 20 sample window before and after each phase arrival.

### Application to the 2019 Ridgecrest sequence

We compared the performance of PLAN with that of other established deep
learning methods for earthquake phase picking (PhaseNet (Zhu and Beroza, 2018)
and EQTransformer (Mousavi et al., 2020)) and location (Aggreated-GNN (van den
Ende and Ampuero, 2020)). All of the methods were retrained on the same
training set and evaluated on a common test set. As shown in the Ridgecrest
application in Fig. 2B-2C, the performance of PLAN in phase picking was
superior to that of the other two deep learning-based methods. Specifically,
the residual distribution of the P-wave picks for PLAN was more concentrated
than that of the other methods, indicating a higher overall accuracy. For
S-wave picks, PLAN performed significantly better than EQTransformer because
the distribution of PLAN was narrower whereas the difference in performance
between PLAN and PhaseNet was relatively minor.

Figure 2:  Distributions of phase picking and location residuals in Ridgecrest
region. (A) Distribution of 16 stations (black triangles) and training event
locations (red circles) used in our study, where the events occurred between
July 4, 2019 and October 4, 2019. (B and C) The results of P-wave and S-wave
arrival time residual, respectively. The blue, green, and orange lines in (B
and C) represent the arrival time residuals for PLAN, PhaseNet, and
EQTransform, respectively. The proposed method yields the most accurate
results in P/S-wave picking. (D and E) The offset and depth residuals between
model predictions and Southern California Seismic Network (SCSN) catalog of
the located events. Regardless of the offset or depth, the residual
distribution of PLAN (blue line) is more concentrated at zero than that of
Aggregated-GNN (orange line).

In terms of localization, our method (PLAN) outperformed the other approaches
(Fig. 2D-2E; Table 1). The distribution of PLAN was notably more concentrated
than that of Aggregated-GNN, particularly in terms of offset prediction. To
further demonstrate the effectiveness of TransformGConv, we replaced the
TransformGConv layers (Fig. S1) with GCN (Kipf and Welling, 2016), SAGE
(Hamilton et al., 2017), and GATv2 (Brody et al., 2021) respectively. Among
the various methods compared, our method yielded the best results in terms of
offset, with an average error of 1.09 km and a standard deviation of 1.41 km.
Furthermore, PLAN also outperformed Aggregated-GNN in terms of depth
localization, regardless of whether it was based on GCN, GATv2, or
TransformGConv. These results demonstrated the superiority of the proposed
PLAN in location estimations.

Furthermore, we used three metrics of mPrecision, mRecall, and mF1 (described
in the Methods section), to quantitatively evaluate the performance of the
five methods (Table 2). In five of the six metric scores for the P-wave and
S-wave picking results, our attention mechanism-based GNN method outperformed
the other methods. The only exception was the mPrecision metric of P-wave
picking, where the EQTransformer showed slightly higher scores than PLAN.
Notably, even the simplified version of the multi-station phase-picking
method, such as the SAGE-based PLAN, outperformed both the single station-
based picking methods of EQTransformer and PhaseNet in mF1 scores for S-wave
picking. This indicated that the phase-picking accuracy is significantly
improved by multi-station picking, which effectively utilizes inter-station
contextual information. We not only adjusted the time threshold while
maintaining a constant picking probability for evaluation but also fixed the
time threshold and changed the probability of picking to calculate and plot
the precision-recall curves for four models (Fig. S2). Consistent with the
aforementioned results, the PLAN model, based on TransformGConv, demonstrated
superior performance in terms of F1, encompassing both P-wave and S-wave.

Table 1: Location Performance in Ridgecrest and Japan regions.

|  |  | Offset MAE (km) | Depth MAE (km)
---|---|---|---|---
Region | Method | Mean | Std | Mean | Std
| Aggregated-GNN | 2.30 | 2.30 | 1.98 | 1.55
|  | GCN | 8.96 | 6.94 | 1.43 | 1.34
|  | GATv2 | 8.95 | 6.90 | 1.42 | 1.33
|  | SAGE | 1.28 | 2.09 | 1.68 | 1.42
Ridgecrest | PLAN | Trans | 1.09 | 1.41 | 1.43 | 1.33
| Aggregated-GNN | 27.92 | 26.78 | 10.30 | 8.95
|  | GCN | 21.30 | 16.47 | 13.50 | 9.95
|  | GATv2 | 10.79 | 10.82 | 5.59 | 6.86
|  | SAGE | 4.87 | 6.11 | 12.85 | 9.41
Hinet | PLAN | Trans | 4.81 | 5.83 | 10.62 | 8.89

00footnotetext: Note: Red and bold values represent the best performance.

Table 2:  Detection Performance in Ridgecrest region.

| P Picking Metrics | S Picking Metrics
---|---|---
Method | mPrecision | mRecall | mF1 | mPrecision | mRecall | mF1
PhaseNet | 94.83 | 92.78 | 93.79 | 84.50 | 80.65 | 82.53
EQtransformer | 95.43 | 91.17 | 93.25 | 86.77 | 78.21 | 82.27
PLAN-GATv2 | 95.05 | 93.02 | 94.03 | 85.55 | 80.49 | 82.95
PLAN-SAGE | 94.99 | 93.07 | 94.02 | 85.65 | 81.48 | 83.51
PLAN-Trans | 94.65 | 94.90 | 94.77 | 86.88 | 84.94 | 85.90

00footnotetext:  Note: The picking probability is 0.3. Red and bold values
represent the best performance.

### Application to seismicity in Japan

We retrained all the methods on the Japan training set for the evaluation.
Compared to its performance in the Ridgecrest region, PLAN exhibited an even
better performance in Japan (Fig. 3B-3C). Further, PLAN demonstrated a
remarkably better performance than PhaseNet and EQTransformer for both P- and
S-wave picks. The offset predicted by PLAN was notably more accurate than that
predicted by Aggregated-GNN, with higher and narrower residuals (Fig. 3D-3E).
In terms of depth estimation, although PLAN maintained a narrower residual
distribution, the highest point of the distribution was shifted
systematically, compared with the Aggregated-GNN method. Table 1 presents the
comprehensive quantitative comparison of the results. Although the
TransformGConv-based PLAN method did not demonstrate particular superiority in
depth estimation, it excelled in offset estimation. Further, the GATv2-based
PLAN showed the lowest depth error, indicating potential improvement of
localization capabilities of the proposed PLAN.

Figure 3: Distributions of phase picking and location residuals in Japan. (A)
Distribution of stations (black triangles) and training event locations (red
circles) used in our study, where the events occurred between January 1, 2011
and December 31, 2011. (B and C) Similar to Fig. 2, (B and C) show the results
of P-wave and S-wave arrival time residuals, respectively. (D and C) The
offset and depth residuals between model predictions and the Japan
Meteorological Agency (JMA) catalog of located events, respectively.  Table 3:
Detection Performance in Japan.

| P Picking Metrics | S Picking Metrics
---|---|---
Method | mPrecision | mRecall | mF1 | mPrecision | mRecall | mF1
PhaseNet | 94.87 | 94.97 | 94.92 | 88.26 | 84.38 | 86.28
EQtransformer | 95.91 | 94.79 | 95.35 | 89.08 | 84.40 | 86.68
PLAN-GATv2 | 95.14 | 93.81 | 94.47 | 88.35 | 81.87 | 84.98
PLAN-SAGE | 95.65 | 94.90 | 95.27 | 88.45 | 84.19 | 86.27
PLAN-Trans | 95.79 | 95.14 | 95.46 | 88.41 | 85.09 | 86.72

00footnotetext:  Note: The picking probability is 0.3. Red and bold values
represent the best performance.

Similar to the Ridgecrest example, we assessed the phase-picking performance
of various models applied to the test data from Japan using mPrecision,
mRecall, and mF1 metrics (Table 3) and precision-recall curves (Fig. S3). The
TransformGConv-based PLAN model achieved superior results in terms of mRecall
(95.14 for P-waves and 85.09 for S-waves) and mF1 (95.46 for P-waves and 86.72
for S-waves), whereas EQTransformer performed best in terms of mPrecision of
P-waves and S-waves. TransformGConv-based PLAN demonstrated high mRecall
scores, indicating that a large proportion of the samples containing P/S-waves
were correctly detected. However, this was achieved at the expense of a
slightly lower mPrecision compared to that of the EQTransformer, with some
non-P/S-waves incorrectly classified as P/S-waves. The mF1 score provided a
more comprehensive evaluation of the model performance, considering both the
reduction in missed detections and the increase in correct detections. In this
context, TransformGConv-based PLAN had the highest F1 score, indicating that
it effectively reduced the missed detections of P/S-waves and increased the
proportion of correct detections.

### Multi-station association module

To simultaneously pick P/S-waves from multiple stations, PLAN utilizes GNNs,
which typically aggregates raw signals received at different stations. Feature
aggregation across multiple stations introduces inter-station constraints and
enhances the features at each station. However, because of different travel
times of the same source across different stations, directly aggregating the
signals from multiple stations would deteriorate multi-station picking.

To address this issue, the proposed method employes a multi-station
association module to estimate the time shifts as illustrated in Fig. 1. The
input to this module is the offset of each station with respect to the event
and its depth. The module output is the corrected time shifts of the P/S-wave
for each station. To align the P/S-wave features, the correction criteria for
the P/S-wave features were set at the 10 and 15 s in the Ridgecrest region and
at the 20 and 32 s in Japan. Using these criteria, the multi-station
association module was trained to estimate the corrections of P/S-wave for
each station. These corrections are then used to align the waveform features,
enabling the graph convolution to aggregate the features in a temporally
aligned space. Consequently, the method could enhance or compensate for the
features at each station by fusing the aligned features from other stations,
allowing simultaneous and accurate multi-station picking.

The multi-station association module can be utilized independently after
training. It converts the distance and depth information into arrival
information and calculates the S-P differential travel time (Crotwell et al.,
1999). Figure 4 illustrates the arrival time differences of the P/S-waves at
various stations in Japan. Although the training process utilizes a maximum of
37 stations for a single event, the module can be adapted to cases with any
number of stations (e.g., hundreds of stations shown in Fig. 4A - Fig. 4D) to
estimate the P/S-wave arrival time differences for all stations. These results
indicated that the module effectively enforced physical constraints based on
time shifts within the overall network.

Figure 4:  Arrival time residuals of P/S-waves at various stations in the test
dataset of Japan. (A to D) Arrival time differences for each event calculated
by multi-station association module, respectively, while (E to H) show
manually picked arrival time differences for the same events. The numbers on
the top of the figures represent the identification numbers of the events in
the Japan Meteorological Agency (JMA) catalog. Above results indicate that the
S-P differential arrival time predicted by our multi-station association
module are consistent with the manually picking differences. They also
demonstrate that our module could calculate the arrival time difference for a
larger number of stations.

## Discussion

Figure 5:  Comparison of prediction results using different numbers of
stations in the Ridgecrest region. (A to D) The distributions of prediction
errors for P-wave, S-wave, offset, and depth, respectively. The x-axis
represents the number of stations, the primary y-axis denotes the number of
events recorded by a specific number of stations, and the secondary y-axis
represents the prediction errors for phase picking and event localization.
Note that for phase picking, prediction residuals of PLAN (blue curves)
decrease evidently as the number of stations increases. Moreover, the location
errors of PLAN are significantly smaller than those of the Aggregated-GNN
method.

PLAN is scalable for accommodating various numbers of stations per event. As
PLAN is a network level picking and location model, we further investigated
the effect of different numbers of stations on the network performance for
phase picking and earthquake location with a test set of the Ridgecrest region
(Fig. 5). We calculated the P- and S-wave picking residuals of the three
different methods relative to the manual picking results, respectively (Fig.
5A-5B). The residuals of the single-station-based picking methods, PhaseNet
and EQTransformer, exhibited oscillations for samples with station numbers
3-13 as the number of stations increased. Contrastingly, the residuals of our
simultaneous multi-station picking method, PLAN, exhibited a significant
residual decrease as the number of stations increased. Although the prediction
residuals of the single-station-based methods should not be significantly
associated with the number of stations, their prediction residuals still
decreased when the number of stations was 13-16. This was probably because the
events recorded by more stations tended to be larger and easier to pick.

A comparison of the distribution of prediction errors for earthquake offsets
and depths with respect to the number of stations indicated that the errors in
PLAN were significantly smaller than those in the Aggregated-GNN method (Fig.
5C-5D). However, the errors in offset prediction did not exhibit a significant
decrease with an increase in the number of stations. This was likely because a
large number of stations would include more distant ones that tended to have
large offset prediction errors. As the offset error metric is defined as the
average value acquired from multiple stations, an increase in the number of
stations can lead to a slightly higher average error for a single event.

Furthermore, the statistical results for Japan (Fig. 6) were similar to those
for the Ridgecrest region, with the PLAN method exhibiting smaller phase-
picking errors than EQTransformer and PhaseNet, especially for S-wave picking.
In addition, as the number of stations increased, the offset prediction error
of PLAN became significantly smaller than that of the Aggregated-GNN.

Figure 6:  Comparison of prediction results using different number of stations
in Japan. (A to D) The four distributions are similar to those described in
Fig. 5 and the only difference is that we have used logarithmic coordinates
for the secondary y-axis in (A) and (B).

The ability of our network to handle varying numbers of stations can be
attributed to the multi-station association module, which can be separated
from the entire network and utilized in a manner similar to the Taup algorithm
for estimating the arrival time of earthquakes at stations. Differing from the
Taup algorithm, our association module does not depend on an input velocity
model. Instead, it empowers the network to comprehend the concept of velocity,
enabling the conversion of offsets into relative time shifts. Additionally,
unlike the sequential processing of one station at a time in the Taup
algorithm, our module simultaneously calculates the time shifts for multiple
stations associated with a single event. In essence, our association module
can be considered a computationally efficient 3D Taup algorithm that operates
without requiring a velocity model. To evaluate the estimation accuracy of the
arrival time using this module, we applied the estimated time shifts to align
different stations (Fig. S4). Because the multi-station association module can
accurately estimate the arrival time, the original waveforms from all stations
were aligned accordingly.

Figure 7: Comparison of the P/S-wave arrival time estimation using different
methods. (A and B) The crossplots of the S-P differential arrival times
computed by the TauP model with the input of offsets and depths from manual
labels and network predications, respectively. The x-axis represents the
manually picked S-P differential arrival times. The y-axis represents the S-P
differential arrival times obtained by different methods. (C and D) The
crossplots of the S-P differential arrival times predicted by our multi-
station association module, and they are consistent with those predicted by
the TauP model. This indicates that the multi-station association module,
detached from the entire trained PLAN model, works physically reasonable
compared to the commonly used TauP model.

To further evaluate the estimation accuracy of the arrival time using this
module, we employed the TauP algorithm based on the PREM model (Dziewonski and
Anderson, 1981) for comparison (Fig. 7). We also calculated the correlation
coefficient (R) between the output of each method and the manually picked
P/S-wave time differences. During the training process, this module used the
offsets and depths obtained from the earthquake location module as inputs.
Therefore, inputting the predicted offsets and depths into this module (Fig.
7D) could yield better P/S-wave time differences than inputting the labeled
offsets and depths (Fig. 7C). The multi-station association module with
manually labeled offsets and depths yielded less consistent results than the
TauP algorithm. This discrepancy may not be solely attributable to errors in
the deep learning estimation. Label inaccuracies may have also contributed to
this outcome. This assertion was supported by the observation that using the
neural network output as the input for the TauP algorithm resulted in greater
correlation coefficients than when label was employed (Fig. 7A-7B). Among all
the evaluated methods, the estimation results in Fig. 7D show the highest
correlation coefficients. Generally, the multi-station association module and
the TauP algorithm based on the PREM model have the same level of accuracy in
calculating P/S-wave time differences.

In addition, the out-of-distribution data is utilized to assess the network’s
temporal generalization ability and application potential. We applied PLAN and
PhaseNet to pick the aftershock sequence of the 2022 M 7.4 Fukushima
earthquake in Japan (Fig. S5). Traditional deep learning-based phase picking
methods, such as PhaseNet, typically focus on picking seismic phases at a
single station and perform pick and association processes step-by-step. In
such a sequentially independent processing flow, the accuracy of phase picking
determines the precision of subsequent earthquake association and location.
Additionally, the consistency constraints among multiple stations for the same
seismic event in the subsequent association process cannot be fed back to the
previous step of phase picking to improve its accuracy. Without the
consistency constraints among multiple stations, the phase picking station-by-
station may be sensitive to noise and fail to pick reasonably pick multiple
P/S waves at stations with short epicental distances as shown in Fig. S5A-S5B.
In contrast, PLAN is a simultaneous multi-station and multi-task processing
approach that allows the aggregation of information from all stations and tend
to pick P/S waves that can be consistently associated to the same events
recorded by all the stations, leading to more reliable picking results.
Furthermore, during the network training process, the picking, association,
and location modules in the PLAN network mutually constrain and provide
feedback to each other. As a result, a coherent and adaptive organic system
can be achieved, simultaneously accomplishing these three tasks in a cohesive
and integrated manner.

Some limitations remain in our method, particularly in handling continuous
waveform data. This is mainly related to the construction of our training
dataset and the corresponding training strategy. In our training data,
although we allow for varying numbers of stations and missing phase picking
labels for some stations, we assume that each training sample contains only
one earthquake event. We overlook the scenario where the sample data does not
contain an earthquake event (only noise), and when the data contains multiple
events, we only provide labels for the main event. These considerations
simplify the process of constructing our training samples but limit the
diversity of the samples and the ability of the trained network model to
handle continuous waveform data. However, we believe that these limitations
can be addressed by using a more diverse and comprehensive training dataset.

In summary, we present a novel all-in-one multi-task multi-station system
called PLAN for earthquake monitoring, which is capable of simultaneous phase
picking, phase association, and earthquake location. Unlike current CNN-based
methods that perform phase picking station-by-station, phase association and
location separately, our proposed GNN-based multi-station multi-task system
best utilizes the inherent inter-task and inter-station constraints. The
multi-station association module estimates the phase shift and improves the
robustness and accuracy of the phase association process. Eventually, the
resulting offsets and depth enables accurate event localization. Our method
demonstrates the need to factor mutual constraints among tasks and stations
into next-generation earthquake monitoring systems.

## Methods

### Graph based neural network

Several studies have shown that GNNs have the potential to deal with
irregularly spaced stations for phase association and event localization
(McBrearty et al., 2019b; van den Ende and Ampuero, 2020; Yano et al., 2021;
McBrearty and Beroza, 2022b, 2023; Zhang et al., 2022; Bilal et al., 2022).
Here, we build a graph-based network (Fig. 1) for mult-station earthquake
monitoring. To utilize the GNN, we first need to change the data from the
matrix format to the graph format and employ a graph-based representation of
the stations, where each station is represented as a node in the graph and the
three-channel data and the station location are used as the features of each
node. In contrast to the current single-station processing methods (Ross et
al., 2018b, a; Zhu and Beroza, 2018; Mousavi et al., 2019; Zhu et al., 2019;
Pardo et al., 2019; Wang et al., 2019; Liu et al., 2020; Mousavi et al., 2020;
Zhu et al., 2022a), which treat each three-channel data as an individual input
sample, our approach inputs all the three-channel data received from multiple
stations per event as a single sample. This allows for efficient aggregation
of information from multiple stations during network training. As a result,
the features of different stations could be effectively integrated using GNNs
during the aggregation process.

In this study, we have evaluated various graph aggregation methods, including
GCN (Kipf and Welling, 2016), GraphSAGE (Hamilton et al., 2017), GAT
(Veličković et al., 2017), GATv2 (Brody et al., 2021), and TransformGCONV (Shi
et al., 2020). Through this evaluation, we have determined that
TransformGCONV, which is based on attention mechanism (Vaswani et al., 2017),
is the most suitable module for the proposed PLAN. The message aggregation of
TransformGCONV could be represented as:

$\mathbf{x}_{i}^{\prime}=\mathbf{W}_{1}\mathbf{x}_{i}+\sum_{j\in\mathcal{N}(i)}\alpha_{i,j}\mathbf{W}_{2}\mathbf{x}_{j},$
(1)

where $\mathbf{x}_{i}^{\prime}$ represents the aggregated features at the
source node, and $\mathbf{x}_{i}$ and $\mathbf{x}_{j}$ represent the features
of the source and distant nodes before aggregation, respectively.
$\mathbf{W}_{1}$ and $\mathbf{W}_{2}$ are the trainable matrices. In addition,
the attention coefficients $\alpha_{i,j}$ are computed via dot-product
attention as follows:

$\alpha_{i,j}={softmax}\left(\frac{\left(\mathbf{W}_{3}\mathbf{x}_{i}\right)^{\top}\left(\mathbf{W}_{4}\mathbf{x}_{j}\right)}{\sqrt{d}}\right),$
(2)

where $\mathbf{W}_{3}$ and $\mathbf{W}_{4}$ are the trainable matrices.
Similar to the attention mechanism(Vaswani et al., 2017), the source feature
$\mathbf{x}_{i}$ and distant feature $\mathbf{x}_{j}$ are transformed into
query vector and key vector, respectively, using $\mathbf{W}_{3}$ and
$\mathbf{W}_{4}$. Compared to other graph aggregation methods, the use of the
attention-based mechanism (equation 1) in TransformGCONV allows for a more
fine-grained representation of the relationship between different stations,
thereby improving the accuracy and efficiency of the proposed method.

### Network Architecture

Here, we design a multi-station multi-task network for simultaneous phase
picking, association, and location. The network (Fig. S1) comprises four
components: a waveform feature extraction module, an earthquake location
module, a multi-station association module, and a physics-informed multi-
station phase-picking module. Similar to previous deep-learning-based phase-
picking approaches (Zhu and Beroza, 2018; Mousavi et al., 2020; Zhu et al.,
2022a, c), we design an encoder to extract waveform features and a decoder to
produce phase-picking results. However, to address the multi-station phase-
picking problem, we introduce the GNN-based TransformGCONV for aggregating
features from multiple stations.

Because aligned waveform features are easily used and aggregated in GNNs for
multi-station phase picking, we do not employ it in the waveform feature
extraction module (Fig. S1A), where the features are relatively shifted in
time. Although we use a U-shape neural network for feature extraction to solve
the phase-picking problem, it could be replaced with other single-station-
based phase-picking networks, such as EQTransformer. No matter what type of
network architecture is used, the features extracted from the middle of the
network are input into the earthquake location module, and the structure of
the final few layers of the network are modified for the purpose of multi-
station phase picking. Additionally, the kernel size of all convolutional
layers in the waveform feature extraction network is set to 7.

For the earthquake location module (Fig. S1B), we first extract features from
the normalized coordinate information of the stations within the range of
[0,1] through two fully connected layers (3-48-96). Simultaneously, the
waveform features extracted from each station are further processed through
several convolutional layers and then flattened. Subsequently, the position
and waveform features are concatenated and passed through two fully connected
layers (192-192-96). This fuses the position and waveform features at each
station. The fused features are further aggregated among multiple stations by
several GNN layers to predict the offsets of each station with respect to the
event and its depth. Because there is only one depth parameter for each
sample, we add a global average pooling before the output. In summary, this
module allows the integration of both location and waveform information into
the feature extraction process, which is crucial for accurate event
localization.

Finally, in the physics-informed multi-station phase-picking module (Fig.
S1D), we incorporate physics-motivated constraints of time alignment among
waveforms corresponding to the same earthquake event. We first utilize a
mulit-station association module (Fig. S1C) to calculate the relative
alignment shifts between stations using the estimated offsets and the depth of
the event. We then use the shifts to align the waveforms to a common time
standard and aggregate the features across multiple stations in the phase-
picking module. Subsequently, the aggregated features at each station are
unaligned and fed to two layers of convolution to yield final P/S-wave picking
results. This process leverages the physical information of the event location
to improve the robustness and accuracy of the multi-station phase picking.

### Loss function and training details

Our multi-task learning network model has three output results corresponding
to phase picking, phase association, and earthquake localization. To train the
model, we define three different loss functions for these three different
tasks. For phase picking, instead of using the commonly used cross-entropy, we
choose the mean square error (MSE) as the loss function, which is suitable for
training in multi-task problems. To estimate offsets and depth, which is
similar to event localization, we also use MSE as the loss function, as
suggested by previous studies (van den Ende and Ampuero, 2020; Zhang et al.,
2022). Finally, to calculate the P/S-wave shift, we define the loss function
as follows:

$\mathcal{L}_{\Delta
p}=\sum_{i=1}^{n}\mid{CTime}_{p}-\left({label}_{p_{i}}+\Delta
t_{p_{i}}\right)\mid,$ (3) $\mathcal{L}_{\Delta
s}=\sum_{i=1}^{n}\mid{CTime}_{s}-\left({label}_{s_{i}}+\Delta
t_{s_{i}}\right)\mid,$ (4)

where ${CTime}_{p}$ and ${CTime}_{s}$ represents the reference times where the
P- and S-wave picks are aligned, respectively. Moreover, ${label}_{p_{i}}$ or
${label}_{s_{i}}$ represents the manually picked P/S-wave arrival time for
each station, and $\Delta t$ represents the predicted P/S-wave shift. Finally,
we combine the three types of loss functions to form the overall objective
function:

$L_{{total}}=\lambda_{1}\mathcal{L}_{{picking-p}}+\lambda_{1}\mathcal{L}_{{picking-s}}+\lambda_{2}\mathcal{L}_{\Delta
p}+\lambda_{2}\mathcal{L}_{\Delta
s}+\lambda_{3}\mathcal{L}_{{offset}}+\lambda_{3}\mathcal{L}_{{depth}}.$ (5)

Here, we set the coefficients $\lambda_{1}$, $\lambda_{2}$, and $\lambda_{3}$
to 1.

During the training process, the model was optimized using the ADAM (Kingma
and Ba, 2014) method with an initial learning rate of 0.001, which is
gradually decreased with a decay rate of 0.9 every 100 epochs. To enhance the
training efficiency, we randomly selected 2048 events from the training set
for each epoch, rather than using the entire data. The model was trained for a
total of 2000 epochs with a batch size of 16, and the training process
required approximately 24 h using 1 NVIDIA Tesla A100 GPU.

### Evaluation metrics

In previous studies (Mousavi et al., 2020; Zhu et al., 2022c), true positive
phase picks were defined as those within 0.5 s of the predicted pick. The rest
were counted as false positives. Nevertheless, owing to potential errors in
the labels of the dataset, such statistical results based on a single
threshold may not be reliable. Thus, to better evaluate the performance of
algorithms, we introduce new metrics, mPrecision, mRecall, and mF1, which are
calculated using multiple thresholds, following previous research(Zheng et
al., 2022). The metrics are defined as:

$\mathrm{mPrecision}=(\mathrm{Precision}@11+\mathrm{Precision}@12+\cdots+\mathrm{Precision}1@50)/40,$
(6)
$\mathrm{mRecall}=(\mathrm{Recall}@11+\mathrm{Recall}@12+\cdots+\mathrm{Recall}1@50)/40,$
(7) $\mathrm{mF}1=(\mathrm{F}1@11+\mathrm{F}1@12+\cdots+\mathrm{F}1@50)/40.$
(8)

where x@11, x@12, $\cdots$ , x@50 are Precision, Recall, or F1 metrics when
the thresholds are 11, 12, $\cdots$, 50 samples (corresponding to 0.11 s, 0.12
s, $\cdots$, 0.5 s of time), respectively. These metrics, mPrecision, mRecall,
and mF1 reward detectors with better picking results and, therefore, can more
reasonably or fairly assess the performance of the different methods.

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## Supplementary Information

Figure S1: Network architecture of PLAN. a waveform feature extraction encoder
and decoder extract features from raw seismic waveforms using a simplified 1D
U-net. These features, along with information about the locations of the
stations, are input into the earthquake location module b, which is a two-
branch module. It extracts and combines waveform and location information for
each station and calculates the offsets of the stations relative to the event
and the depth of the event. c multi-station association module then uses the
offsets and depth information to estimate the relative time shifts between
different stations which are further used to temporally align the waveform
features from different stations. d finally, the phase-picking module
aggregates features (among multiple stations) in the aligned space and then
predicts P/S-wave phase arrivals in the original space. Furthermore, in 1DConv
blocks, the preceding number indicates the size of the convolutional kernel,
while the subsequent numbers respectively denote the input and output
channels. Regarding the TransformerGConv Blocks, the following numbers
correspondingly represent the input and output features.  Figure S2:
Comparison of the precision-recall curves of picking results in the Ridgecrest
region. True positive phase picks were defined as those within 0.5 s of the
predicted pick. The numbers in legend represent the maximum F1 scores of each
model.  Figure S3: Comparison of the precision-recall curves of picking
results in Japan. True positive phase picks were defined as those within 0.5 s
of the predicted pick. The numbers in legend represent the maximum F1 scores
of each model.  Figure S4: Example of raw waveforms (first line) and aligning
raw waveforms of P waves (second line) and S waves (third line) using the time
shifts predicted by the multi-station association module. The numbers on the
top of the figures represent the identification number of the events in the
Japan Meteorological Agency (JMA) catalog. The alignment results indicate that
the multi-station association module can accurately estimate the time shifts
and further utilize it to align the waveform features at the same time
temporal position.  Figure S5: Comparison of waveform picking results for the
aftershock sequence of the 2022 M 7.4 Fukushima earthquake in the Japan using
PLAN and PhaseNet. The red, blue, and green markers represent the manual
labels, PLAN results, and PhaseNet results. The lines in b, c, e and f are
obtained by linear fitting based on the picking results. PhaseNet picks may
become mixed in near-offset stations, making it challenging to obtain a
reliable result without phase association. In contrast, due to its nature as a
multi-task method that simultaneously performs phase picking and phase
association, PLAN exhibits stronger consistency in picking results across
stations.


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