$\mathbf{\mathbb{E}^{FWI}}$: Multiparameter Benchmark Datasets for Elastic Full Waveform Inversion of Geophysical Properties
Authors: Shihang Feng
Hanchen Wang
Chengyuan Deng
Yinan Feng
Yanhua Liu
Min Zhu
Peng Jin
Yinpeng Chen
Youzuo Lin
Venue: NeurIPS 2023 Datasets and Benchmarks Poster (2023)
Keywords: elastic; full waveform inversion; seismic; open dataset; data-driven
TL;DR: We present a large-scale open-access multi parameter benchmark dataset for elastic seismic full-waveform inversion

Abstract: Elastic geophysical properties (such as P- and S-wave velocities) are of great importance to various subsurface applications like CO$_2$ sequestration and energy exploration (e.g., hydrogen and geothermal). Elastic full waveform inversion (FWI) is widely applied for characterizing reservoir properties. In this paper, we introduce $\mathbf{\mathbb{E}^{FWI}}$, a comprehensive benchmark dataset that is specifically designed for elastic FWI. $\mathbf{\mathbb{E}^{FWI}}$ encompasses 8 distinct datasets that cover diverse subsurface geologic structures (flat, curve, faults, etc). The benchmark results produced by three different deep learning methods are provided. In contrast to our previously presented dataset (pressure recordings) for acoustic FWI (referred to as OpenFWI), the seismic dataset in $\mathbf{\mathbb{E}^{FWI}}$ has both vertical and horizontal components. Moreover, the velocity maps in $\mathbf{\mathbb{E}^{FWI}}$ incorporate both P- and S-wave velocities. While the multicomponent data and the added S-wave velocity make the data more realistic, more challenges are introduced regarding the convergence and computational cost of the inversion. We conduct comprehensive numerical experiments to explore the relationship between P-wave and S-wave velocities in seismic data. The relation between  P- and S-wave velocities provides crucial insights into the subsurface properties such as lithology, porosity, fluid content, etc.  We anticipate that $\mathbf{\mathbb{E}^{FWI}}$ will facilitate future research on multiparameter inversions and stimulate endeavors in several critical research topics of carbon-zero and new energy exploration. All datasets, codes and relevant information can be accessed through our website at https://efwi-lanl.github.io/

E FW Multiparameter Benchmark Datasets for
Elastic Full Waveform Inversion of Geophysical Properties
Shihang Feng 1M
Hanchen Wang!
Chengyuan Deng 1.2
Yinan Feng'
Yanhua Liu
Min Zhu
Peng Jin 1,5
Yinpeng Chen
Youzuo Lin
Los Alamos National Laboratory 'Rutgers University CColoado School of Mines University of Pennsylvania TThe Pennsylvania State University Microsoot University of North Carolina Chapel Hill shihang fengelive.cc.
(hanchen, wang, charles deng, ynf, yanhualiu, minzhu, pjin, ylin)@lanl.go gov yi piche@microsoft com, yzlin@unc.edu
Abstract
Elastic geophysical properties (such as P- and S-wave velocities) are of great importance to various subsurface applications like CO2 sequestration and energy exploration (e.g.. hydrogen and geothermal). Elastic full waveform inversion (FWI) is widely applied for characterizing reservoir properties. In this paper, we introduce EFWI, comprehensive benchmark dataset that is specifically designed for elastic FWI. EFWI encompasses distinct datasets that cover diverse subsurface geologic structures (flat, curve, faults, etc). The benchmark results produced by three differ- ent deep learning methods are provided. contrast to our previously presented dataset (pressure recordings) for acoustic FWI (referred to OPENFWI), the seismic dataset E FWI has both vertical and horizontal components. Morcover, the velocity maps in FWI incorporate both P- and S-wave velocities. While the multicomponent data and the added S-wave velocity make the data more realistic, challenges introduced regarding the convergence and computational cost the inversion. We conduct comprehensive numerical experiments to explore the relationship between P-wave and S-wave velocities in seismic data. The relation between P- and S-wave velocities provides crucial insights into the subsurface properties such lithology, porosity, fluid content, etc. We anticipate that FW will facilitate future research on multiparameter inversions and stimulate endeavors in several critical research topics of carbon-zero zero and new energy exploration. All datasets, codes" and relevant information can be accessed through our website at httpss///fwii lanl, rithub..10
Introduction
Seismic imaging is similar to how submarines use sonar to map out underwater landscapes and locate objects. Just as sonar sends out sound waves and interprets the echoes to figure out distances and
"Equal contribution
Codess will be released upon approval by Los Alamos National Laboratory and U.S. Department of Energy.
37th Conference on Neural Information Processing Systems (NeurIPS 2023) Track on Datasets and Benchmarks.

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EPVRupp
BPVB.y
EPFBB.P
E.PB.p
EPFB.y
Depth
vp
gCVR.ys
gerB.yp
gorD.ys
Depth
Length
Length
Longth
Length
Length
Length
1500
4500
612
3000
Vp (m/s)
Va (m/s)
Figure 1: Gallery of FFW,, one example of reservoir structure (Pr) and velocity maps (Vp, Vs) from the EVV REFB pBvB ECFB datasets. Pr refers the designed reservoir, which is the Poisson's 's ratio anomaly calculated explicitly by Vp and Vs, kinds of traveling speed each spatial point.
shapes underwater objects. geoscientists send seismic waves deep into the Earth. By analyzing how these waves are reflected back, they can generate detailed images of the subsurface and deduce properties rock formations.
Seismic waves, propagating through the subsurface medium, can unveil the physical properties the rock formations. Full waveform inversion (FWI) has emerged as effective technique for obtaining high-resolution models of the subsurface physical properties 2 3 In essence, it's like refining underwater sonar map capture more details and nuances. The determination of such properties from seismic data is posed an inverse problem. This means use the reflected waves (akin to sonar echoes) to infer the properties of the rocks they passed through. FWI refines this process. striving to find the most accurate representation by minimizing the difference between observed and synthetic seismic data [4] This technique has made substantial contributions across a range of domains, including geothermal energy exploration, earthquake monitoring, subsurface imaging for engineering applications, and many others [S
Acoustic approximations have been widely employed in wavefield simulation for FWI, resulting in substantial reduction in computational cost 66 77. It assumes that the subsurface medium behaves as a fluid and focuses on simulating the kinematic aspects of compressional (P) wave propagation within the medium. However, acoustic wave propagation is oversimplified representation of real-world scenarios, as it solely considers P-wave propagation and does not udequately model the dynamics of the wavefield [8] 9] Consequently, this oversimplification leads suboptimal accuracy of the
reconstructed medium parameters [10
13
FFI
FWI
OpenFWI Acoustic Data
Elastic Data
Elastic Data
X component
0
Z component
T (S)
((s)
(6)
0.5
0.5
0.35 X (km)
0.7
0.35
0.7
0.35
0.7
X (km)
X (km)
Figure 2: Comparison of clastic data in E FW and acoustic data in OPENFWI. Acoustic data only contain P-waves propagation while elastic data contain both P- and S-waves.
Why elastic FWI: Flastic inversion, which considers both P- and shear (S-) waves, provides more comprchensive and precise representation of the subsurface. The correlation between the P-

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(Vp) and S-wave velocities (Vs) holds significant implications in the determination of Poisson's s ratio (i.e.. Vp-Vs ratio) and Young's modulus. These parameters play a vital role in the reservoir characterization and serve as essential indicators in the identification and assessment of hydrogen and geothermal reservoirs
15 16 17 18].
The following aspects highlight their significance:
Lithllogy discrimination: Combination Vp and Vs velocities is useful for the lithology estimation, while Vp alone introduces significant ambiguity because of the overlap of P for different types of rocks [19].
Fracture characterization: Using the Poisson's 'ss ratio (Vp-Vs ratio) and S-wave splitting estimate fracture orientation and facilitate hydraulic fracturing stimulation [20].
Estimation of fluid content and saturation: Poisson's 's ratio (Vp-Vs ratio) allows us to estimate the compressibility and estimate the fluid property qualitatively with other relevant reservoir parameters such as the pressure and temperature (2T).
Elastic FWI, prominent culliparametee-inversiooo technique, allows to simultancously estimate P- and S-wave velocities [22]. However, the simultancous consideration of multiple parameters and the expanded dimensions of seismic data significantly increases the complexity of the objec- tive function. This escalation results from the enhanced nonlinearity and the induced trade-offs between the velocities. The coupled impact of P- and S-wave velocities seismic response further complicates the iterative update process for each parameter. Additionally, the nonlinearity becomes even more pronounced when multiple parameter classes are incorporated into the inversion, this substantially expands the model space by introducing an increased degree of freedom [23]. Thus, the multidimensionality of elastic FWI renders the problem considerably more complex and challenging compared to the acoustic single-parameter counterpart. With the recent development of machine learning, researchers have been actively exploring data-driven solutions for multiparameter FWI, including multilayer perceptron (MLP) (24), encoder-decoder-be -based convolutional neural networks (CNNs) 25 26]. recurrent network (27 28), generative adversarial networks (GANs) [2)] etc. Nonetheless, the absence of publicly available elastic dataset poses challenges in facilitating fair comparison of these methods.
To illustrate the essence of these parameters and the efficacy of elastic FWI, we spotlight the Gallery of EFWI in Figure 1 This visualization showcases four sets of samples, each hailing from one of the datasets EFVE EFFB ECVB ECFB Each set encompasses three distinct subplots:
P-wave Velocity Map (Vp): Demonstrating the speed at which Primary P-waves traverse, these velocities provide insights into the composition and layering of the subsurface, such the presence of fluids or gas.
S-wave Velocity Map (Vs):: Reflecting the pace of Secondary or S-waves, these velocities are sensitive to the rigidity and shear strength of the geological formations, offering more detailed perspective on rock and sediment characteristics.
Poisson's 's Ratio Map (Pr):: Derived from the Vp and Vs maps, this visualization quantifies the subsurface's 's ability to deform under compressive stress. A higher Poisson's 's ratio typically indicates a more ductile material, while lower value suggests a more britte nature. making this measure crucial for understanding the geomechanical behavior of subsurface formations.
EFWI; is constructed upon our previously published open-access acoustic seismic dataset, known as OPENEWI 30). Our approach incorporates the advantageous characteristics of mulli-scale, multi- domain, and multi-subsuuffuce-comm EFWI entails the creation of S-wave velocity maps and employs the clastic wave equation in the forward modcling phase (Figure 2). The computational demands associated with conducting clastic forward modeling are substantial. Consequently, the availability of this dataset would significantly alleviate the burden on researchers.
inherited from the OPENEWI framework. Furthermore,
FWI facilitates equitable comparisons across various methodologies using multiple datasets. In this study, we evaluate the effectiveness of three prominent methodologies derived from pre-existing networks, namely InversionNet (31, VelocityGAN [32] and SimFWI [5] The objective of this evaluation is to establish benchmark for future investigations. For comprehensive replication attempts, including the GitHub repository, pre-trained models, and associated licenses, we direct readers to the resources referenced in Section of supplementary materials.
3

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The rest of this paper is organized as follows: Section 2 offers a comprehensive overview of the fundamental principles governing elastic FWI. Seection presents a detailed description of the methodology employed in the construction of the dataset. [Section 4 offfers succinct introduction to three deep learning methods employed for henchmarking purposes, alongside the presentation of inversion performance each dataset. The investigation of the interdependence between P- and S-waves is conducted through ablation experiments, as outlined in Section [Section 6 outlines the challenges faced and discusses the future implications of the dataset. Lastly, /Section 7 7fffers conclusive remarks summarizing the key findings and contributions.
/attase._Sectton
Elastic Forward Modeling (Mgz F.tVp. Yg)
Velocity Maps
Seismic Data
V,
V/
8"u 2 Vio(V3 - (V w)] (vvltuu
Data-driver Elastic FWI (Vr, fa" Mg)
Networks
Figure 3: Schematic depiction of the data-driven approach for elastic forward modeling and FWI The forward modeling process involves utilizing elastic forward modeling compute seismic data by employing governing elastic wave equations, while elastic FWI employs neural networks to infer the and S-wave velocity maps from seismic data containing vertical and horizontal components.
Elastic Forward Modeling and Data-driven FWI
Figure 3
provides concise illustration of 2D data-driver elastic FWI and the relationship between P-, S-wave velocity maps and the input horizontal and vertical components of particle displacement therein. In general, the objective of data-driven elastic FWI is employ neural networks to determine the subsurface velocity maps of the P- (Vp) and S-waves (Vs). The velocities depict the propagation speed of P- and S-waves through the subsurface medium and depend the spatial coordinates (rr, 2).
We also consider the density of the subsurface as The source term, represented by s, depends on spatial coordinates and time 2,,,, This source term excites both the and S-wave components. The particle displacement in horizontal and vertical directions is denoted by the vector u (Mg ug The governing equation for the elastic wave forward modeling in an isotropic medium is given 34
I u
VVV - 2V3) u) V (VV (Vu))) ss
0t
In the above equation:
V represents the gradient calculation of scalar field in space, specifically;
Of 0f
Ox 0z
V. denotes the divergence of vector field in space, which expressed as:
Do, + Oz
Or:
V v
dr
For simplicity. we assume constant density P with the value of 3.3 The forward modeling problem can expressed as (Wz, uz) = (V,, Vss,, where fa(.) signifies the highly nonlinear elastic forward modeling. It details how the P- and S-waves, initiated by the source 8, navigate through the subsurface characterized by Vp and Vs over time l. Receivers then record these waves components Uy and u.. The ultimate goal of data-driven elastic FWI is to harness neural networks

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Table I: Dataset summary of EFWT Velocity maps are represented dimensions depth x width x length,
while scismic data is presented as #sources x time x #receivers in width x #receivers in length.
Group
Dataset
Size
#Train/#Test
Seismic Data Size
Velocity Map Size
RVeel
EFVA/B B
123GB
24K / YKK
x 1000 x 70
70 x x 70
Family
ECVA/B
123GB
24K / 6K
5 x 1000 X 1 70
70 x 1 x 70
Eaullt
BPFA/B
222GB
48K / 66K
5xx 1000 x 70
70 x x 70
Family
E BCFA/B
222GB
48K / 6K
5x 1000 x 1 70
70 x 1 x 70
to learn the inverse mapping (Vp, Vs)) = fu (ug,uu)))) U2). This inverse process enables to deduce the subsurface velocity maps (Vp and Vs) from the recorded particle displacements (ug and uz) acquired from the receivers. By training neural networks with datasets of recorded waveforms and matching velocity maps, we can fine-tune the network parameters for a precise estimation of the subsurface velocities.
3
FWI Dataset
This section describes the methodology used to extend the velocity maps from the OPENFWI dataset elastic FWI and generate our new dataset EFWI, Our intention is provide accessible, open- source benchmark dataset that can comprehensively facilitate the development and evaluation of the machine learning algorithms elastic FWI.
The basic information and physical meaning of all the datasets EFWI is summarized in Table 1 and Table 2 The velocity maps encompass P- Vp and S-wave velocities Vs. whereas the seismic particle displacement, Uy and ūz. The geophysical attributes in Vel Family" and the "aFltt Family" have been constructed utilizing the Vp maps derived from two distinct groups, namely the "Vel Family" and the "Faulr Family" within the OPENFWI dataset. Similar OPENFWI, the dataset has been categorized into distinet versions, namely easy (A) and hard (B), based on the relative complexity of the subsurface structures. thorough examination of the methodologies employed in the construction of the Vp maps and the detailed analysis of the complexity inherent in the velocity maps can be found in [3]]
data comprise the horizontal and vertical components
The P-wave velocity (Vp) maps in EFWI are identical to those in the previously published OPENFWI dataset. For example, Vp in EFVA is corresponding to "FlatVel-A" in OPENFWI, Vp in ECFB is corresponding "CurveFault-BB B" in OPENFWI, and the same naming rule applies to the rest datasets. These velocity maps incorporate a wide range of geological scenarios reflecting diverse subsurface complexities, thereby providing extensive testbed for machine learning methodologies.
In order to construct the S-wave velocity (Vs) maps, we incorporate the Poisson's 's ratio (Pr) maps 35 which provide a representation of the relationship between the P- (Vp) and the S-wave velocities (Vs)
V3 2V 2V3 2V3
Pr
The initial step involves the generation of Poisson's ratio (Pr) maps by selecting two values within the reasonable range of 0.1 to 0.4 in a random manner [36]. One of these values is allocated to represent the background, whereas the other value is assigned represent thin-layer reservoir. Thin-layer reservoirs are selected due to their significance in representing areas where pores are saturated with fluids, making them crucial targets for subsurface exploration and reservoir detection. In the FWT framework, the S-wave velocity (Vs) maps are synthesized by multiplying the models of P-wave velocity (Vp) with the respective Poisson's 's ratio (Pr) maps, adhering the following relationship:
0.5 Pr Vs3 = V
I-Pr Pr Vp.
This approach ensures a wide range of velocity contrasts, resulting in diverse wavefield behaviors, thus expanding the scope of scenarios for machine learning tests elastic FWI. The details of the clastic forward modeling are given in Section of the supplementary materials.
5

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Table 2: Physical meaning of EFWT dataset
Grid
Velocity
Source
Source Line
Receiver Line
Receiver Line
Time
Resorded
Dataset
Spacing
Spatial Size
Spacing
Length
Spacing
Length
Spacing
Time
EVel FFull Family
5
0.35 x 0,35 kom?
87.5
0.35 km
0.35 Avm
0,001 1
4
E FWI Benchmarks
4.1
Deep Learning Methods for Elastic FWI
Our benchmark presents inversion results by three deep learning-base -baiin approaches, namely ElastieNet, ElasticGAN, and Elastic' rrasfoerr.nss.rmmer. These methods are derived from pre-existing networks, namely InversionNet (3I), VelocityGAN [32], and SimFWI [33], with modifications tailored to address the challenges posed by clastic FWI. We provide a summary of each method separately as follows:
ElasticNet is extended from the vanilla InversionNet
the elastic setting with pairs of input and output. It is colly-convolutional neural network taking seismic data and as the input of two encoders learn the latent embeddings independently. The mutual representations of inputs are concatenated and then forwarded to two independent decoders to obtain the estimated velocity maps Vp and Vg as output.
ElasticGAN follows the design of VelocityGAN 32 but substitutes the original generator with an -ecoderrdecoder network such as ElasticNet. The estimated velocity maps Vp and Vs produced by the generator are fed to two independent discriminators to identify the real and fake predictions. A CNN architecture is employed for both discriminators.
PlasticTTransfrmne follows similar seismic-encoder and velocity-decoder architecture design the SimFWI deseribed in [3 It consists of two two-layer transformer encoders that take u, and U, as inputs and two two-layer transformer decoders to output Vp and Vs separately. Two latent embeddings of uh and ug concatenated and passed through two Maxout converters, then transformed embeddings fed into the decoders. Unlike the linear upsampler utilized at the end of the stack upsampling and convolution blocks construct the upsampler.
velocity decoder in 33
4.2 Inversion Benchmarks
Good Prediction
Bad Prediction
B,
Predicted
m/s
Predicted
mb
Predicted
Predicted V
mvs
Predicted
m/s
2400
2200
3900 I
M
W
0275
2000
2400
True P:
6.200
V/3
True P.
True 1/2
3200
3000
W
038
W
2200
W
7508
10200
M500
3000
014
2009
0350
1100
20ce1
328
Figure 4: Examples of both successful and inadequate predictions in T2. FW/ benchmarks performed by the ElasticNet.
The experiments were conducted using Nvidia Tesla V100 GPUs, and the training parameters were kept consistent across all datasets. The training process is conducted utilizing the -nom and fz-norm loss functions, respectively. In our study, we assess not only the accuracy of the predicted velocities Vp and Vg but also the degree of decoupling between them by evaluating the accuracy of the predicted Poisson ratio (Pr). To quantify the performance of our predictions, we utilize three evaluation metrics: mean absolute error (MAE), root mean square error (RMSE), and structural similarity index (SSIM). These metrics provide comprehensive assessment of the quality of our predictions and their similarity to the ground truth values. The performance of RelasticNet on various datasets is presented in Table 3 while Table provides the estimated training time per

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epoch for each method on the E datasets. In Figure 4, examples of inverted velocity maps obtained using the ElasticNet are presented alongside the corresponding ground truth velocity maps. These visual representations highlight instances where the inversion process successfully predicts accurate velocities, as well as instances where further improvement is required. The benchmarks with are given in Section 6 of the supplementary materials.
ElasticGAN and
The performance of all three models exhibits decline as the complexity of the dataset increases. Notably, in the case of the dataset with version B, it consistently exhibits lower performance compared to the dataset with version A. The network provides direct predictions for Vp and Vs. whereas Pr is obtained indirectly through calculations based on Vp and Vs. As a result, Pr consistently exhibits lower SSIM compared Vp and Vs. However, it should be noted that Pr represents sparser map compared to Vp and Vs, leading to lower MAE and RMSE values for Pr compared to Vp and Vs.
Table 3: Quantitative results of ElasticNet on E datasets.
ElasticNet
Dataset
Loss
Vp
Vs
Pr
MAET
RMSEL
SSIM
MAET
RMSEL
SSIM
MAE,
RMSE!
SSIM
EFVA
f1
0.0308
0.0559
0.9615
0.0259
0.0500
0.9596
0.0329
0.0664
0.8455
82
0.0235
0.0455
0.9702
0.0196
0.0385
0.9683
0.0307
0.0583
0.8644
BFVB
4
0.0668
0.1468
0.8891
0.0483
0.1053
0.8951
0.0542
0.1057
0.7138
8
0.1016
0.1901
0.8354
0.0691
0.1322
0.8599
0.0756
0.1302
0.6227
BOVA
&
0.0745
0.1345
0.8055
0.0600
0,1080
0.8051
0.0574
0.1
0.5766
82
0.0745
0.1343
0.8033
0.0616
0.1087
0,8020
0.0604
0.1131
0.6131
ECVB
4
0.1722
0.2982
0.6529
0.1258
0.2165
0.6827
0.0915
0.1580
0.4612
6/
0.1682
0.3048
0.6566
0.1234
0.2220
0.6875
0.0956
0.1660
0.4337
R FFPA
4
0.0543
0.1026
0.9042
0.0647
0.1349
0.8225
0.0710
0.1501
0.6447
82
0.0937
0.1537
0.8607
0.0769
0.1309
0.8305
0.0830
0.1369
0.6251
EFFB
81
0.1198
0.1859
0.7014
0.0947
0.1462
0.7346
0.0802
0.1312
0.4902
82
0.1084
0.1704
0.7131
0,0811
0.1290
0.7523
0.0719
0.1225
0.5270
ECPA
4
0.0551
0.1128
0.8814
0.0518
0.1042
0.8445
0.0528
0.1150
0.6562
0.0972
0.1636
0.8223
0.0886
0.1390
0.7891
0.0927
0,1443
0,5536
ECPR
81
0.1535
0.2307
0.5981
0.1123
0.1698
0.6408
0.1012
0.1602
0.3576
E2
0.1562
0.2305
0.6160
0.1138
0.1697
0.6608
0.0854
0.1393
0.4490
5
Ablation Study
5.1 Independent vs. Joint Inversion: Impact on Pr Maps
The first experiment examined the impact of separate versus joint inversion of Vp and Vs on the accuracy of predicted Poisson ratio (Pr) maps. This process involved individually training two InversionNets on the EFW dataset to predict Vp and Vs maps, which were then used to calculate the Pr maps. The results revealed substantial deterioration map quality, with the independent inversion maps exhibiting significantly higher MAE and MSE, and lower SSIM values, as outlined in Table 5] compared to those reconstructed from joint inversion, shown Table 3 especially for the complex B datasets, such as "ECFB". These findings reinforce the significance of considering the Vp- Vs relationship and P-S wave coupling, with the lingl-pparamee inversion approach being deemed unviable. Detailed information on this experiment can be found in Section 6 of the supplementary materials.
Table 4: Training time in each epoch by each benchmarking method on IE datasets. All the models trained on single GPU.
ElasticNet
ElasticGAN
E. Vel Family
4m15s
2m20s
1m 155
Fault Family
8m35s
3m50s
2m30s
7

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Table 5: Quantitative results OPENFWI's InversionNet trained with E data. Input z-ommponett data and oulput the Vp/Vs maps independenty. The performance is benchmark of ElasticNet.
InversionNet
Dataset
Loss
Vp
Vs
Pr
MAEL
RMSEL
SSIM
MAE]
RMSEL
SSIM
MAE,
RMSEJ
SSIM
EPVA
4
0.0392
0.0712
0.9455
0.0239
0.0447
0.9590
0.0461
0.0885
0.8282
82
0.0451
0.0745
0.9414
0.0251
0.0469
0.9585
0.0541
0.1039
0.8071
E BVV
&
0.1030
0.1986
0.8260
0,0643
0,1318
0.8615
0.1290
0.2773
0,6063
82
0.0883
0.1832
0.8453
0,0620
0.1269
0.8665
0.0905
0.1980
0.6603
BCVA
4
0,1016
0.1699
0.7636
0,0736
0.1245
0.7837
0.5000
0.2141
0.5607
82
0,1052
0.1730
0.7460
0.0720
0.1236
0.7798
0. 194
0.2381
0,5454
RCVB
4
0.1854
0.3266
0.6270
0.1388
0.2405
0.65578
0.1523
0.3064
0.4695
8
0.1820
0.3260
0.6323
0.1331
0.2344
0.6674
0.1553
0.3230
0.4648
B BFFA
&
0.0818
0.1413
0.8625
0.0584
0.1034
0.8681
0.0784
0.1585
0.6937
82
0.0788
0.1343
0.8930
0.0946
0,1525
0.7918
0.1351
0.2485
0,6174
EFFB
4
0.1323
0.2001
0.6790
0.0943
0,1453
0.7312
0. 180
0.2283
0,5280
f2
0.1301
0.1979
0.6808
0.0898
0.1382
0.7399
0. 124
0.2095
0.5494
ECFA
4
0.1012
0.1638
0.8624
0.0710
0,1182
0.8485
0.0778
0.1586
0.6857
8
0.0962
0.1663
0.8443
0.0833
0.1394
0.8106
0.1032
0.1911
0.6393
ECFB
&1
0.1702
0.2485
0.6020
0.1243
0.1807
0.6531
0.1317
0.2378
0.5091
82
0.1745
0.2563
0.5849
0.1219
0.1775
0.6588
0.1379
0.2529
0.4841
5.2 Investigating P- and S-waves Coupling via Machine Learning
The second experiment focused on examining the interaction between P- and S-waves in the context of seismic data inversion. Two InversionNets were trained, one focusing on P-wave velocity (Vp) and the other on S-wave velocity (Vs), while adjusting the structural characteristics of the ignored wave. This experiment, trained with the OPENFWI's InversionNet using data from E FWT revealed that any minor change in the disregarded wave velocity structure significantly degraded the network's performance, as evidenced in Table 6) This outcome was clearly demonstrated in the more complex datasets, such "ECFB" test set, where changes in structure led to substantial increase in MAE and RMSE, along with a decrease in the SSIM. For a more detailed analysis, refer to the supplementary materials.
Discussion
6.1 Future Challenge
The interaction between P- and S-waves during seismic wave propagation poses significant challenge when attempting to simultaneously determine P and velocities. The networks described in this paper exhibit limited success in separating P- and S- S-waves within the seismic data. Consequently, we anticipate the development of robust methodologies that can precisely estimate both P and S velocities while effectively mitigating the interdependence between these wave components.
Decouple P- and S-waves:
Generalization of data-driven methods: The clastic approximation provides a more accurate representation of field data in comparison to acoustic data. As a result, we expect the neural networks trained on the FWI dataset to exhibit improved resilience in handling real-world field data. However, it should be noted that there are additional physical phenomena, such as anisotropy and viscosity, which are not accounted for in the FWT dataset. The question of how to incorporate these phenomena into the analysis of field data remains open and unanswered challenge.
Forward modeling: The computational expense associated with elastic forward modeling surpasses that of acoustic cases due to various factors. These include the increased memory requirements and the implementation of smaller grid sizes to counteract dispersion phenomena, among others. detailed comparison highlighting these aspects can be found in the last section of supplementary
8

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Table Quantitative results InversionNet trained with E data. The performance compared between testing on the same and different disregarded velocity structural datascts.
InversionNet
Dataset
Loss
Vp: different Vs structure
Vs: different Vp structure
MAEJ
RMSEL
SSIMT
MAEІ
RMSE,
SSIM
BFVA
0.1162
0.1919
0.8974
0.2040
0.2716
0.7977
0.1245
0.2101
0.8849
0,2189
0.2928
0.7793
0,2098
0.3527
0.7086
0,2479
0,3285
0.7182
EVB
0.1940
0.3265
0.7279
0,2540
0,3382
0.7022
ECVA
4
0,1624
0,2590
0.7233
0,2202
0,2924
0.6794
2
0.1678
0.2647
0.7043
0,2249
0.2987
0.6824
0.3014
0.4828
0.5206
0.3136
0,4246
0.5398
ECVE
82
0.3067
0.4900
0,5181
0.3207
0,4349
0.5341
R.PA
4
0.1741
0.2732
0.7464
0,2200
0,2865
0.7362
82
0.1303
0.2052
0.8490
0.2228
0.2913
0.6952
EFFR
&
0.1575
0.2291
0.6501
0.2350
0.3030
0.6480
8/
0.1627
0,2336
0.6492
0,2319
0,2982
0.6517
0.1404
0.2244
0.7951
0.2327
0.3059
0.7360
ECFA
82
0.1319
0,2134
0.8159
0,2399
0,3194
0.7139
RCFB
0.1937
0,2798
0,5747
0,2465
0.3215
0.5785
82
0. 1928
0.2788
0.5613
0,2445
0.3183
0.5915
materials. Despite the possibility of bypassing extensive forward modeling by providing the EFWI dataset, there remains need to explore an efficient forward modeling algorithm to accommodate the growing volume of data in the field.
6.2 Broader Impact
Multiparameter inversion techniques have found wide-ranging appli- cations across diverse scientific and engineering domains, including but not limited to geophysics, medical imaging, and material science. The introduction E FWT serves as a catalyst for further investigation and the pursuit of innovative methodologies in these fields. By addressing the inherent limitations and complexities associated with multiparameter inversion, this advancement encourages ongoing research and the exploration of novel solutions.
Multiparameter inversion:
Carbon-zero emission: The attainment of carbon- zero emissions holds paramount significance in addressing climate change, safeguarding human well-being, and fostering sustainable development. While researchers continue to explore effective strategies towards achieving this goal, elastic FWI emerges promising approach that contribute significantly. Particularly, elastic FWI plays crucial role in assessing and developing geothermal energy resources, as well as in facilitating carbon capture and storage projects, among other applications. The introduction of FWT as fundamental dataset for elastic FWI is expected to stimulate further research and innovation in this direction, thereby enhancing our understanding and capabilities in the pursuit of carbon-zero emissions.
New energy exploration: Elastic FWI can be utilized to evaluate the geological viability of potential sites for hydrogen storage, including underground formations or depleted oil and gas reservoirs. The suitability, capacity, and feasibility of storage site heavily rely on the effectiveness of a geophysical survey and characterization approaches. With the availability of the FF dataset, it would yield great potential to enhance the accuracy in characterizing the subsurface reservoir, therefore providing better identification of hydrogen storage locations.
Potential Social Impacts: Our research, while advancing inverse problems in natural science, may inadvertently support increased fossil fuel consumption if applied to optimize oil and gas drilling, raising environmental concerns. However, the same techniques can equally bolster positive initiatives, such as geothermal exploration and hydrogen storage, highlighted in Sec 6.2. The dual potential of

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our methodologies underscores the importance of their judicious application, aligning with sustainable development goals.
7
Conclusion
This paper presents EFW open-source elastic FWI dataset. EPWT comprises eight datasets and includes benchmarks for three deep learning methods. The datasets released with EFWT provide diverse P-wave and S S-wave velocities, specifically addressing the coupling problem encountered in multiparameter inversion. The initial benchmarks demonstrate promising results on certain datasets, while others may require further investigation. Additionally, coupling tests conducted provide insights into network design for multiparameter inversion problems. Furthermore, this paper discusses the future challenges that can be explored using these datasets and outlines the envisioned future advancements as EFWI continues to evolve.
10

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Acknowledgement
This work was funded by the Los Alamos National Laboratory (LANL) Technology Evaluation and Demonstration (TED) program and by the U.S. Department of Energy (DOE) Office of Fossil Energy's 8 Carbon Storage Research Program via the Science-Informed Machine Learning to Accelerate Real-Time Decision Making for Carbon Storage (SMART-CS) Initiative.
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13


Reviews:
[{"review_id": "Oa8qqQyDPc", "reviewer": "Reviewer_yFAK", "summary": "", "questions": "", "limitations": "Yes, they are discussed in section 6.1.", "rating": 7, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "* **[Useful domain]** Predicting velocity maps from seismic data has multiple geological applications, including earthquake prediction and information for extracting oil and gas.\n\n* **[Gathering collection of open-access data into one dataset]** the paper collects open-access data into their format. Therefore, a researcher interested in this problem can attempt fewer datasets yet having access to more data.\n\n* **[Open-sourcing data that is otherwise computationally-expensive to compute]** the paper explains the formulas for computing the S velocity maps (Vs; equations 2 and 3) -- it seems to be a recurrence relation. Computing the Vs maps is computationally-expensive. Open-sourcing these values (1) standardizes the dataset and (2) allows researchers with lower computational budget to train models.\n\n* **[Baseline Models]** Paper attempts 3 baseline models (based on InversionNet; VelocityGAN, and SimFWI). Further, they mention that they open-source pre-trained models.", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": ""}, {"review_id": "pZ2RsiQMiL", "reviewer": "Reviewer_6MVi", "summary": "", "questions": "", "limitations": "The comment in checklist 1c) about not having seen any negative impacts about this work is a bit amusing given that I assume a major use of these inverse problems solutions will be in areas like drilling for oil and gas, and extracting these more efficiently, and the world is currently facing a climate crisis because of the use of these products :-). However, positive aspects can be framed as enabling more self-sufficiency in energy, with less dependence on unstable or undemocratic parts of the world, and as pointed out in Sec 6.2 finding geothermal and hydrogen sotrage options.\n\nHowever, this should not prevent the work from being used, it is just that the authors are maybe not thinking about the impact issues as clearly as they could", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "dataset for an interesting scientific problem, for a range of geological structures along with 3 different deep learning methods as initial benchmarks.", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": ""}, {"review_id": "eeJrXca4Cb", "reviewer": "Reviewer_fegx", "summary": "", "questions": "", "limitations": "Limitations are adequately addressed.", "rating": 7, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "The paper is responsive to the conference topic, it is well written, the approach is sound, and overall methodology is appropriate. This submission merits acceptance.", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": ""}]

Author rebuttal:

Meta-review: This paper presents a novel benchmark dataset for elastic full waveform inversion (a key technique for Seismic Imaging) and a few  deep learning methods as initial benchmarks. The reviewers agree that this is a very good paper in an interesting domain where not a lot of data is available- which makes it very valuable. 
The authors did a good job in addressing all the reviewer questions.
Decision: Accept (Poster)