Pith. sign in

REVIEW 3 major objections 6 minor 125 references

Automatic Differentiation-based Full Waveform Inversion with Flexible Workflows

T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper introduces ADFWI, an open-source automatic-differentiation framework that computes full waveform inversion gradients by backpropagation through the wave simulation, removing the need to derive adjoint equations and adjoint…

desk verdict A genuinely useful open-source AD-FWI workbench, but the 'robustness' headline outruns the synthetic evidence. read the letter →

arxiv 2412.00486 v1 pith:DFG5LDAP submitted 2024-11-30 cs.LG eess.SPphysics.geo-ph

Feng Liu , Haipeng Li , Guangyuan Zou , Junlun Li This is my paper · ORCID
classification cs.LGeess.SPphysics.geo-ph
keywords fullwaveforminversionautomaticdifferentiationadjointstatemethodelasticwaveequationsseismicanisotropydeeplearninguncertaintyquantificationopen-sourcesoftware
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Full waveform inversion traditionally obtains its gradients from the adjoint state method, which requires a separate derivation and numerical implementation for each wave equation, objective function, and boundary condition. The paper claims that automatic differentiation removes this burden entirely: if the finite-difference forward simulation is written as a differentiable computational graph, backpropagation through that graph yields the same model gradients without any explicit adjoint equations or adjoint sources. The authors implement this claim in ADFWI, an open-source framework supporting isotropic-acoustic, isotropic-elastic, and VTI/HTI elastic wave propagation, and demonstrate the workflow on synthetic inversions that recover velocity, density, and anisotropy parameters. A sympathetic reader would care because ADFWI turns the steepest part of FWI research, deriving and verifying adjoints for new physics or misfit functions, into a matter of defining a differentiable forward script.

What carries the argument

The central object is the computation graph of the staggered-grid finite-difference wave simulation, traversed in reverse by automatic differentiation. Each arithmetic operation in the forward modeling, from the initial wavefield through all time steps to the misfit evaluation, is recorded, and backpropagation applies the chain rule along this graph to produce gradients with respect to model parameters. This is what lets a single forward code act as its own adjoint, which is why new objective functions, regularizers, or neural-network reparameterizations can be added without deriving adjoint sources. Checkpointing the time axis and processing shots in mini-batches are the mechanisms that keep this graph's memory footprint manageable.

What would settle it

For each supported media and objective-function branch, compute the AD gradient on a small model and compare it against a central-difference gradient of the same objective; a mismatch in any branch, or a failed dot-product test between the forward operator and the AD-induced adjoint, would refute the claim of unified gradient correctness.

Watch

Extended reading notes

Core claim

The central claim is that automatic differentiation can serve as a complete replacement for the adjoint state method in full waveform inversion, provided the wave simulation is coded inside a differentiable computation graph. In this setup, the graph that produces synthetic seismograms also produces the gradient of any differentiable objective with respect to any model parameter, so the framework can support isotropic-acoustic, isotropic-elastic, and VTI/HTI elastic media without per-media adjoint derivations. The paper shows that objective functions such as soft-DTW and Wasserstein-Sinkhorn, whose adjoint sources are difficult to derive, are integrated simply by computing their scalar value and letting backpropagation handle the gradient. Synthetic tests on the Marmousi2 and Overthrust models, an elastic Marmousi2 test recovering both vp and vs, and a VTI anomaly test recovering both epsilon and delta, along with comparisons of objective functions, optimizers, regularizers, and neural-network reparameterization, are offered as evidence that the framework is practical and flexible.

Load-bearing premise

The framework's promise depends on backpropagation through the discretized finite-difference graph giving correct gradients for every wave equation and objective function it supports, but the paper directly validates this against central-difference gradients for only one isotropic-acoustic case.

Editorial extensions

If this is right

  • Any differentiable misfit, including soft-DTW and Wasserstein-Sinkhorn, becomes immediately usable in FWI because the gradient is supplied by backpropagation rather than by an analytically derived adjoint source.
  • The same inversion workflow applies across isotropic-acoustic, isotropic-elastic, and VTI/HTI elastic media, so multi-parameter inversions such as vp/vs or epsilon/delta can be run from one codebase.
  • Neural-network reparameterization becomes a direct optimization route in which automatic differentiation updates the network weights, providing learned regularization and enabling fast dropout-based uncertainty estimates.
  • Mini-batch shot processing and time-axis checkpointing reduce the memory overhead of automatic differentiation enough to make large-scale AD-based FWI practical on a single GPU.
  • Because automatic differentiation differentiates through any smooth regularizer, the framework's support for total-variation and Tikhonov regularization extends by construction to future regularizers, since only the regularization value needs to be computed.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If backpropagation is correct for every branch, FWI research shifts from deriving adjoints to implementing accurate forward physics, which should accelerate experimentation with viscoelastic attenuation, three-dimensional media, and other formulations that are currently expensive to derive by hand.
  • The paper's direct gradient validation covers only one isotropic-acoustic case, so a natural stress test is to repeat the central-difference comparison for the elastic and VTI/HTI branches and for each non-L2 objective; a mismatch in any branch would silently corrupt those inversions.
  • Dropout-based uncertainty should initially be read as a fast sensitivity indicator tied to the reparameterizing network architecture, not as a calibrated posterior; comparing it with ensemble inversions would clarify what the uncertainty maps measure.
  • The same computation-graph convenience that makes total-variation and Tikhonov regularization trivial should extend to learned regularizers such as diffusion-model priors or dictionary transforms, though the paper only sketches this direction.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The manuscript presents ADFWI, an open-source PyTorch-based automatic-differentiation framework for full waveform inversion. The framework implements forward modeling for isotropic-acoustic, isotropic-elastic, and VTI/HTI-elastic media using staggered-grid finite differences with PML boundaries, and computes gradients by backpropagation rather than by hand-derived adjoint equations. It integrates seven objective functions, eight optimizers, Tikhonov/TV regularization, DNN-based model reparameterization with dropout uncertainty estimation, and memory-reduction strategies (mini-batching and checkpointing). The authors validate the framework on Marmousi2 and Overthrust acoustic tests, an elastic Marmousi2 test, a VTI anomaly test, objective-function and optimizer comparisons, and regularization/uncertainty demonstrations, concluding that ADFWI eliminates manual adjoint derivation and serves as a flexible workbench for FWI.

Significance. ADFWI is a substantial engineering contribution with clear practical value: the public repository and reproducible examples lower the barrier to experimenting with non-L2 misfits, anisotropic wave equations, and neural-network reparameterization. The systematic comparison of objective functions and optimizers under a common setup is useful. If the AD gradients are correct across all supported branches, the framework delivers on its central promise. However, the current evidence does not yet establish that correctness for the elastic, VTI/HTI, and non-L2 objective branches, and several evaluation choices (smoothed-true initial models, same-solver observed data) weaken the generality claims. The missing gradient verification is the main load-bearing gap.

major comments (3)
  1. [Section 2.2 and Supporting Figure S1] The only direct validation of the AD gradients is Supporting Figure S1, which compares AD gradients with finite-difference gradients for a single isotropic-acoustic experiment. No equivalent gradient check is reported for the ISO-elastic, VTI/HTI-elastic, or any non-L2 objective branch (envelope, global correlation, soft-DTW, Wasserstein-Sinkhorn), nor for the checkpointed or mini-batched computation graphs described in Section 4.3. Because AD differentiates the implemented forward code, a bug in the staggered-grid update, the Thomsen-to-stiffness mapping, the PML boundary, or the objective-function implementation would still yield low-misfit, visually plausible inversions when observed data are generated with the same forward solver. The paper's central claim in Section 5 that ADFWI 'eliminates the need for manual derivation and implementation of adjoint equations and sources' for all supported media and objectives therefore rests on an unverified branch. I request gradient checks (e.g., against finite differences or an adjoint-state reference, with a quantitative error metric) for at least one representative case in each wave-equation family and each objective-function family, or a correspondingly narrowed claim.
  2. [Section 3.1 and Table 1] All synthetic inversions start from initial models obtained by Gaussian smoothing of the true model (Table 1; Figures 3b, 4c-d, 6b), and all observed data are generated by the same forward solver used in inversion. The VTI test in Section 3.1.3 goes further: vp, vs, and rho are fixed at their true values, and only epsilon and delta are inverted from constant background values equal to the true background. These tests therefore demonstrate that the framework can refine a good starting model, but they do not independently confirm the correctness of the elastic/VTI forward modeling or the corresponding AD gradients, nor do they exercise the multi-parameter trade-offs that dominate practical elastic/anisotropic FWI. In addition, the HTI case advertised in the abstract and Section 2.1 is not exercised in any numerical test. I recommend adding at least one test with a non-trivial initial model (e.g., from travel-time tomography or a coarse model without smoothing the target) and, if possible, a dataset produced by an independent solver or with added noise, or alternatively stating this limitation explicitly and softening the generality claims in Sections 3.1.3 and 5.
  3. [Section 4.3] The checkpointing and mini-batch strategies modify the computation graph over which gradients are accumulated. The paper reports memory and runtime trade-offs but does not verify that the gradients obtained with checkpointing and gradient accumulation are identical (or acceptably close) to those from a full uncheckpointed backpropagation. Since a mismatch would introduce biased gradients and could silently degrade inversion quality, a gradient accuracy check (e.g., comparing checkpointed and uncheckpointed gradients on the Marmousi2 example) should be added before claiming that these strategies are 'practical for large-scale full waveform inversion' (Section 5).
minor comments (6)
  1. [Abstract; Section 2.3] Typos and naming inconsistencies should be corrected: 'forword modeling' in the abstract, 'Pytorch' in Section 2.3 and Figure 1 caption, and 'T-Distribution' in Section 2.3.1 should be 'PyTorch' and 'Student-t distribution'.
  2. [Section 3.1.3 / Figure 5] The text states that δ in the anomaly inclusions ranges from 0.1 to 0.25, while the Figure 5 caption states 0.1 to 0.3; these values should be harmonized.
  3. [Supporting Text S1, Eq. (7)] The sigmoid weighting expression is missing parentheses: it should read w(i) = 1/(1+exp(-(i - N/2))), and the text should state the value of N used in the WEC test in Section 4.1.
  4. [Section 2.3.1 / Table 2] The same objective is called 'Wasserstein-Sinkhorn' in Section 2.3.1 and 'Wasserstein Dist.' in Table 2; use one name consistently throughout.
  5. [Section 4.2] The dropout-based uncertainty maps are only qualitative; since no comparison with a reference uncertainty estimate (e.g., from multiple noise realizations or a Bayesian method) is provided, the claim of 'rapid estimation of uncertainty' should be accompanied by a caveat that the maps are uncalibrated.
  6. [Supporting Figure S1] The gradient check reports no quantitative error metric or the Δm used for the finite-difference reference; please add a normalized error or maximum-relative-error value.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: ADFWI integrates standard components, and its tests are self-consistency checks rather than results reduced to inputs by construction.

full rationale

ADFWI is an engineering integration: the forward staggered-grid finite-difference propagators, objective functions, optimizers, and DNN reparameterization are standard components cited from external literature (e.g., Virieux 1986; Thomsen 1986; Cuturi & Blondel 2017; Kingma & Ba 2017). The central claim—that automatic differentiation replaces hand-derived adjoint sources—is a property of reverse-mode AD applied to the explicitly constructed computational graph, not a result defined in terms of the claim itself. The gradient validation in Supporting Figure S1 compares AD gradients with central-difference derivatives of the same discretized forward operator, which is an implementation-consistency check; it does not make the inversion results true by construction. The synthetic Marmousi2/Overthrust and VTI tests use data generated by the same forward solver and start from smoothed true models, so they are self-consistency benchmarks rather than independent predictions, but they do not reduce any claimed result to an input parameter or to a self-citation. The only self-citation (F. Liu et al., 2024) appears in a literature survey and is not load-bearing. No equation or result in the paper is equivalent to its inputs by construction.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard numerical wave modeling, PyTorch's backpropagation correctness, and the representativeness of synthetic tests. The paper adds no new physical entities. The main audit findings are that gradient correctness is tested only for one acoustic case, synthetic tests are self-referential, and several influential tuning parameters are omitted.

free parameters (4)
  • Tikhonov/TV regularization weights alpha = not reported
    Section 3.3.1 and Table 4 compare regularization methods but omit the weights chosen, which control the trade-off and directly affect the reported MAPE/SSIM.
  • Optimizer learning rates and adaptive-method hyperparameters = not reported
    Section 3.2.2 states hyperparameters are tuned for fairness but does not list them; the optimizer ranking in Table 3 depends on these choices.
  • WEC weighting schedule parameter N = not reported
    Supporting Text S1 Eq. (7) defines the sigmoid schedule with total iteration count N; the hybrid objective results in Section 4.1 depend on this hand-chosen schedule.
  • CNN architecture and training choices for DNN reparameterization = 2-5 blocks, latent 100, 4x4 kernels, channel counts 4-256, LeakyReLU 0.1, dropout p=0.1/0.2
    Section 3.3.2 and Table S1; inversion quality varies strongly with block count (MAPE 5.54 to 9.62), so the architecture is an influential hand-chosen design parameter.
assumptions (5)
  • domain assumption The staggered-grid finite-difference propagators used in ADFWI accurately solve the acoustic and elastic wave equations for the tested 2D scenarios.
    Invoked throughout Section 3; no convergence study or analytic benchmark is reported beyond the gradient check in Figure S1.
  • domain assumption Backpropagation through the discretized simulation graph yields gradients equivalent to adjoint-state gradients for all implemented media and objective functions.
    Relied on in Section 2.2; the paper validates AD gradients only against central-difference gradients for one acoustic case (Figure S1), citing W. Zhu et al. (2021) for general equivalence.
  • domain assumption Synthetic observed data generated with the same propagator used in inversion constitute a valid test of FWI framework behavior.
    Used in Section 3; these tests are self-consistency checks rather than independent benchmarks and may not predict field-data performance.
  • domain assumption For the VTI test, fixing the true vp, vs, and rho models while inverting only epsilon and delta does not bias the assessment of crosstalk.
    Section 3.1.3; real VTI FWI would need simultaneous estimation, and parameter trade-offs may be underestimated.
  • domain assumption PyTorch optimizer implementations with user-tuned hyperparameters produce behavior representative of each method's general performance.
    Section 3.2.2 tunes hyperparameters but does not report them, so rankings may depend on tuning choices.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Automatic Differentiation-based Full Waveform Inversion with Flexible Workflows." pith.science (2026). https://pith.science/paper/DFG5LDAP

@misc{pith2026241200486,
  author       = {Pith},
  title        = {Pith review of: Automatic Differentiation-based Full Waveform Inversion with Flexible Workflows},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DFG5LDAP}},
  note         = {Machine review of arXiv:2412.00486}
}
read the original abstract

Full waveform inversion (FWI) is able to construct high-resolution subsurface models by iteratively minimizing discrepancies between observed and simulated seismic data. However, its implementation can be rather involved for complex wave equations, objective functions, or regularization. Recently, automatic differentiation (AD) has proven to be effective in simplifying solutions of various inverse problems, including FWI. In this study, we present an open-source AD-based FWI framework (ADFWI), which is designed to simplify the design, development, and evaluation of novel approaches in FWI with flexibility. The AD-based framework not only includes forword modeling and associated gradient computations for wave equations in various types of media from isotropic acoustic to vertically or horizontally transverse isotropic elastic, but also incorporates a suite of objective functions, regularization techniques, and optimization algorithms. By leveraging state-of-the-art AD, objective functions such as soft dynamic time warping and Wasserstein distance, which are difficult to apply in traditional FWI are also easily integrated into ADFWI. In addition, ADFWI is integrated with deep learning for implicit model reparameterization via neural networks, which not only introduces learned regularization but also allows rapid estimation of uncertainty through dropout. To manage high memory demands in large-scale inversion associated with AD, the proposed framework adopts strategies such as mini-batch and checkpointing. Through comprehensive evaluations, we demonstrate the novelty, practicality and robustness of ADFWI, which can be used to address challenges in FWI and as a workbench for prompt experiments and the development of new inversion strategies.

Figures

Figures reproduced from arXiv: 2412.00486 by the authors.

Figure 1
Figure 1. Workflow of ADFWI, which includes five essential steps with an optional neural network-based reparameterization/regularization step. Step 1: define the isotropic or anisotropic acoustic/elastic Earth model and the data acquisition system. Step 2: perform forward wavefield modeling using propagators implemented in Pytorch on CPU or GPU. Step 3: measure the discrep￾ancy between observed and synthetic waveforms based o… view at source ↗
Figure 2
Figure 2. FWI workflow with model reparameterization using a deep neural network. The process begins by generating a velocity model from a random vector using a generative network, which typically is a multilayer convolutional neural network. The velocity model is then used in the forward propagator for waveform modeling, and the gradients from AD are then back-propagated to update the neural network. 3 Results 3.1 Evaluation… view at source ↗
Figure 3
Figure 3. FWI tests using the ISO-acoustic Marmousi2 and Overthrust models. (a) The true Marmousi2 model, where the red stars indicate source locations and the white triangles indicate the receiver positions; (b) the initial model, obtained by applying a 240 × 240 m Gaussian smoothing filter to the true model; (c) inverted Marmousi2 model after 300 iterations; (d)-(f) are similar to (a)-(c), but for the Overthrust model. The … view at source ↗
Figures from the paper (12 more)
Figure 4
Figure 4. Figure 4: Test for ADFWI using the ISO-elastic Marmousi2 model. (a) The true P-wave velocity (vp), and (b) true S-wave velocity (vs) of the elastic Marmousi2 model. The red stars indicate source locations, and the white inverted triangles indicate the receiver positions; (c)-(d)…
Figure 5
Figure 5. Figure 5: VTI-elastic FWI tests using a model containing multiple anomaly inclusions with perturbed ϵ and δ. (a)-(b) The true ϵ and δ models, where red stars indicate source locations and white inverted triangles mark receiver positions. The background values are ϵ=0.1 and δ=0.0…
Figure 6
Figure 6. Figure 6: Comparison of the inversion results using various objective functions. (a) The true P￾wave velocity model, with the red stars indicating sources and white triangles indicating receivers. (b) The initial P-wave velocity model obtained by applying a 480 × 480 m Gaussian …
Figure 7
Figure 7. Figure 7: Variations of model similarities (SSIM, higher is better) with iterations for different objective functions. –15– [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]
Figure 8
Figure 8. Figure 8: Comparison for eight different optimizers for ADFWI. (a) The true velocity model, with red stars indicating the source locations and white triangles indicating the receiver positions. Inversion results using the (b) SGD, (c) ASGD, (d) Adagrad, (e) RMSprop, (f) Radam, (…
Figure 9
Figure 9. Figure 9: Variations of data misfit and model similarity (SSIM) for different optimizers. (a) The L2-norm for data misfit, and (b) the SSIM for model similarity for eight different optimizers with iterations [PITH_FULL_IMAGE:figures/full_fig_p017_9.png]
Figure 10
Figure 10. Figure 10: Comparison of the inversion results using different regularization methods. (a) The raw dataset (left panel) and noisy dataset which has a mean signal-to-noise ratio of -4.10 dB (right panel) used for the tests; (b) inverted model without regularization; (c)-(d) inver…
Figure 11
Figure 11. Figure 11: Variations of data misfit and model similarity (SSIM) with iterations using the global correlation objective function with various regularization terms. (a) Change of data misfit, and (b) change of SSIM with iterations. –18– [PITH_FULL_IMAGE:figures/full_fig_p018_11.png]
Figure 12
Figure 12. Figure 12: Comparison of the inversion results using neural networks with different numbers of CNN blocks. (a) The inverted model with 2 CNN blocks, (b) 3 CNN blocks, (c) 4 CNN blocks and (d) 5 CNN blocks for model reparameterization. The true and initial model used for FWI are …
Figure 13
Figure 13. Figure 13: Comparison of the inversion results using individual and hybrid objective functions. The inversion results obtained by the (a) envelop, (b) global correlation, and (c) WEC hybrid objective functions at the 100th iteration; (d)-(f) are similar to (a)-(c), but show the …
Figure 14
Figure 14. Figure 14: Uncertainty estimation using the two-layer CNN optimized in the learned regular￾ization tests outlined in Section 3.3.2. (a) The true Marmousi2 model; (b) the inverted model with no neurons deactivated, same as Figure 12a; estimated uncertainty based on 1,000 models i…
Figure 15
Figure 15. Figure 15: Comparison of memory demand (blue) and runtime per iteration (red) with different checkpointing and mini-batch strategies. The tests are based on the ISO-acoustic Marmousi2 model described in Section 3.1.1 on a single NVIDIA GeForce RTX 4090 GPU. (a) Impact of varying…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

125 extracted references · 40 canonical work pages

  1. [1]

    apacite url apacite =6pt Acknowledgments. 6pt 1sp \@dates Received \@recvdate\@empty\@rcvaccrule \@recvdate \@revisedate\@empty ; revised \@revisedate; \@accptdate\@empty \@revisedate\@empty; accepted \@accptdate \@pubdate\@empty. ; published \@pubdate. -2pt \@authaddrs @list\@empty =.15in @list 1sp @list =9pt plus 2pt minus 6pt \@sluginfo width 4pc =3000...

    2001

  2. [2]

    gc" journal option for G-Cubed Nov 3, 2003 M Kelly, fixed noindent in subsubsubsection titles and for all sections in rog option Oct 2, 2003 M Kelly, added

    \@ifstar \@figbox \@figbox \@figbox#1#2#3 to !#1! #3 [#1][c] !#2!#3 \@tempdima#2 \@tempdima by2 \@tempdima by- \@tempdima by- \@height\@tempdima\@depth\@tempdima\@width @ to @ #3 Bib ??? ??? ??? =0 =0 = @figure=0 @table=0 #1 --#1 -24pt -2ex #1 0= #1 to 0 #1 I NDEX T ERMS: #1 #1 Citation: #1 Feb 9, 2009 Changed name and references to name from agu2001 to a...

    arXiv 2009

  3. [3]

    APACrefauthors \ 2009

    abokhodair_2009_Complex APACrefauthors Abokhodair, A A. APACrefauthors \ 2009 . Complex Differentiation Tools for Geophysical Inversion Complex differentiation tools for geophysical inversion . Geophysics 74 2 H1-H11 . APACrefDOI doi:10.1190/1.3052111 APACrefDOI

    work page doi:10.1190/1.3052111 2009

  4. [4]

    , Gholami, A

    aghamiry_2020_Compound APACrefauthors Aghamiry, H S. , Gholami, A. \ Operto, S. APACrefauthors \ 2020 . Compound Regularization of Full-Waveform Inversion for Imaging Piecewise Media Compound regularization of full-waveform inversion for imaging piecewise media . IEEE Transactions on Geoscience and Remote Sensing 58 2 1192--1204 . APACrefDOI doi:10.1109/T...

    arXiv 2020

  5. [5]

    , da Silva, N V

    agudo_2018_acoustic APACrefauthors Agudo, \`O C. , da Silva, N V. , Warner, M. \ Morgan, J. APACrefauthors \ 2018 . Acoustic full-waveform inversion in an elastic world Acoustic full-waveform inversion in an elastic world . Geophysics 83 3 R257--R271

    2018

  6. [6]

    , Kelly, K

    alford_1974_ACCURACY APACrefauthors Alford, R. , Kelly, K. \ Boore, D M. APACrefauthors \ 1974 . Accuracy of finite-difference modeling of the acoustic wave equation Accuracy of finite-difference modeling of the acoustic wave equation . Geophysics 39 6 834--842

    1974

  7. [7]

    APACrefauthors \ 2000

    alkhalifah_2000_Acoustic APACrefauthors Alkhalifah, T. APACrefauthors \ 2000 . An Acoustic Wave Equation for Anisotropic Media An acoustic wave equation for anisotropic media . Geophysics 65 4 1239--1250 . APACrefDOI doi:10.1190/1.1444815 APACrefDOI

    work page doi:10.1190/1.1444815 2000

  8. [8]

    APACrefauthors \ 1996

    aminsadeh_1996_3D APACrefauthors Aminsadeh, F. APACrefauthors \ 1996 . 3-D Salt and Overthrust Seismic Models 3-d salt and overthrust seismic models \ (P. Weimer\ T L. Davis, ). American Association of Petroleum Geologists . APACrefDOI doi:10.1306/St42605C29 APACrefDOI

    work page doi:10.1306/st42605c29 1996

Show all 125 references
  1. [9]

    , Van Leeuwen, T

    aravkin_2011_Robust APACrefauthors Aravkin, A. , Van Leeuwen, T. \ Herrmann, F. APACrefauthors \ 2011 . Robust Full-waveform Inversion Using the Student's T-distribution Robust full-waveform inversion using the student's t-distribution . SEG Technical Program Expanded Abstract...

    2011 doi

  2. [10]

    , Pearlmutter, B A

    baydin_2015_Automatic APACrefauthors Baydin, A G. , Pearlmutter, B A. , Radul, A A. \ Siskind, J M. APACrefauthors \ 2015 . Automatic Differentiation in Machine Learning: A Survey Automatic differentiation in machine learning: A survey . Journal of Machine Learning Research 18...

    2015 doi arXiv

  3. [11]

    APACrefauthors \ 1994

    berenger_1994_Perfectly APACrefauthors Berenger, J P. APACrefauthors \ 1994 . A Perfectly Matched Layer for the Absorption of Electromagnetic Waves A perfectly matched layer for the absorption of electromagnetic waves . Journal of Computational Physics 114 2 185--200 . APACref...

    1994

  4. [12]

    \ Iturrar \'a n-Viveros , U

    bernal-romero_2020_Accelerating APACrefauthors Bernal-Romero , M. \ Iturrar \'a n-Viveros , U. APACrefauthors \ 2020 . Accelerating Full Waveform Inversion through Adaptive Gradient Optimization Methods and Dynamic Simultaneous Sources Accelerating full waveform inversion thro...

    2020 doi

  5. [13]

    , Buhendwa, A B

    bezgin_2024_JAXFluids APACrefauthors Bezgin, D A. , Buhendwa, A B. \ Adams, N A. APACrefauthors \ 2024 . JAX-Fluids 2.0: Towards HPC for Differentiable CFD of Compressible Two-Phase Flows. Jax-fluids 2.0: Towards hpc for differentiable cfd of compressible two-phase flows. arXi...

    2024 doi arXiv

  6. [14]

    , B \"u cker, H M

    bischof_2007_Automatic APACrefauthors Bischof, C H. , B \"u cker, H M. , Rasch, A. , Slusanschi, E. \ Lang, B. APACrefauthors \ 2007 . Automatic Differentiation of the General-Purpose Computational Fluid Dynamics Package FLUENT Automatic differentiation of the general-purpose ...

    2007 doi

  7. [15]

    , Hole, J A

    bleibinhaus2007structure APACrefauthors Bleibinhaus, F. , Hole, J A. , Ryberg, T. \ Fuis, G S. APACrefauthors \ 2007 . Structure of the California Coast Ranges and San Andreas Fault at SAFOD from seismic waveform inversion and reflection imaging Structure of the california coa...

    2007

  8. [16]

    , Peter, D

    bozdaug2016global APACrefauthors Bozda g , E. , Peter, D. , Lefebvre, M. , Komatitsch, D. , Tromp, J. , Hill, J. Pugmire, D. APACrefauthors \ 2016 . Global adjoint tomography: first-generation model Global adjoint tomography: first-generation model . Geophysical Supplements to...

    2016

  9. [17]

    , Trampert, J

    bozdag_2011_Misfit APACrefauthors Bozda g , E. , Trampert, J. \ Tromp, J. APACrefauthors \ 2011 . Misfit Functions for Full Waveform Inversion Based On Instantaneous Phase and Envelope Measurements Misfit functions for full waveform inversion based on instantaneous phase and e...

    2011 arXiv

  10. [18]

    , Operto, S

    Brossier_2009_Seismic APACrefauthors Brossier, R. , Operto, S. \ Virieux, J. APACrefauthors \ 2009 . Seismic Imaging of Complex Structures by 2D Elastic Frequency-Domain Full-Waveform Inversion Seismic imaging of complex structures by 2d elastic frequency-domain full-waveform ...

    2009

  11. [19]

    , Operto, S

    brossier_2010_Which APACrefauthors Brossier, R. , Operto, S. \ Virieux, J. APACrefauthors \ 2010 . Which Data Residual Norm for Robust Elastic Frequency-Domain Full Waveform Inversion? Which data residual norm for robust elastic frequency-domain full waveform inversion? Geophy...

    2010 doi

  12. [20]

    , Washbourne, J

    bube2016self APACrefauthors Bube, K. , Washbourne, J. , Ergas, R. \ Nemeth, T. APACrefauthors \ 2016 . Self-adjoint, energy-conserving second-order pseudoacoustic systems for VTI and TTI media for reverse time migration and full-waveform inversion Self-adjoint, energy-conservi...

    2016

  13. [21]

    \ Liao, W

    cao_2015_Computational APACrefauthors Cao, D. \ Liao, W. APACrefauthors \ 2015 . A Computational Method for Full Waveform Inversion of Crosswell Seismic Data Using Automatic Differentiation A computational method for full waveform inversion of crosswell seismic data using auto...

    2015 doi

  14. [22]

    , Sandu, A

    carmichael_1997_Sensitivity APACrefauthors Carmichael, G R. , Sandu, A. \ Potra, F A. APACrefauthors \ 1997 . Sensitivity Analysis for Atmospheric Chemistry Models via Automatic Differentiation Sensitivity analysis for atmospheric chemistry models via automatic differentiation...

    1997 doi

  15. [23]

    APACrefauthors \ 2004

    chapman_2004_Fundamentals APACrefauthors Chapman, C. APACrefauthors \ 2004 . Fundamentals of Seismic Wave Propagation Fundamentals of seismic wave propagation \ ( 1 \ ). Cambridge University Press . APACrefDOI doi:10.1017/CBO9780511616877 APACrefDOI

    2004 doi

  16. [24]

    , Peter, D

    chen_2022_Cycleskipping APACrefauthors Chen, F. , Peter, D. \ Ravasi, M. APACrefauthors \ 2022 . Cycle-Skipping Mitigation Using Misfit Measurements Based on Differentiable Dynamic Time Warping Cycle-skipping mitigation using misfit measurements based on differentiable dynamic...

    2022 doi

  17. [25]

    , Roussillon, P

    chizat_2020_Faster APACrefauthors Chizat, L. , Roussillon, P. , L \'e ger, F. , Vialard, F X. \ Peyr \'e , G. APACrefauthors \ 2020 . Faster Wasserstein Distance Estimation with the Sinkhorn Divergence Faster wasserstein distance estimation with the sinkhorn divergence . Advan...

    2020 doi arXiv

  18. [26]

    \ Alkhalifah, T

    choi_2012_Application APACrefauthors Choi, Y. \ Alkhalifah, T. APACrefauthors \ 2012 . Application of Multi-source Waveform Inversion to Marine Streamer Data Using the Global Correlation Norm Application of multi-source waveform inversion to marine streamer data using the glob...

    2012

  19. [27]

    APACrefauthors \ 2008

    claerbout_2008_basic APACrefauthors Claerbout, J F. APACrefauthors \ 2008 . Basic earth imaging. Basic earth imaging. Stanford Exploration Project

    2008

  20. [28]

    \ Blondel, M

    cuturi_2017_SoftDTW APACrefauthors Cuturi, M. \ Blondel, M. APACrefauthors \ 2017 . Soft-DTW: A Differentiable Loss Function for Time-Series Soft-dtw: A differentiable loss function for time-series . Proceedings of the 34th International Conference on Machine Learning Proceedi...

    2017

  21. [29]

    , Beyer, L

    dosovitskiy_2020_Image APACrefauthors Dosovitskiy, A. , Beyer, L. , Kolesnikov, A. , Weissenborn, D. , Zhai, X. , Unterthiner, T. Houlsby, N. APACrefauthors \ 2020 . An Image Is Worth 16x16 Words: Transformers for Image Recognition at Scale. An image is worth 16x16 words: Tran...

    2020 doi arXiv

  22. [30]

    APACrefauthors \ 2016

    dozat_2016_Incorporating APACrefauthors Dozat, T. APACrefauthors \ 2016 . Incorporating Nesterov Momentum into Adam Incorporating nesterov momentum into adam . Proceedings of the 4th International Conference on Learning Representations Proceedings of the 4th international conf...

    2016

  23. [31]

    , Hazan, E

    duchi_2011_Adaptive APACrefauthors Duchi, J. , Hazan, E. \ Singer, Y. APACrefauthors \ 2011 . Adaptive Subgradient Methods for Online Learning and Stochastic Optimization Adaptive subgradient methods for online learning and stochastic optimization . Journal of Machine Learning...

    2011

  24. [32]

    , Pevzner, R

    egorov2017time APACrefauthors Egorov, A. , Pevzner, R. , B \'o na, A. , Glubokovskikh, S. , Puzyrev, V. , Tertyshnikov, K. \ Gurevich, B. APACrefauthors \ 2017 . Time-lapse full waveform inversion of vertical seismic profile data: Workflow and application to the CO2CRC Otway p...

    2017

  25. [33]

    , Hanke-Bourgeois , M

    engl_2000_Regularization APACrefauthors Engl, H W. , Hanke-Bourgeois , M. \ Neubauer, A. APACrefauthors \ 2000 . Regularization of Inverse Problems Regularization of inverse problems \ ( 375). Dordrecht Kluwer Acad. Publ

    2000

  26. [34]

    , Froese, B D

    engquist_2016_Optimal APACrefauthors Engquist, B. , Froese, B D. \ Yang, Y. APACrefauthors \ 2016 . Optimal Transport for Seismic Full Waveform Inversion Optimal transport for seismic full waveform inversion \ ( \ arXiv:1602.01540). arXiv

    2016 arXiv

  27. [35]

    , S \'e journ \'e , T

    feydy_2019_interpolating APACrefauthors Feydy, J. , S \'e journ \'e , T. , Vialard, F X. , Amari, S i. , Trouve, A. \ Peyr \'e , G. APACrefauthors \ 2019 . Interpolating between Optimal Transport and MMD using Sinkhorn Divergences Interpolating between optimal transport and mm...

    2019

  28. [36]

    APACrefauthors \ 2010

    fichtner_2010_Full APACrefauthors Fichtner, A. APACrefauthors \ 2010 . Full Seismic Waveform Modelling and Inversion Full seismic waveform modelling and inversion . Berlin, Heidelberg Springer Berlin Heidelberg . APACrefDOI doi:10.1007/978-3-642-15807-0 APACrefDOI

    2010 doi

  29. [37]

    , Bunge, H P

    fichtner_2006_Adjoint APACrefauthors Fichtner, A. , Bunge, H P. \ Igel, H. APACrefauthors \ 2006 . The Adjoint Method in Seismology The adjoint method in seismology . Physics of the Earth and Planetary Interiors 157 1-2 86--104 . APACrefDOI doi:10.1016/j.pepi.2006.03.016 APACrefDOI

    2006 doi

  30. [38]

    , Kennett, B L

    fichtner2009full APACrefauthors Fichtner, A. , Kennett, B L. , Igel, H. \ Bunge, H P. APACrefauthors \ 2009 . Full seismic waveform tomography for upper-mantle structure in the Australasian region using adjoint methods Full seismic waveform tomography for upper-mantle structur...

    2009

  31. [39]

    \ Trampert, J

    fichtner_2011_Resolution APACrefauthors Fichtner, A. \ Trampert, J. APACrefauthors \ 2011 . Resolution Analysis in Full Waveform Inversion Resolution analysis in full waveform inversion . Geophysical Journal International 187 3 1604--1624 . APACrefDOI doi:10.1111/j.1365-246X.2...

    2011 arXiv

  32. [40]

    \ Villase \ n or, A

    fichtner_2015_crust APACrefauthors Fichtner, A. \ Villase \ n or, A. APACrefauthors \ 2015 . Crust and upper mantle of the western Mediterranean--Constraints from full-waveform inversion Crust and upper mantle of the western mediterranean--constraints from full-waveform invers...

    2015

  33. [41]

    APACrefauthors \ 1964

    fletcher_1964_Function APACrefauthors Fletcher, R. APACrefauthors \ 1964 . Function Minimization by Conjugate Gradients Function minimization by conjugate gradients . The Computer Journal 7 2 149--154 . APACrefDOI doi:10.1093/comjnl/7.2.149 APACrefDOI

    1964 doi

  34. [42]

    APACrefauthors \ 1990

    frolkovic_1990_Numerical APACrefauthors Frolkovi c , P. APACrefauthors \ 1990 . Numerical recipes: The art of scientific computing Numerical recipes: The art of scientific computing . Acta Applicandae Mathematicae 19 3 297--299

    1990

  35. [43]

    \ Ghahramani, Z

    gal_2015_Dropout APACrefauthors Gal, Y. \ Ghahramani, Z. APACrefauthors \ 2015 . Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning Dropout as a bayesian approximation: Representing model uncertainty in deep learning \ ( \ arXiv:1506.02142). A...

    2015 doi arXiv

  36. [44]

    , Gardner, L W

    gardner_1974_FORMATION APACrefauthors Gardner, G H F. , Gardner, L W. \ Gregory, A R. APACrefauthors \ 1974 . FORMATION VELOCITY AND DENSITY---THE DIAGNOSTIC BASICS FOR STRATIGRAPHIC TRAPS Formation velocity and density---the diagnostic basics for stratigraphic traps . Geophys...

    1974 doi

  37. [45]

    , Bengio, Y

    goodfellow_2016_Deep APACrefauthors Goodfellow, I. , Bengio, Y. \ Courville, A. APACrefauthors \ 2016 . Deep Learning Deep learning . Cambridge, Massachusetts The MIT Press

    2016

  38. [46]

    , Kaltofen, E

    grabmeier_2003_Computer APACrefauthors Grabmeier, J. , Kaltofen, E. \ Weispfenning, V. APACrefauthors \ ( ). \ 2003 . Computer Algebra Handbook Computer algebra handbook . Berlin, Heidelberg Springer Berlin Heidelberg . APACrefDOI doi:10.1007/978-3-642-55826-9 APACrefDOI

    2003 doi

  39. [47]

    APACrefauthors \ 2014

    graves_2014_Generating APACrefauthors Graves, A. APACrefauthors \ 2014 . Generating Sequences with Recurrent Neural Networks Generating sequences with recurrent neural networks \ ( \ arXiv:1308.0850). arXiv . APACrefDOI doi:10.48550/arXiv.1308.0850 APACrefDOI

    2014 doi arXiv

  40. [48]

    , Munos, R

    gruslys_2016_Memoryefficient APACrefauthors Gruslys, A. , Munos, R. , Danihelka, I. , Lanctot, M. \ Graves, A. APACrefauthors \ 2016 . Memory-efficient backpropagation through time Memory-efficient backpropagation through time . Proceedings of the 30th International Conference...

    2016

  41. [49]

    \ Symes, W W

    guitton_2003_Robust APACrefauthors Guitton, A. \ Symes, W W. APACrefauthors \ 2003 . Robust Inversion of Seismic Data Using the Huber Norm Robust inversion of seismic data using the huber norm . Geophysics 68 4 1310--1319 . APACrefDOI doi:10.1190/1.1598124 APACrefDOI

    2003 doi

  42. [50]

    , Tan, Q

    guo_2023_Leastsquares APACrefauthors Guo, X. , Tan, Q. , Li, X. , Huang, J. \ Ma, Z. APACrefauthors \ 2023 . Least-Squares Reverse-Time Migration in VTI Media Using a T-Distribution-Based Misfit Function Least-squares reverse-time migration in vti media using a t-distribution-...

    2023 doi

  43. [51]

    , Zhang, X

    he_2016_Deep APACrefauthors He, K. , Zhang, X. , Ren, S. \ Sun, J. APACrefauthors \ 2016 . Deep Residual Learning for Image Recognition Deep residual learning for image recognition . Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Proceedings of t...

    2016

  44. [52]

    \ Wang, Y

    he_2021_Reparameterized APACrefauthors He, Q. \ Wang, Y. APACrefauthors \ 2021 . Reparameterized Full-Waveform Inversion Using Deep Neural Networks Reparameterized full-waveform inversion using deep neural networks . Geophysics 86 1 V1-V13 . APACrefDOI doi:10.1190/geo2019-0382...

    2021 doi

  45. [53]

    , Hoeber, H

    hicks2016time APACrefauthors Hicks, E. , Hoeber, H. , Houbiers, M. , Lescoffit, S P. , Ratcliffe, A. \ Vinje, V. APACrefauthors \ 2016 . Time-lapse full-waveform inversion as a reservoir-monitoring tool—A North Sea case study Time-lapse full-waveform inversion as a reservoir-m...

    2016

  46. [54]

    , Jain, A

    ho_2020_Denoising APACrefauthors Ho, J. , Jain, A. \ Abbeel, P. APACrefauthors \ 2020 . Denoising Diffusion Probabilistic Models Denoising diffusion probabilistic models \ ( \ arXiv:2006.11239). arXiv . APACrefDOI doi:10.48550/arXiv.2006.11239 APACrefDOI

    2020 doi arXiv

  47. [55]

    \ Koehler, A B

    hyndman_2006_Another APACrefauthors Hyndman, R J. \ Koehler, A B. APACrefauthors \ 2006 . Another Look at Measures of Forecast Accuracy Another look at measures of forecast accuracy . International Journal of Forecasting 22 4 679--688 . APACrefDOI doi:10.1016/j.ijforecast.2006...

    2006 doi

  48. [56]

    , Liang, H

    kazei2023acquisition APACrefauthors Kazei, V. , Liang, H. \ AlDawood, A. APACrefauthors \ 2023 . Acquisition and near-surface impacts on VSP mini-batch FWI and RTM imaging in desert environment Acquisition and near-surface impacts on vsp mini-batch fwi and rtm imaging in deser...

    2023

  49. [57]

    kingma_2017_Adam APACrefauthors Kingma, D P. \ Ba, J. APACrefauthors \ 2017 . Adam: A Method for Stochastic Optimization Adam: A method for stochastic optimization \ ( \ arXiv:1412.6980). arXiv . APACrefDOI doi:10.48550/arXiv.1412.6980 APACrefDOI

    2017 doi arXiv

  50. [58]

    , Yuval, J

    kochkov_2024_Neural APACrefauthors Kochkov, D. , Yuval, J. , Langmore, I. , Norgaard, P. , Smith, J. , Mooers, G. Hoyer, S. APACrefauthors \ 2024 . Neural General Circulation Models for Weather and Climate Neural general circulation models for weather and climate . Nature 632 ...

    2024 doi

  51. [59]

    \ Tromp, J

    komatitsch_2003_Perfectly APACrefauthors Komatitsch, D. \ Tromp, J. APACrefauthors \ 2003 . A Perfectly Matched Layer Absorbing Boundary Condition for the Second-Order Seismic Wave Equation A perfectly matched layer absorbing boundary condition for the second-order seismic wav...

    2003 arXiv

  52. [60]

    , Sutskever, I

    krizhevsky_2012_ImageNet APACrefauthors Krizhevsky, A. , Sutskever, I. \ Hinton, G E. APACrefauthors \ 2012 . ImageNet Classification with Deep Convolutional Neural Networks Imagenet classification with deep convolutional neural networks . Advances in Neural Information Proces...

    2012

  53. [61]

    APACrefauthors \ 1983

    lailly_1983_Seismic APACrefauthors Lailly, P. APACrefauthors \ 1983 . The Seismic Inverse Problem as a Sequence of before Stack Migrations The seismic inverse problem as a sequence of before stack migrations . Conference on Inverse Scattering, Theory and Application, Society f...

    1983

  54. [62]

    , Bengio, Y

    lecun_2015_Deep APACrefauthors LeCun, Y. , Bengio, Y. \ Hinton, G. APACrefauthors \ 2015 . Deep Learning Deep learning . Nature 521 7553 436--444 . APACrefDOI doi:10.1038/nature14539 APACrefDOI

    2015 doi

  55. [63]

    , Bottou, L

    lecun_1998_Gradientbased APACrefauthors Lecun, Y. , Bottou, L. , Bengio, Y. \ Haffner, P. APACrefauthors \ 1998 . Gradient-Based Learning Applied to Document Recognition Gradient-based learning applied to document recognition . Proceedings of the IEEE 86 11 2278--2324 . APACre...

    1998 doi

  56. [64]

    APACrefauthors \ 1988

    levander_1988_Fourth APACrefauthors Levander, A R. APACrefauthors \ 1988 . Fourth-order Finite-difference P-SV Seismograms Fourth-order finite-difference p-sv seismograms . Geophysics 53 11 1425--1436 . APACrefDOI doi:10.1190/1.1442422 APACrefDOI

    1988 doi

  57. [65]

    \ Harris, J M

    li_2018_Full APACrefauthors Li, D. \ Harris, J M. APACrefauthors \ 2018 . Full Waveform Inversion with Nonlocal Similarity and Model-Derivative Domain Adaptive Sparsity-Promoting Regularization Full waveform inversion with nonlocal similarity and model-derivative domain adapti...

    2018 doi

  58. [66]

    li2023continent APACrefauthors Li, H. , Li, J. , Luo, S. , Bem, T S. , Yao, H. \ Huang, X. APACrefauthors \ 2023 . Continent-continent collision between the south and north China plates revealed by seismic refraction and reflection at the southern segment of the Tanlu fault zo...

    2023

  59. [67]

    , Tan, J

    li_2021_FDwave3D APACrefauthors Li, L. , Tan, J. , Zhang, D. , Malkoti, A. , Abakumov, I. \ Xie, Y. APACrefauthors \ 2021 . FDwave3D: A MATLAB Solver for the 3D Anisotropic Wave Equation Using the Finite-Difference Method Fdwave3d: A matlab solver for the 3d anisotropic wave e...

    2021 doi

  60. [68]

    APACrefauthors \ 2011

    liao_2011_Accurate APACrefauthors Liao, W. APACrefauthors \ 2011 . An Accurate and Efficient Algorithm for Parameter Estimation of 2D Acoustic Wave Equation An accurate and efficient algorithm for parameter estimation of 2d acoustic wave equation . International Journal of App...

    2011 doi

  61. [69]

    liu_2024_Multimodal APACrefauthors Liu, F. , Li, J. , Fu, L. \ Lu, L. APACrefauthors \ 2024 . Multimodal Surface Wave Inversion with Automatic Differentiation Multimodal surface wave inversion with automatic differentiation . Geophysical Journal International 238 1 290--312 . ...

    2024 doi

  62. [70]

    , Jiang, H

    liu_2019_Variance APACrefauthors Liu, L. , Jiang, H. , He, P. , Chen, W. , Liu, X. , Gao, J. \ Han, J. APACrefauthors \ 2019 . On the Variance of the Adaptive Learning Rate and Beyond. On the variance of the adaptive learning rate and beyond. arXiv . APACrefDOI doi:10.48550/AR...

    2019 doi arXiv

  63. [71]

    \ Tromp, J

    liu_2006_FiniteFrequency APACrefauthors Liu, Q. \ Tromp, J. APACrefauthors \ 2006 . Finite-Frequency Kernels Based on Adjoint Methods Finite-frequency kernels based on adjoint methods . Bulletin of the Seismological Society of America 96 6 2383--2397 . APACrefDOI doi:10.1785/0...

    2006 doi

  64. [72]

    \ Hutter, F

    loshchilov_2019_Decoupled APACrefauthors Loshchilov, I. \ Hutter, F. APACrefauthors \ 2019 . Decoupled Weight Decay Regularization Decoupled weight decay regularization \ ( \ arXiv:1711.05101). APACrefDOI doi:10.48550/arXiv.1711.05101 APACrefDOI

    2019 doi arXiv

  65. [73]

    \ Hale, D

    ma_2013_wave APACrefauthors Ma, Y. \ Hale, D. APACrefauthors \ 2013 . Wave-equation Reflection Traveltime Inversion with Dynamic Warping and Full Waveform Inversion Wave-equation reflection traveltime inversion with dynamic warping and full waveform inversion . Geophysics 78 6...

    2013

  66. [74]

    , Wiley, R

    martin_2006_Marmousi2 APACrefauthors Martin, G S. , Wiley, R. \ Marfurt, K J. APACrefauthors \ 2006 . Marmousi2: An Elastic Upgrade for Marmousi Marmousi2: An elastic upgrade for marmousi . The Leading Edge 25 2 156--166 . APACrefDOI doi:10.1190/1.2172306 APACrefDOI

    2006 doi

  67. [75]

    , Brossier, R

    metivier_2016_Measuring APACrefauthors M \'e tivier, L. , Brossier, R. , M \'e rigot, Q. , Oudet, E. \ Virieux, J. APACrefauthors \ 2016 . Measuring the Misfit between Seismograms Using an Optimal Transport Distance: Application to Full Waveform Inversion Measuring the misfit ...

    2016 doi

  68. [76]

    \ Tromp, J

    modrak_2016_seismic APACrefauthors Modrak, R. \ Tromp, J. APACrefauthors \ 2016 . Seismic waveform inversion best practices: regional, global and exploration test cases Seismic waveform inversion best practices: regional, global and exploration test cases . Geophysical Journal...

    2016

  69. [77]

    , Warner, M

    morgan2013next APACrefauthors Morgan, J. , Warner, M. , Bell, R. , Ashley, J. , Barnes, D. , Little, R. Jones, C. APACrefauthors \ 2013 . Next-generation seismic experiments: wide-angle, multi-azimuth, three-dimensional, full-waveform inversion Next-generation seismic experime...

    2013

  70. [78]

    , Beroza, G C

    mousavi_2023_Applications APACrefauthors Mousavi, S M. , Beroza, G C. , Mukerji, T. \ Rasht-Behesht , M. APACrefauthors \ 2023 . Applications of Deep Neural Networks in Exploration Seismology: A Technical Survey Applications of deep neural networks in exploration seismology: A...

    2023 doi

  71. [79]

    , Jang, U G

    nakata2022seismic APACrefauthors Nakata, R. , Jang, U G. , Lumley, D. , Mouri, T. , Nakatsukasa, M. , Takanashi, M. \ Kato, A. APACrefauthors \ 2022 . Seismic Time-Lapse Monitoring of Near-Surface Microbubble Water Injection by Full Waveform Inversion Seismic time-lapse monito...

    2022

  72. [80]

    APACrefauthors \ 1980

    nocedal_1980_Updating APACrefauthors Nocedal, J. APACrefauthors \ 1980 . Updating Quasi-Newton Matrices with Limited Storage Updating quasi-newton matrices with limited storage . Mathematics of Computation 35 151 773--782 . APACrefDOI doi:10.1090/S0025-5718-1980-0572855-7 APACrefDOI

    1980 doi

  73. [81]

    , Virieux, J

    operto2006crustal APACrefauthors Operto, S. , Virieux, J. , Dessa, J X. \ Pascal, G. APACrefauthors \ 2006 . Crustal seismic imaging from multifold ocean bottom seismometer data by frequency domain full waveform tomography: Application to the eastern Nankai trough Crustal seis...

    2006

  74. [82]

    , Gross, S

    paszke_2017_Automatic APACrefauthors Paszke, A. , Gross, S. , Chintala, S. , Chanan, G. , Yang, E. , DeVito, Z. Lerer, A. APACrefauthors \ 2017 . Automatic Differentiation in PyTorch Automatic differentiation in pytorch . NIPS 2017 Workshop on Autodiff. Nips 2017 workshop on a...

    2017

  75. [83]

    \ Milcik

    plessix_2006_review APACrefauthors Plessix, R. \ Milcik. APACrefauthors \ 2006 . A Review of the Adjoint-State Method for Computing the Gradient of a Functional with Geophysical Applications A review of the adjoint-state method for computing the gradient of a functional with g...

    2006 arXiv

  76. [84]

    , Milcik, P

    Plessix_2013_Multiparameter APACrefauthors Plessix, R. , Milcik, P. , Rynja, H. , Stopin, A. , Matson, K. \ Abri, S. APACrefauthors \ 2013 . Multiparameter Full-Waveform Inversion: Marine and Land Examples Multiparameter full-waveform inversion: Marine and land examples . The ...

    2013 doi

  77. [85]

    , Wolf, A

    rath_2006_Joint APACrefauthors Rath, V. , Wolf, A. \ B \"u cker, H M. APACrefauthors \ 2006 . Joint Three-Dimensional Inversion of Coupled Groundwater Flow and Heat Transfer Based on Automatic Differentiation: Sensitivity Calculation, Verification, and Synthetic Examples Joint...

    2006 arXiv

  78. [86]

    APACrefauthors \ 2018

    richardson_2018_Seismic APACrefauthors Richardson, A. APACrefauthors \ 2018 . Seismic Full-Waveform Inversion Using Deep Learning Tools and Techniques Seismic full-waveform inversion using deep learning tools and techniques \ ( \ arXiv:1801.07232). arXiv . APACrefDOI doi:10.48...

    2018 doi arXiv

  79. [87]

    APACrefauthors \ 2023

    richardson_2023_Deepwave APACrefauthors Richardson, A. APACrefauthors \ 2023 . Deepwave. Deepwave. Zenodo . APACrefURL https://doi.org/10.5281/zenodo.8381177 APACrefURL APACrefDOI doi:10.5281/zenodo.8381177 APACrefDOI

    2023 doi

  80. [88]

    , Fischer, P

    ronneberger_2015_Unet APACrefauthors Ronneberger, O. , Fischer, P. \ Brox, T. APACrefauthors \ 2015 . U-Net: Convolutional Networks for Biomedical Image Segmentation U-net: Convolutional networks for biomedical image segmentation . N. Navab, J. Hornegger, W M. Wells \ A F. Fra...

    2015

  81. [89]

    , Osher, S

    rudin_1992_Nonlinear APACrefauthors Rudin, L I. , Osher, S. \ Fatemi, E. APACrefauthors \ 1992 . Nonlinear Total Variation Based Noise Removal Algorithms Nonlinear total variation based noise removal algorithms . Physica D: Nonlinear Phenomena 60 1-4 259--268 . APACrefDOI doi:...

    1992 doi

  82. [90]

    , Hinton, G E

    rumelhart_1986_Learning APACrefauthors Rumelhart, D E. , Hinton, G E. \ Williams, R J. APACrefauthors \ 1986 . Learning Representations by Back-Propagating Errors Learning representations by back-propagating errors . Nature 323 6088 533--536 . APACrefDOI doi:10.1038/323533a0 A...

    1986 doi

  83. [91]

    , Rickwood, P

    sambridge_2007_Automatic APACrefauthors Sambridge, M. , Rickwood, P. , Rawlinson, N. \ Sommacal, S. APACrefauthors \ 2007 . Automatic Differentiation in Geophysical Inverse Problems Automatic differentiation in geophysical inverse problems . Geophysical Journal International 1...

    2007 arXiv

  84. [92]

    APACrefauthors \ 2017

    schuster_2017_Seismic APACrefauthors Schuster, G T. APACrefauthors \ 2017 . Seismic Inversion Seismic inversion . Society of Exploration Geophysicists . APACrefDOI doi:10.1190/1.9781560803423 APACrefDOI

    2017 doi

  85. [93]

    , Mettes, P

    shi_2021_Measuring APACrefauthors Shi, Z. , Mettes, P. , Maji, S. \ Snoek, C G M. APACrefauthors \ 2021 . On Measuring and Controlling the Spectral Bias of the Deep Image Prior On measuring and controlling the spectral bias of the deep image prior \ ( \ arXiv:2107.01125). arXiv

    2021 arXiv

  86. [94]

    , Wang, Y

    song_2023_Weighted APACrefauthors Song, C. , Wang, Y. , Richardson, A. \ Liu, C. APACrefauthors \ 2023 . Weighted Envelope Correlation-Based Waveform Inversion Using Automatic Differentiation Weighted envelope correlation-based waveform inversion using automatic differentiatio...

    2023

  87. [95]

    , Hinton, G

    srivastava_2014_Dropout APACrefauthors Srivastava, N. , Hinton, G. , Krizhevsky, A. , Sutskever, I. \ Salakhutdinov, R. APACrefauthors \ 2014 . Dropout: A Simple Way to Prevent Neural Networks from Overfitting Dropout: A simple way to prevent neural networks from overfitting ....

    2014

  88. [96]

    , Arridge, S R

    stanziola_2023_Jwave APACrefauthors Stanziola, A. , Arridge, S R. , Cox, B T. \ Treeby, B E. APACrefauthors \ 2023 . J-Wave: An Open-Source Differentiable Wave Simulator J-wave: An open-source differentiable wave simulator . SoftwareX 22 101338 . APACrefDOI doi:10.1016/j.softx...

    2023

  89. [97]

    , Innanen, K

    sun_2021_Physicsguided APACrefauthors Sun, J. , Innanen, K. \ Huang, C. APACrefauthors \ 2021 . Physics-Guided Deep Learning for Seismic Inversion with Hybrid Training and Uncertainty Analysis Physics-guided deep learning for seismic inversion with hybrid training and uncertai...

    2021 doi

  90. [98]

    , Innanen, K

    sun_2023_Implicit APACrefauthors Sun, J. , Innanen, K. , Zhang, T. \ Trad, D. APACrefauthors \ 2023 . Implicit Seismic Full Waveform Inversion With Deep Neural Representation Implicit seismic full waveform inversion with deep neural representation . Journal of Geophysical Rese...

    2023 doi

  91. [99]

    , Yang, F

    sun_2023_FullWaveform APACrefauthors Sun, P. , Yang, F. , Liang, H. \ Ma, J. APACrefauthors \ 2023 . Full-Waveform Inversion Using a Learned Regularization Full-waveform inversion using a learned regularization . IEEE Transactions on Geoscience and Remote Sensing 61 1--15 . AP...

    2023

  92. [100]

    , Brytik, V

    tan_2010_Verification APACrefauthors Tan, L. , Brytik, V. , Baumstein, A. \ Hinkley, D. APACrefauthors \ 2010 . Verification of Gradient and Hessian Computation for Full Wavefield Inversion Using Automatic Differentiation Verification of gradient and hessian computation for fu...

    2010

  93. [101]

    , Grand, S P

    tao_2017_Fullwaveform APACrefauthors Tao, K. , Grand, S P. \ Niu, F. APACrefauthors \ 2017 . Full-Waveform Inversion of Triplicated Data Using a Normalized-Correlation-Coefficient-Based Misfit Function Full-waveform inversion of triplicated data using a normalized-correlation-...

    2017 doi

  94. [102]

    APACrefauthors \ 1984

    tarantola1984linearized APACrefauthors Tarantola, A. APACrefauthors \ 1984 . Linearized inversion of seismic reflection data Linearized inversion of seismic reflection data . Geophysical prospecting 32 6 998--1015

    1984

  95. [103]

    APACrefauthors \ 1986

    tarantola_1986_Strategy APACrefauthors Tarantola, A. APACrefauthors \ 1986 . A Strategy for Nonlinear Elastic Inversion of Seismic Reflection Data A strategy for nonlinear elastic inversion of seismic reflection data . Geophysics 51 10 1893--1903 . APACrefDOI doi:10.1190/1.144...

    1986 doi

  96. [104]

    , Wang, F

    taufik_2024_Learned APACrefauthors Taufik, M H. , Wang, F. \ Alkhalifah, T. APACrefauthors \ 2024 . Learned Regularizations for Multi-parameter Elastic Full Waveform Inversion Using Diffusion Models Learned regularizations for multi-parameter elastic full waveform inversion us...

    2024 doi

  97. [105]

    APACrefauthors \ 1986

    thomsen_1986_Weak APACrefauthors Thomsen, L. APACrefauthors \ 1986 . Weak Elastic Anisotropy Weak elastic anisotropy . Geophysics 51 10 1954--1966 . APACrefDOI doi:10.1190/1.1442051 APACrefDOI

    1986 doi

  98. [106]

    APACrefauthors \ 2020

    tromp2020seismic APACrefauthors Tromp, J. APACrefauthors \ 2020 . Seismic wavefield imaging of Earth’s interior across scales Seismic wavefield imaging of earth’s interior across scales . Nature Reviews Earth & Environment 1 1 40--53

    2020

  99. [107]

    , Vedaldi, A

    ulyanov_2018_Deep APACrefauthors Ulyanov, D. , Vedaldi, A. \ Lempitsky, V. APACrefauthors \ 2018 . Deep Image Prior Deep image prior . Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Proceedings of the ieee conference on computer vision and...

    2018

  100. [108]

    APACrefauthors \ 1986

    virieux_1986_PSV APACrefauthors Virieux, J. APACrefauthors \ 1986 . P-SV Wave Propagation in Heterogeneous Media: Velocity-stress Finite-difference Method P-sv wave propagation in heterogeneous media: Velocity-stress finite-difference method . Geophysics 51 4 889--901 . APACre...

    1986 doi

  101. [109]

    \ Operto, S

    virieux_2009_Overview APACrefauthors Virieux, J. \ Operto, S. APACrefauthors \ 2009 . An Overview of Full-Waveform Inversion in Exploration Geophysics An overview of full-waveform inversion in exploration geophysics . Geophysics 74 6 WCC1-WCC26 . APACrefDOI doi:10.1190/1.32383...

    2009 doi

  102. [110]

    APACrefauthors \ 2002

    vogel_2002_Computational APACrefauthors Vogel, C R. APACrefauthors \ 2002 . Computational Methods for Inverse Problems Computational methods for inverse problems \ ( 23). Philadelphia Society for Industrial and Applied Mathematics

    2002

  103. [111]

    \ Etgen, J

    vyas_2022_FWI APACrefauthors Vyas, M. \ Etgen, J. APACrefauthors \ 2022 . FWI by Utilizing the Diversity of Local Minima Fwi by utilizing the diversity of local minima . Second International Meeting for Applied Geoscience & Energy Second international meeting for applied geosc...

    2022 doi

  104. [112]

    , Huang, X

    wang_2023_Prior APACrefauthors Wang, F. , Huang, X. \ Alkhalifah, T. APACrefauthors \ 2023 . A Prior Regularized Full Waveform Inversion Using Generative Diffusion Models A prior regularized full waveform inversion using generative diffusion models . IEEE Transactions on Geosc...

    2023

  105. [113]

    , Jiang, Y

    wang_2023_Memory APACrefauthors Wang, S. , Jiang, Y. , Song, P. , Tan, J. , Liu, Z. \ He, B. APACrefauthors \ 2023 . Memory Optimization in RNN-Based Full Waveform Inversion Using Boundary Saving Wavefield Reconstruction Memory optimization in rnn-based full waveform inversion...

    2023

  106. [114]

    , McMechan, G A

    wang_2021_Elastic APACrefauthors Wang, W. , McMechan, G A. \ Ma, J. APACrefauthors \ 2021 . Elastic Isotropic and Anisotropic Full-Waveform Inversions Using Automatic Differentiation for Gradient Calculations in a Framework of Recurrent Neural Networks Elastic isotropic and an...

    2021 doi

  107. [115]

    , Bovik, A

    wang_2004_Image APACrefauthors Wang, Z. , Bovik, A. , Sheikh, H. \ Simoncelli, E. APACrefauthors \ 2004 . Image Quality Assessment: From Error Visibility to Structural Similarity Image quality assessment: From error visibility to structural similarity . IEEE Transactions on Im...

    2004

  108. [116]

    , Ratcliffe, A

    warner_2013_Anisotropic APACrefauthors Warner, M. , Ratcliffe, A. , Nangoo, T. , Morgan, J. , Umpleby, A. , Shah, N. Bertrand, A. APACrefauthors \ 2013 . Anisotropic 3D Full-Waveform Inversion Anisotropic 3d full-waveform inversion . Geophysics 78 2 R59-R80 . APACrefDOI doi:10...

    2013 doi

  109. [117]

    , Luo, J

    wu_2014_seismic APACrefauthors Wu, R S. , Luo, J. \ Wu, B. APACrefauthors \ 2014 . Seismic Envelope inversion and modulation signal model Seismic envelope inversion and modulation signal model . Geophysics 79 3 WA13--WA24

    2014

  110. [118]

    , Bai, L

    xiao_2024_FengWu4DVar APACrefauthors Xiao, Y. , Bai, L. , Xue, W. , Chen, K. , Han, T. \ Ouyang, W. APACrefauthors \ 2024 . FengWu-4DVar: Coupling the Data-Driven Weather Forecasting Model with 4D Variational Assimilation Fengwu-4dvar: Coupling the data-driven weather forecast...

    2024 arXiv

  111. [119]

    , Chauris, H

    xie_2024_Stochastic APACrefauthors Xie, Y. , Chauris, H. \ Desassis, N. APACrefauthors \ 2024 . Stochastic Full Waveform Inversion with Deep Generative Prior for Uncertainty Quantification Stochastic full waveform inversion with deep generative prior for uncertainty quantifica...

    2024 doi arXiv

  112. [120]

    , Zhu, H

    xue_2017_Fullwaveform APACrefauthors Xue, Z. , Zhu, H. \ Fomel, S. APACrefauthors \ 2017 . Full-Waveform Inversion Using Seislet Regularization Full-waveform inversion using seislet regularization . Geophysics 82 5 A43-A49 . APACrefDOI doi:10.1190/geo2016-0699.1 APACrefDOI

    2017 doi

  113. [121]

    , Gao, J

    yang_2014_RTM APACrefauthors Yang, P. , Gao, J. \ Wang, B. APACrefauthors \ 2014 . RTM using effective boundary saving: A staggered grid GPU implementation Rtm using effective boundary saving: A staggered grid gpu implementation . Computers & Geosciences 68 64-72 . APACrefDOI ...

    2014 doi

  114. [122]

    , Engquist, B

    yang_2018_Application APACrefauthors Yang, Y. , Engquist, B. , Sun, J. \ Hamfeldt, B F. APACrefauthors \ 2018 . Application of Optimal Transport and the Quadratic Wasserstein Metric to Full-Waveform Inversion Application of optimal transport and the quadratic wasserstein metri...

    2018 doi

  115. [123]

    , Bozda g , E

    zhu_2015_seismic APACrefauthors Zhu, H. , Bozda g , E. \ Tromp, J. APACrefauthors \ 2015 . Seismic structure of the European upper mantle based on adjoint tomography Seismic structure of the european upper mantle based on adjoint tomography . Geophysical Journal International ...

    2015

  116. [124]

    zhu_2021_General APACrefauthors Zhu, W. , Xu, K. , Darve, E. \ Beroza, G C. APACrefauthors \ 2021 . A General Approach to Seismic Inversion with Automatic Differentiation A general approach to seismic inversion with automatic differentiation . Computers & Geosciences 151 10475...

    2021

  117. [125]

    zhu_2022_Integrating APACrefauthors Zhu, W. , Xu, K. , Darve, E. , Biondi, B. \ Beroza, G C. APACrefauthors \ 2022 . Integrating Deep Neural Networks with Full-Waveform Inversion: Reparameterization, Regularization, and Uncertainty Quantification Integrating deep neural networ...

    2022 doi

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.