TomoATT: An open-source package for Eikonal equation-based adjoint-state traveltime tomography for seismic velocity and azimuthal anisotropy

Jing Chen; Masaru Nagaso; Mijian Xu; Ping Tong

REVIEW 4 major objections 7 minor 10 references

TomoATT: An open-source package for Eikonal equation-based adjoint-state traveltime tomography for seismic velocity and azimuthal anisotropy

T0 review · 4 major / 7 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read TomoATT packages Eikonal-based adjoint-state tomography for velocity and azimuthal anisotropy into an open-source, three-file workflow that runs regional and teleseismic inversions in under two hours on 64 processors.

desk verdict A well-engineered open-source tomography package; the synthetic validation is internally consistent but thin, and the real-data sections need resolution tests before 'effectiveness' is fully earned. read the letter →

arxiv 2412.00031 v1 pith:PKYQHAJD submitted 2024-11-21 physics.geo-ph

Jing Chen , Masaru Nagaso , Mijian Xu , Ping Tong This is my paper · ORCID

classification physics.geo-ph

keywords TomoATTadjoint-statetraveltimetomographyEikonalequationazimuthalanisotropyseismicfastsweepingmethodteleseismicregional

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

The paper presents TomoATT, an open-source package that performs regional and teleseismic traveltime tomography by solving the anisotropic Eikonal equation for synthetic traveltimes and using the adjoint-state method to compute volumetric sensitivity kernels. The central claim is that this implementation makes adjoint-state tomography practical: an inversion starts from three input files, runs to completion in under two hours on 64 processors, and recovers both isotropic velocity structure and azimuthal anisotropy. The claim is supported by toy experiments on forward modeling, multipathing, regularization, and parallelization, plus a synthetic inversion and two real-data benchmarks in central California near Parkfield and in Thailand. The paper argues that agreement of the real-data images with regional tectonics and earlier studies verifies the package's effectiveness.

What carries the argument

The central object is the adjoint-state traveltime tomography workflow, built on the anisotropic Eikonal equation in spherical coordinates, $\nabla T^t M(\mathbf{x};\xi,\eta)\nabla T = s^2(\mathbf{x})$, solved with the fast sweeping method and multiplicative factorization. The adjoint equation $\nabla\cdot(P(\mathbf{x}) M(-\nabla T)) = \sum_m R_m \delta(\mathbf{x}-\mathbf{x}_m)$ turns receiver misfits into volumetric sensitivity kernels $K_s, K_\xi, K_\eta$, which are then projected onto coarse multiple-grid basis functions and normalized by kernel density. This combination is what lets the package handle multipathing, avoid ray-path undersampling, and regularize uneven data coverage.

What would settle it

A controlled synthetic inversion on the same grid spacings as the real-data cases (for example, $5$ km $\times$ $5$ km $\times$ $1$ km) using a strongly heterogeneous model with sharp velocity contrasts and realistic noise levels would settle the accuracy question: if reconstructed anomalies are smeared or displaced beyond the grid scale, or if traveltime residuals exceed the forward-model errors reported in Section 3.1, the claimed effectiveness for real Earth would be undercut.

Watch

Extended reading notes

Core claim

TomoATT's core claim is that Eikonal equation-based adjoint-state traveltime tomography can be packaged as an efficient, user-friendly tool for routine seismic imaging. It solves for slowness $s(\mathbf{x})$ and azimuthal anisotropy parameters $\xi(\mathbf{x})$, $\eta(\mathbf{x})$ by minimizing a weighted sum of traveltime, common-source differential, and common-receiver differential misfits. Each iteration solves the anisotropic Eikonal equation for every source (or, via reciprocity, every receiver), solves the adjoint equation to obtain gradient kernels, and updates model parameters by step-size-controlled gradient descent with multiple-grid parameterization and kernel density normalization. The synthetic experiment recovers staggered velocity and anisotropy perturbations, while the two real-data inversions reproduce features such as the velocity contrast across the San Andreas Fault and the high-velocity Khorat Plateau lithosphere. From these results the paper concludes that TomoATT is a verified, efficient tool for both regional and teleseismic tomography.

Load-bearing premise

The load-bearing premise is that the fast sweeping Eikonal solver, validated only on simple synthetic models and the AK135 teleseismic test, remains accurate enough on the moderately coarse inversion grids used for the real-data benchmarks to produce trustworthy sensitivity kernels in strongly heterogeneous crust and mantle.

Editorial extensions

If this is right

Regional and teleseismic inversions can be set up from three files, so the package removes much of the scripting burden in traveltime tomography.
The source-receiver reciprocity trick reduces the Parkfield inversion to 607 Eikonal solves per iteration instead of 32,721, making 80 iterations feasible in 57 minutes.
Multiple-grid parameterization and kernel density normalization let the inversion recover anomalies in sparsely sampled regions while suppressing parameter-count artifacts.
The same machinery relocates hypocenters, so simultaneous inversion can avoid the artifacts shown when source locations are inaccurate.
Users can image azimuthal anisotropy as well as isotropic velocity from first P arrivals, enabling stress and fabric interpretation near faults.

Reading between the lines

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

If the claimed two-hour turnaround holds on typical HPC nodes, adjoint-state Eikonal tomography could become a routine replacement for ray-based tomography in regional networks, where kernel accuracy and multipathing have been the main barriers.
The kernel density normalization trades noise amplification against anomaly recovery; the paper shows that high $\zeta$ values can create artifacts in poorly constrained regions, so an adaptive or data-driven choice of $\zeta$ would be a natural extension.
The solver validation suggests that users on coarser grids or in very strong-contrast media should first run the package's traveltime-error tests on their own models before trusting recovered anomalies.
Because the package is open source and supports YAML, HDF5, and TEXT formats, it could serve as a building block for joint inversions or full-waveform approaches that need a fast, trustworthy traveltime prior.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

TomoATT is a real contribution, but it is a contribution of integration and packaging, not new theory. The methods (adjoint-state traveltime tomography, Eikonal solver, multiple-grid parameterization, kernel density normalization) all come from the authors' earlier papers. What is new here is a well-engineered open-source C++ package with a Python companion, multi-level MPI parallelization, and a clean three-file input interface. That is a legitimate and useful thing to publish, and the paper does it honestly: the code is GPL-licensed, the documentation is linked, and the run times on real problems are reported.

The forward modeling checks are the strongest part. Errors against an analytic linear model converge at first order, and the teleseismic differential times agree with TauP to 0.03 s standard deviation. The toy experiment in Section 3.3 includes noise and shows the multiple-grid and kernel density regularization actually do something. The parallelization benchmark is straightforward and useful for people choosing job sizes.

The soft spots are real but not disqualifying. The synthetic case study in Section 4.1 generates noise-free data with the same Eikonal solver and the same grid used in the inversion, so it is an inverse-crime test. It verifies that the code is internally consistent and that the relocation loop works, but it does not by itself demonstrate robustness to real data errors. The real-data images for Parkfield and Thailand reproduce structures seen in independent studies, which is meaningful, but neither case includes formal resolution tests, checkerboard recovery on the actual acquisition geometry, or uncertainty estimates. The 'strict data selection criteria' are deferred to prior papers, so a reader cannot fully audit the input data. And the kernel density normalization exponent zeta is a free parameter with a known noise-amplification trade-off, which the paper acknowledges but does not quantify for the real cases.

None of this undermines the package's usefulness. The paper is exactly what a software paper should be: it tells the community what the code does, shows the components work, and points to the code. The verification could be stronger, but for a package whose methods have already been peer-reviewed, this is enough to justify publication. I would send it to review with a request for a resolution/uncertainty discussion in the real-data sections and a note in Section 4.1 clarifying that the synthetic test is a code-consistency check, not a physical validation.

Worth citing if you work in traveltime tomography, and worth bringing to a reading group that cares about reproducible seismic imaging.

Referee Report

4 major / 7 minor

Summary. The manuscript presents TomoATT, an open-source C++/Python package for Eikonal-equation-based adjoint-state traveltime tomography for seismic velocity and azimuthal anisotropy. It reviews the mathematical formulation (objective function with traveltime and differential arrival times, anisotropic Eikonal equation, adjoint-state kernels, multiple-grid parameterization, kernel density normalization), describes the multi-level parallelization architecture, and demonstrates the package through toy experiments, a synthetic inversion with earthquake relocation, and two real-data benchmarks (Parkfield, California; Thailand). The central claim is that the package is efficient and user-friendly, with inversions starting from three input files and completing within about two hours on 64 processors, and that synthetic recovery plus consistency with previous studies verifies the package's effectiveness.

Significance. If the central claims are substantiated, TomoATT would be a valuable open-source contribution: it provides a complete workflow for Eikonal-based traveltime tomography, including azimuthal anisotropy, with validated forward modeling, multipathing-aware kernels, and multi-level parallelism. The paper's strengths include the open-source availability under GPLv3, the companion PyTomoATT module, forward-model validation against analytic solutions and TauP (Sections 3.1-3.2), and the reproduction of several independently published structural features in the real-data images. However, as argued in the major comments, the verification of the inversion's physical accuracy is not yet complete, and several reproducibility-critical parameters are not reported.

major comments (4)

[Section 4.1] The synthetic verification is an 'inverse-crime' test. Observational data are generated by the same Eikonal solver on the same grid as used in the inversion, with no added noise. This verifies that the inversion code can invert its own forward operator, but it does not verify robustness to modeling error, data noise, or discretization mismatch. The abstract's claim that 'successful recovery of the synthetic model ... verifies the effectiveness of TomoATT' is therefore too strong. I recommend adding a synthetic test where data are generated on a different (finer) grid or with a different forward solver, or with realistic noise and outlier contamination, and showing recovery statistics.
[Sections 4.2-4.3] The real-data benchmarks lack resolution tests and uncertainty quantification. No checkerboard or spike recovery tests are shown for the Parkfield or Thailand geometries, and the images are presented without any measure of reliability such as model covariance or depth-resolution surfaces. Because the data selection criteria are deferred to Chen et al. (2023) and the regularization choices are not fully reported (see next comment), the reader cannot determine whether the imaged anomalies are required by the data. I recommend adding standard resolution tests (e.g., checkered/spike restorations with the actual station-event geometry) or at least discussing sensitivity to regularization.
[Sections 4.2-4.3 (reproducibility)] The values of the objective-function weights alpha, beta, gamma; the kernel-density exponent zeta in Eq. (18); the multiple-grid configuration H; and the gradient-descent step size are not reported for the two real-data inversions. These parameters have a direct effect on the images (as shown for zeta in Section 3.3), and without them the claimed benchmarks cannot be reproduced, which is a central issue for an open-source package. Please provide the exact parameter files (or a table listing all parameters) for both case studies.
[Section 4] The consistency of the real-data results with 'previous studies' partly refers to the authors' own earlier papers (Chen et al. 2023a,b), since the text states that the two cases were 'detailed in our previous studies.' The comparisons to independent references (e.g., Eberhart-Phillips and Michael, 1993; Thurber et al., 2006; Yang et al., 2015) are more persuasive, but the discussion should clearly separate those independent comparisons from self-comparisons, and ideally add quantitative misfit or correlation metrics rather than qualitative agreement.

minor comments (7)

[Figure 7 caption] 'syntehtic' should be 'synthetic'.
[Figure 6 caption] 'relative the number of processors' should be 'relative to the number of processors'.
[Section 3.3] 'with a standard derivation of 0.1 s' should be 'standard deviation'.
[Section 2.1] Equation numbering is duplicated: two separate equations are labeled (4), the second being the anisotropic Eikonal equation; renumber the equations.
[Keywords] 'teleiseismic' is misspelled; it should be 'teleseismic'.
[Figure 8 caption] 'Figure 8. Figure 8.' is duplicated; remove the repeated text.
[Appendix B] Several equations (B5)-(B11) appear typeset with a heavy or bold font that is inconsistent with the main text; please ensure uniform notation.

Circularity Check

1 steps flagged · score 2.0 of 10

Mild self-referential synthetic benchmark; method equations and real-data comparisons retain independent support.

other [Section 4.1 and Abstract]
"Observational traveltime data are generated using the true model and true earthquake locations. ... The successful recovery of the synthetic model, along with the imaging results that are consistent with previous studies and regional tectonics, verifies the effectiveness of TomoATT."

The synthetic benchmark generates the observations with the package's own Eikonal forward solver, starting from the true model, and then inverts them with the same forward operator to recover that same model. With no independent data or noise specified, the inversion is asked to invert the output of its own forward code, so the target model lies exactly in the representable solution space. A successful recovery therefore mainly demonstrates internal consistency of the forward and inverse routines, not an independent physical prediction; any systematic error in the forward solver is common to both data generation and inversion and cancels out.

full rationale

The paper is primarily a software description that carries the adjoint-state traveltime tomography equations over from the authors' prior publications; this is not circular because the current claims are about implementation performance, and the equations are not re-derived from the conclusions. The Eikonal solver is checked against an analytic solution (Section 3.1) and against TauP for the teleseismic test (Section 3.2), which are external references, and the real-data images are compared with independent studies (Eberhart-Phillips and Michael, Lippoldt et al., Thurber et al., etc.). The main self-referential element is the synthetic experiment in Section 4.1, where data generated with the same forward solver are used to verify recovery of the generating model; this is an inverse-crime style consistency check that would not expose errors shared by the forward and inverse operators. Because the paper does not rely solely on that test and includes independent comparisons, the circularity is mild and partial rather than load-bearing. No fitted parameter is renamed as a prediction, and no uniqueness theorem or ansatz is smuggled in via self-citation.

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

The paper introduces no new physical entities; it is a software implementation. The free parameters are user-chosen hyperparameters and weights, none of which are fitted to data or derived from first principles. The axioms are standard geophysical modeling assumptions and mathematical background.

free parameters (4)

Kernel density normalization exponent zeta = 0.3, 0.6, 0.9 (tested in toy experiment)
Controls the degree of normalization in Eq. (18); the paper notes higher zeta increases anomaly recovery but also magnifies noise, and provides no criterion for choosing it in real-data inversions.
Objective function weights alpha, beta, gamma = Not specified
Weights for traveltime, common-source, and common-receiver misfits in Eq. (1). Their values are never reported, yet they determine the balance between the three data types in the inversion.
Multiple-grid parameterization H and grid node distributions = H not specified; grid for Parkfield 5 km x 5 km x 1 km, Thailand 10 km x 10 km x 5 km
The multiple-grid parameterization (Section 3.3) requires the user to choose H and node locations, which affects smoothing and resolution. The paper does not report H for the real inversions.
Gradient descent step size = Not specified
The step size-controlled gradient descent in Section 2.1 requires a step-size policy; the paper does not describe how step sizes are selected for the benchmarks.

assumptions (5)

domain assumption The anisotropic Eikonal equation with parameters (s, xi, eta) accurately describes first-arrival traveltimes in the crust and upper mantle, including multipathing situations.
Invoked as the forward model in Section 2.1; the inversion's validity depends on this physical model being adequate for real Earth.
standard math The reciprocity principle is valid in the anisotropic medium, allowing station-source swapping to reduce computational cost.
Used in Section 4.2 and Appendix B to solve 607 Eikonal equations instead of 32,721; a standard result but required for the claimed efficiency.
domain assumption The adjoint-state method computes correct sensitivity kernels, including in the presence of multipathing.
The kernels in Eqs. (6)-(8) are quoted from prior work, not derived here; the paper relies on the prior justification.
standard math The fast sweeping method converges to the viscosity solution of the anisotropic Eikonal equation on the chosen meshes.
Relied on in Section 3.1; convergence is cited from Zhao (2005), but the paper only verifies on selected smooth models.
domain assumption The traveltime picks and differential times from public data centers are accurate enough after the 'strict data selection criteria' to constrain the inverted structures.
The real-data inversions (Sections 4.2, 4.3) use data filtered by undisclosed criteria; errors in the picks would map into the tomographic images.

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Cite this review

Pith. "Pith review of TomoATT: An open-source package for Eikonal equation-based adjoint-state traveltime tomography for seismic velocity and azimuthal anisotropy." pith.science (2026). https://pith.science/paper/PKYQHAJD

@misc{pith2026241200031,
  author       = {Pith},
  title        = {Pith review of: TomoATT: An open-source package for Eikonal equation-based adjoint-state traveltime tomography for seismic velocity and azimuthal anisotropy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PKYQHAJD}},
  note         = {Machine review of arXiv:2412.00031}
}

read the original abstract

TomoATT is an open-source software package, aiming at determining seismic velocity and azimuthal anisotropy based on adjoint-state traveltime tomography methods. Key features of TomoATT include Eikonal equation modeling, adjoint-state method, sensitivity kernel regularization, and multi-level parallelization. Through several toy experiments, we demonstrate TomoATT's capability in accurate forward modeling, handling multipathing phenomenon, delivering reliable tomographic results, and achieving high-performance parallelization. Additionally, TomoATT is benchmarked with a synthetic experiment and two real-data applications in central California near Parkfield and Thailand. The successful recovery of the synthetic model, along with the imaging results that are consistent with previous studies and regional tectonics, verifies the effectiveness of TomoATT. Each inversion starts with only three simple input files (about model, data, and parameters) and completes within 2 hours using 64 processors. Overall, TomoATT offers an efficient and user-friendly tool for regional and teleseismic traveltime tomography, empowering researchers to image subsurface structures and deepen our understanding of the Earth's interior.

Figures

Figures reproduced from arXiv: 2412.00031 by the authors.

**Figure 3.** [PITH_FULL_IMAGE:figures/full_fig_p022_3.png] view at source ↗

**Figure 4.** [PITH_FULL_IMAGE:figures/full_fig_p022_4.png] view at source ↗

Figures from the paper (14 more)

**Figure 5.** Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p023_5.png]

**Figure 6.** Figure 6 [PITH_FULL_IMAGE:figures/full_fig_p023_6.png]

**Figure 7.** Figure 7: M [PITH_FULL_IMAGE:figures/full_fig_p023_7.png]

**Figure 8.** Figure 8: Test results in the [PITH_FULL_IMAGE:figures/full_fig_p023_8.png]

**Figure 9.** Figure 9 [PITH_FULL_IMAGE:figures/full_fig_p024_9.png]

**Figure 10.** Figure 10 [PITH_FULL_IMAGE:figures/full_fig_p024_10.png]

**Figure 1.** Figure 1: The workflow of TomoATT to implement adjoint-state traveltime tomography, including anisotropic velocity model determination and earthquake location [PITH_FULL_IMAGE:figures/full_fig_p025_1.png]

**Figure 2.** Figure 2: Validation of the Eikonal solver for calculating traveltime. (a) The true traveltime field 𝑇𝑡𝑟𝑢𝑒(𝒙) calculated in the velocity model. The red star indicates the earthquake. The black curves represent traveltime isochrones at an [PITH_FULL_IMAGE:figures/full_fig_p025_2.png]

**Figure 5.** Figure 5: A toy experiment demonstrating multiple-grid parameterization and kernel density normalization in tomography. (a) Initial velocity model with 8 stations on the surface (blue triangles) and 10,000 unevenly distributed earthquakes. (b) Velocity perturbation of the target…

**Figure 6.** Figure 6: Illustration of multi-level parallelization in TomoATT. (a) Level 1: Source parallelization demonstrates numerically solving Eikonal equations in parallel for two earthquakes. The blue triangles denote stations, and the red star marks the earthquake. Gray circles denot…

**Figure 7.** Figure 7: Model setting of a syntehtic experiment. (a) Velocity perturbation of the true model relative to the initial model. Yellow bars represent azimuthal anisotropy, aligned with fast velocity directions. Blue triangles are stations on the surface. True earthquake hypocenter…

**Figure 8.** Figure 8: Test results in the synthetic experiment. Notations follow [PITH_FULL_IMAGE:figures/full_fig_p030_8.png]

**Figure 9.** Figure 9: Tectonic setting and imaging results in central California near Parkfield. (a) Topography map. Red box outlines the study region. Earthquakes and stations are denoted by red dots and blue triangles, respectively. Black lines mark active faults. (b) Horizontal sections …

**Figure 10.** Figure 10: Tectonic setting and imaging results in Thailand and adjacent regions. (a) Topography map. Black dashed lines denote major faults: DBPF (Dien Bien Phu Fault), WCF (Wang-Chao Fault), and TPF (Three Pagodas Fault). The solid black line indicates the Khorat Plateau. Stat…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

10 extracted references · 10 canonical work pages

[1]

Figure 1: The workflow of TomoATT to implement adjoint -state traveltime tomography, including anisotropic velocity model determination and earthquake location

work page
[2]

(a) The true traveltime field 𝑇𝑡𝑟𝑢𝑒(𝑥) calculated in the velocity model

Figure 2: Validation of the Eikonal solver for calculating traveltime. (a) The true traveltime field 𝑇𝑡𝑟𝑢𝑒(𝑥) calculated in the velocity model. The red star indicates the earthquake. The black curves represent traveltime isochrones at an interval of 20 s. (b) Traveltime errors at surface stations (depth = 0 km) relative to epicenter distance. The blue, ye...

work page
[3]

(a) The teleseismic earthquake (red star) and the study region (red box)

Figure 3: Validation of the Eikonal solver for teleseismic differential arrival time. (a) The teleseismic earthquake (red star) and the study region (red box). Black dashed circles denote epicenter distances of 30∘ and 60∘. (b) Calculated traveltime field within the study region. The blue triangles denote stations deployed on the surface. (c) Histogram of...

work page
[4]

(a) P -wave velocity model

Figure 4: A toy experiment illustrating the multipathing phenomenon. (a) P -wave velocity model. The blue triangles denote stations, and the red star marks the earthquake. White curves represent traveltime isochrones at an interval of 1 s. (b) Sensitivity kernel comp uted with artificial adjoint sources 𝑅𝑛,𝑚 = 1. The adjoint -state short author name: Prep...

work page
[5]

(a) Initial velocity model with 8 stations on the surface (blue triangles) and 10,000 unevenly distributed earthquakes

Figure 5: A toy experiment demonstrating multiple -grid parameterization and kernel density normalization in tomography. (a) Initial velocity model with 8 stations on the surface (blue triangles) and 10,000 unevenly distributed earthquakes. (b) Velocity perturbation of the target model relative to the initial model. (c) Original sensitivity kernel at the ...

work page
[6]

(a) Level 1: Source parallelization demonstrates numerically solving Eikonal equations in parallel for two earthquakes

Figure 6: Illustration of multi-level parallelization in TomoATT. (a) Level 1: Source parallelization demonstrates numerically solving Eikonal equations in parallel for two earthquakes. The blue triangles denote stations, and the red star marks the earthquake. Gray circles denote grid nodes discretizing the computational domain. Level 2: A 2-by-2 domain d...

work page
[7]

(a) Velocity perturbation of the true model relative to the initial model

Figure 7: Model setting of a synthetic experiment. (a) Velocity perturbation of the true model relative to the initial model. Yellow bars represent azimuthal anisotropy, aligned with fast velocity directions. Blue triangles are stations on the surface. True earthquake hypocenters are evenly distributed at depths of 10 km (red dots), 20 km (green dots), an...

work page
[8]

Test results in the synthetic experiment

Figure 8: Figure 8. Test results in the synthetic experiment. Notations follow Figure 7. (a) Test 1: Earthquake locations determined in the true model, verifying the relocation function. (b) Test 2: Earthquake locations determined in the initial model, showing slight deviation due to inaccurate velocity a nd anisotropy. (c) Test 3: Velocity and anisotropi...

work page

Show all 10 references

[9]

(a) Topography map

Figure 9: Tectonic setting and imaging results in central California near Parkfield. (a) Topography map. Red box outlines the study region. Earthquakes and stations are denoted by red dots and blue triangles, respectively. Black lines mark active faults. (b) Horizontal section...
[10]

(a) Topography map

Figure 10: Tectonic setting and imaging results in Thailand and adjacent regions. (a) Topography map. Black dashed lines denote major faults: DBPF (Dien Bien Phu Fault), WCF (Wang -Chao Fault), and TPF (Three Pagodas Fault). The solid black line indicates the Khorat Plateau. S...

Pith tools

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

[1] [1]

Figure 1: The workflow of TomoATT to implement adjoint -state traveltime tomography, including anisotropic velocity model determination and earthquake location

work page

[2] [2]

(a) The true traveltime field 𝑇𝑡𝑟𝑢𝑒(𝑥) calculated in the velocity model

Figure 2: Validation of the Eikonal solver for calculating traveltime. (a) The true traveltime field 𝑇𝑡𝑟𝑢𝑒(𝑥) calculated in the velocity model. The red star indicates the earthquake. The black curves represent traveltime isochrones at an interval of 20 s. (b) Traveltime errors at surface stations (depth = 0 km) relative to epicenter distance. The blue, ye...

work page

[3] [3]

(a) The teleseismic earthquake (red star) and the study region (red box)

Figure 3: Validation of the Eikonal solver for teleseismic differential arrival time. (a) The teleseismic earthquake (red star) and the study region (red box). Black dashed circles denote epicenter distances of 30∘ and 60∘. (b) Calculated traveltime field within the study region. The blue triangles denote stations deployed on the surface. (c) Histogram of...

work page

[4] [4]

(a) P -wave velocity model

Figure 4: A toy experiment illustrating the multipathing phenomenon. (a) P -wave velocity model. The blue triangles denote stations, and the red star marks the earthquake. White curves represent traveltime isochrones at an interval of 1 s. (b) Sensitivity kernel comp uted with artificial adjoint sources 𝑅𝑛,𝑚 = 1. The adjoint -state short author name: Prep...

work page

[5] [5]

(a) Initial velocity model with 8 stations on the surface (blue triangles) and 10,000 unevenly distributed earthquakes

Figure 5: A toy experiment demonstrating multiple -grid parameterization and kernel density normalization in tomography. (a) Initial velocity model with 8 stations on the surface (blue triangles) and 10,000 unevenly distributed earthquakes. (b) Velocity perturbation of the target model relative to the initial model. (c) Original sensitivity kernel at the ...

work page

[6] [6]

(a) Level 1: Source parallelization demonstrates numerically solving Eikonal equations in parallel for two earthquakes

Figure 6: Illustration of multi-level parallelization in TomoATT. (a) Level 1: Source parallelization demonstrates numerically solving Eikonal equations in parallel for two earthquakes. The blue triangles denote stations, and the red star marks the earthquake. Gray circles denote grid nodes discretizing the computational domain. Level 2: A 2-by-2 domain d...

work page

[7] [7]

(a) Velocity perturbation of the true model relative to the initial model

Figure 7: Model setting of a synthetic experiment. (a) Velocity perturbation of the true model relative to the initial model. Yellow bars represent azimuthal anisotropy, aligned with fast velocity directions. Blue triangles are stations on the surface. True earthquake hypocenters are evenly distributed at depths of 10 km (red dots), 20 km (green dots), an...

work page

[8] [8]

Test results in the synthetic experiment

Figure 8: Figure 8. Test results in the synthetic experiment. Notations follow Figure 7. (a) Test 1: Earthquake locations determined in the true model, verifying the relocation function. (b) Test 2: Earthquake locations determined in the initial model, showing slight deviation due to inaccurate velocity a nd anisotropy. (c) Test 3: Velocity and anisotropi...

work page