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Quantifying the influence of fault geometry via mesh morphing with applications to earthquake dynamic rupture and thermal models of subduction

T0 review · 2 major / 8 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Deforming one mesh into many fault geometries produces simulation outputs accurate enough to train fast surrogate models for geometric uncertainty.

desk verdict A careful, honest methods paper that makes geometric UQ practical for rupture and subduction thermal models; needs a revision to fix the Slab2 validation gap and the speedup arithmetic. read the letter →

arxiv 2506.15892 v1 pith:JNKRIWNG submitted 2025-06-18 physics.geo-ph

Gabrielle M. Hobson , Dave A. May , Alice-Agnes Gabriel This is my paper · ORCID
classification physics.geo-ph
keywords meshmorphingreduced-ordermodelsdynamicrupturesubductionthermalstructuresensitivityanalysisuncertaintyquantificationradialbasisfunctionsfaultdip
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

This paper seeks to establish that RBF-based mesh morphing, which deforms a single reference mesh into many geometric configurations while preserving mesh connectivity, is a practical and general tool for quantifying geometric uncertainty in computational geophysics. The authors show that morphed meshes for 3D dynamic earthquake rupture (fault dip from 40 to 80 degrees) and 2D subduction thermal models (slab curvature and Slab2 depth uncertainty) retain acceptable quality, and that simulations on them closely match results from exactly generated meshes. Because connectivity is preserved, the outputs can train data-driven reduced-order models, which reproduce full-model behavior with errors of roughly 1e-3 m/s in receiver velocities and at most 0.007 m in held-out surface displacement, at speedups up to 1e9 times. If true, this makes geometric sensitivity analysis and uncertainty quantification feasible for problems that were previously limited by manual remeshing and computational cost.

What carries the argument

The central object is the RBF mesh-morphing interpolant: displacements prescribed along boundary and interface curves or surfaces are interpolated by radial basis functions (linear kernel augmented with a polynomial basis), then evaluated at every mesh vertex to displace the whole mesh without changing connectivity. Successive morphing steps enforce geometric constraints such as fault planarity, uniform slab width, and straight subdomain boundaries. The preserved connectivity is what makes the output suitable for data-driven ROMs built from proper orthogonal decomposition, allowing snapshots from different geometries to share a common representation.

What would settle it

Re-run the dip study on the unmodified TPV13 benchmark: if rupture fails to nucleate for dips outside 55–63 degrees, or if a ROM trained on modified-benchmark runs fails to match unmodified-benchmark surface displacements within the reported 0.007 m error, the dip-sensitivity and ROM conclusions hold only for the tuned setup.

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Extended reading notes

Core claim

The central claim is that mesh morphing preserving connectivity yields simulation outputs suitable both as accurate replacements for exact-mesh runs and as training data for non-intrusive reduced-order models. For the TPV13-3D dynamic rupture benchmark, morphed faults with dip between 40 and 80 degrees lie within 140–150 m of exactly meshed faults, which is comparable to the local mesh resolution, and simulated receiver velocities agree to roughly 1e-3 m/s RMS. A correction step keeps the morphed fault planar to within 1 m. Using interpolated proper orthogonal decomposition with a quintic RBF interpolant on POD coefficients, a surface-displacement ROM evaluated at held-out dips between 50.5 and 69.5 degrees reaches a maximum L-infinity error of 0.007 m. For subduction thermal models, morphing slab curvature over the global range changes slab-interface temperature by up to 85 K, while morphing within Slab2 depth uncertainty changes it by up to 40 K.

Load-bearing premise

The dip-sensitivity and ROM results depend on modifying the TPV13 benchmark by lowering the nucleation static friction from 0.54 to 0.48 and the bulk cohesion from 5e6 to 1e6 Pa, because under the unmodified benchmark rupture nucleates only for dips in 55–63 degrees.

Editorial extensions

If this is right

  • Geometric uncertainty quantification becomes practical for dynamic rupture and subduction thermal models, as ensembles of morphed meshes can be generated in tens of seconds on a laptop without manual remeshing.
  • Reduced-order models trained on morphed-mesh outputs can replace full simulations for rapid sensitivity analysis, with evaluations in about 1e-4 seconds and speedups of 1e8 to 1e9 relative to forward models.
  • Fault dip is shown to be a first-order control on surface ground motion, with vertical displacement varying by up to 2.9 m across the 50–70 degree dip range at the final simulation time.
  • Slab interface curvature across the global range changes slab-interface temperatures by up to 85 K, and Slab2 depth uncertainty translates to at most 40 K of temperature uncertainty, with a mean of 22 K above 150 km depth.
  • The general, solver-agnostic nature of the approach suggests it can extend to other mesh-based geophysical simulations and, with careful treatment of intersections, to multi-fault systems.

Reading between the lines

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

  • A natural extension not demonstrated in the paper is simultaneous morphing of multiple geometric parameters (e.g., dip and strike, or curvature and depth), which would allow higher-dimensional geometric uncertainty quantification with the same connectivity-preserving framework.
  • Because the reordering permutation fixes the local-time-stepping output ordering, the methodology likely carries over to other solvers that permute output, enabling ROM construction without modifying the forward code.
  • The reported temperature sensitivities could be propagated into derived quantities such as dehydration depths or the thermally controlled seismogenic zone limits, which the paper leaves implicit.
  • A useful cross-check would be to compare morphed-mesh dip sensitivities against an independently generated set of meshes without connectivity constraints at matched resolution, to isolate geometric accuracy from discretization error common to both morphed and exactly generated meshes.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 8 minor

Summary. The manuscript presents an RBF-based mesh morphing workflow that deforms a reference mesh to represent different geometric configurations while preserving connectivity, and demonstrates it in two applications: 3D dynamic rupture (varying fault dip theta in a TPV13-style model) and 2D subduction thermal modeling (varying slab curvature alpha and Slab2-uncertainty scaling beta). For the dynamic rupture case, the authors compare accumulated slip, peak slip rate, 12 receiver velocity traces, and uplift profiles between morphed and exactly generated meshes, and build interpolated POD (iPOD) ROMs for receiver velocity and surface displacement, validating via leave-one-out cross-validation and held-out dips with a maximum reported error of 0.007 m. For the thermal case, they compare temperature-depth curves for the curvature parameterization and report mesh quality and geometric accuracy for the Slab2 uncertainty case. The central claim is that mesh morphing preserves connectivity and yields simulation outputs matching exactly generated meshes, thereby enabling ROM-based geometric sensitivity analysis.

Significance. If verified, this is a substantial methodological contribution: it removes the manual meshing bottleneck for geometric ensembles and, because connectivity is preserved, enables non-intrusive ROMs for geometric parameters. The verification is unusually thorough for a methods paper: exact-mesh comparisons cover multiple output quantities, ROM validation includes leave-one-out cross-validation and genuinely held-out dip values, and the code and data are openly archived. The Slab2 uncertainty example, however, currently lacks an exact-mesh thermal comparison, and the dynamic rupture sensitivity analysis relies on modified TPV13 parameters; both points need to be addressed before the claims in the abstract and conclusions are fully supported.

major comments (2)
  1. [Section 4.4 (Slab2 uncertainty example)] The Slab2 uncertainty example reports geometric accuracy (maximum 5-5.5 km offset in the upper 10-20 km of the mesh) and thermal variability (up to 40 K, mean 22 K above 150 km depth), but it never compares thermal simulation output on morphed meshes against simulations on exactly generated meshes. This is the only application in which the central claim of the abstract, that morphed meshes lead to accurate simulation results that closely match those obtained using exactly generated meshes, is not verified. Because the geometric error is concentrated exactly where the temperature variability is largest, the reported 40 K variability could be partly attributable to morphing error rather than to Slab2 depth uncertainty. Please run the thermal model on the exact meshes for the beta values and report the interface temperature and temperature-depth comparisons.
  2. [Section 3 and Table S3] The dip range theta in [50,70] degrees used for the ROMs and the sensitivity analysis is only accessible after modifying two TPV13 benchmark parameters: the nucleation-patch static friction coefficient is lowered from 0.54 to 0.48 and the bulk cohesion from 5.0e6 to 1.0e6 Pa. With the unmodified benchmark, rupture nucleates only for theta in [55,63] degrees. The paper should test whether the reported dip sensitivity and ROM accuracy are robust to the specific way the parameter space is widened (e.g., by instead changing the prestress or nucleation size), or should state explicitly that the dip-sensitivity conclusions are conditional on the modified setup. Without such a test or caveat, the quantitative statements about dip control of surface displacement are tied to a tuned model rather than to the published TPV13 benchmark.
minor comments (8)
  1. [Section 3.3] The text reports a slight over-prediction of accumulated slip of 0.3 m/s at t = 1 s; accumulated slip has units of meters, so the stated units appear to be a typo and should be corrected.
  2. [Section 5.1 and Table 3] The text states that leave-one-out cross-validation errors are low for theta in [52,68] degrees, while Table 3 defines the interior as theta_int = [53,57] degrees; please reconcile these ranges.
  3. [Sections 5.1 and 5.2] The number of retained POD modes is never reported; since this is a tunable parameter of the ROM construction, please specify it for each ROM and ideally show the sensitivity of the cross-validation error to the truncation rank.
  4. [Section 4.4.4] The phrase 'Between 0 and 150 km depths' should read 'between 0 and 150 km depth', and the sentence reporting a mean variability of 3 K should explicitly state that this applies below 150 km depth.
  5. [Figure 12] The caption does not identify the color or line mapping for the different alpha values; please add a legend or describe the mapping in the caption.
  6. [Section 2.1] In the definition of discretization, 'dented by triangle' appears to be a typographical error for 'denoted by triangle'.
  7. [Table 2] The mesh quality metrics for theta = 70 and theta = 80 are identical in the table; if this reflects symmetry or rounding, please state this explicitly.
  8. [Section 5.2] The text refers to 'vertical ground velocity u_z' while the ROM is for vertical displacement at the final time step; please use consistent terminology throughout the section.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: morphing accuracy is benchmarked against independent exact meshes and ROMs are tested on held-out parameter values.

full rationale

The paper's central claim is that mesh morphing preserves connectivity while reproducing exactly generated mesh results. This is tested, not assumed: morphed-mesh fault locations are compared against independently generated GMSH meshes (Secs. 3.1, 4.3.3, 4.4.3), and dynamic rupture and thermal outputs on morphed meshes are compared with outputs on exactly generated meshes (Sec. 3.3, Fig. 12). The ROMs are data-driven surrogates trained on FOM snapshots at integer dips and validated by leave-one-out cross-validation and by held-out half-integer dips (Sec. 5.2, max error 0.007 m). Geometry parameters (dip θ, curvature α, Slab2 uncertainty fraction β) are prescribed inputs, not fitted outputs. The only notable self-citations are to Hobson and May (2025) for the thermal model and to the companion code repository; these provide the solver and data, not the target conclusion, so they are not load-bearing. A validation gap exists in the Slab2 example (Sec. 4.4), where geometric accuracy is checked but no thermal simulation on exactly generated meshes is compared to the morphed-mesh thermal output; this is a completeness/correctness limitation, not circularity. Similarly, the TPV13 parameter modification (lowered nucleation friction and cohesion) is a stated modeling choice affecting the domain of validity, not a fitted quantity renamed as a prediction.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The method introduces no new physical entities. It relies on standard RBF interpolation and domain assumptions from prior literature (TPV13, England and May slab parameterization, Slab2, and Hobson and May thermal model). Two benchmark parameters (nucleation friction and bulk cohesion) are modified to make the dynamic rupture demonstration work, and the ROM truncation rank is an unstated modeling choice.

free parameters (3)
  • Nucleation patch static friction coefficient = 0.48 (TPV13 benchmark: 0.54)
    Reduced in Table S3 to enable rupture nucleation over theta in [50,70] degrees; this modifies the benchmark and directly affects the dip sensitivity and ROM results.
  • Bulk cohesion = 1.0e6 Pa (TPV13 benchmark: 5.0e6 Pa)
    Changed in Table S3; an additional modification to the benchmark plasticity parameters that is required to make the demonstration work.
  • POD truncation rank = not reported
    The number of retained POD modes for the reduced-order models is not stated in the paper; ROM accuracy depends on this choice.
assumptions (6)
  • standard math RBF interpolation with the linear kernel augmented with a polynomial basis yields a unique and smooth displacement field.
    Section 2.2, Equation (4), after Sieger et al. (2014); this is the mathematical foundation of the morphing method.
  • domain assumption TPV13-3D benchmark (Harris et al., 2018) is a valid reference case for dynamic rupture verification.
    Section 3; rupture and off-fault outputs from morphed meshes are compared against exactly meshed TPV13 simulations.
  • domain assumption The parabolic form y = -alpha x^2 from England and May (2021) describes slab interface geometry with RMS misfit less than Slab2 depth uncertainty.
    Section 4.3, Equation (5); used to generate global curvature variability, and acknowledges that this parameterization simplifies real 3D slab shapes.
  • domain assumption Slab2 vertical depth uncertainties (Hayes et al., 2018) are the relevant geometric uncertainties, with horizontal uncertainty negligible.
    Section 4.4 and Supporting Information S1; the beta morphing moves the interface vertically by beta times the reported standard deviation, ignoring horizontal uncertainty.
  • domain assumption The kinematic-dynamic thermal model and its parameter values from Hobson and May (2025) are a valid description of subduction zone thermal structure.
    Section 4.1; the model solves conservation of mass, momentum, and energy with temperature- and strain-rate dependent viscosity, and is inherited from prior work.
  • domain assumption Mesh quality metrics (AR, SJ, MA) with thresholds such as AR < 20-40 for SeisSol are sufficient to guarantee simulation accuracy.
    Sections 2.3 and 3.1; mesh quality is verified with these metrics, but the link between these geometric measures and physical simulation accuracy is empirical and application-specific.

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Pith. "Pith review of Quantifying the influence of fault geometry via mesh morphing with applications to earthquake dynamic rupture and thermal models of subduction." pith.science (2026). https://pith.science/paper/JNKRIWNG

@misc{pith2026250615892,
  author       = {Pith},
  title        = {Pith review of: Quantifying the influence of fault geometry via mesh morphing with applications to earthquake dynamic rupture and thermal models of subduction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JNKRIWNG}},
  note         = {Machine review of arXiv:2506.15892}
}
abstract

Subsurface geometries are often poorly constrained, yet they exert first-order control on key geophysical processes, including subduction zone thermal structure and earthquake rupture dynamics. Quantifying model sensitivity to geometric variability remains challenging due to the manual effort of mesh generation and the computational cost of exploring high-dimensional parameter spaces in high-fidelity simulations. We present a mesh morphing approach that deforms a reference mesh into geometrically varying configurations while preserving mesh connectivity. This enables the automated generation of large ensembles of geometrically variable meshes with minimal user input. Importantly, the preserved connectivity allows for the application of data-driven, non-intrusive reduced-order models (ROMs) to perform robust sensitivity analysis and uncertainty quantification. We demonstrate mesh morphing in two geophysical applications: (i) 3D dynamic rupture simulations with fault dip angles varying across a 40{\deg} range, and (ii) 2D thermal models of subduction zones incorporating realistic slab interface curvature and depth uncertainties informed by the Slab2 geometry dataset. In both cases, morphed meshes retain high quality and lead to accurate simulation results that closely match those obtained using exactly generated meshes. For the dynamic rupture case, we further construct ROMs that efficiently predict surface displacement and velocity time series as functions of fault geometry, achieving speedups of up to $10^9 \times$ relative to full simulations. Our results show that mesh morphing can be a powerful and generalizable tool for incorporating geometric uncertainty into physics-based modeling. The method supports efficient ensemble modeling for rigorous sensitivity studies applicable across a range of problems in computational geophysics.

Figures

Figures reproduced from arXiv: 2506.15892 by the authors.

Figure 1
Figure 1. Mesh morphing applied to a simple 2D geometry: (a) shows the initial geometry G1 with mesh M1, while (b) shows the displacement field D required to morph M1 into a new configuration, shown in (c), where M2 is the morphed mesh representative of the target geometry G2. use of robust global sensitivity analysis techniques requiring many model evaluations. Reduced-order modeling is a well-established approach in enginee… view at source ↗
Figure 2
Figure 2. The angle θ is the geometric parameter (e.g., q = (θ)), and the objective is to morph a reference mesh M1 with vertices XM defined for some angle θ1 into a new mesh M2 with vertices Xˆ M which has an embedded plane at a different angle θ2. To begin, points Xqref are defined, which lie on the boundaries and interface (the embed￾ded plane) of the reference geometry ( [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 2
Figure 2. Illustration of the mesh morphing method. (a) The reference geometry, in black, as well as points Xqref which lie on Γ0, in green, and those which lie on Γa, in blue. (b) The new geometry, in black, as well as points Xqnew which lie on Γ0, in green, and those which lie on Γa, in blue. (c) the reference mesh in gray, with vertices XM, and the displacement applied to each vertex, DM. (d) The morphed mesh, Xˆ M. –16– … view at source ↗
Figures from the paper (15 more)
Figure 3
Figure 3. Figure 3: Subpanel (a): the TPV13 geometry. The fault trace is highlighted in orange, the boundary of the nucleation patch is in blue, and the fault dip is in purple. The union of all outer surfaces is denoted SA, while the surface defining the embedded fault plane is SF , and t…
Figure 4
Figure 4. Figure 4: The reference mesh (θ = 60◦ ) shown from a side on view (a) and angled view (b). The morphed mesh with θ = 40◦ is shown in (c) and (d). Faults are colored as in [PITH_FULL_IMAGE:figures/full_fig_p022_4.png]
Figure 5
Figure 5. Figure 5: Accumulated slip (ASl) on the fault for θ = 70◦ . The left column shows output from exactly generated meshes, while the center column shows output from morphed meshes. The right column shows contour plots with both exact and morphed output interpolated to the same mesh…
Figure 6
Figure 6. Figure 6: Measured components of velocity at 5 of the receivers for θ = 50◦ . Output from the exactly generated mesh is in black, while output from the morphed mesh is in orange. tured triangular mesh, locally refined near the slab interface, created using the same GMSH version …
Figure 7
Figure 7. Figure 7: (a) The subdomains used in 2D subduction models, where SA, SB, and SC cor￾respond to the slab, overlying plate, and mantle wedge respectively. The model domain is given by SD = SA ∪ SB ∪ SC . (b) The slab interfaces obtained using Equation (5) for α ∈ [PITH_FULL_IMAGE…
Figure 8
Figure 8. Figure 8: Boundaries of the mesh after each successive morph is applied, with the full domain in panel (a) and insets shown in panels (b) and (c). Boundaries are colored according to whether they are moved when a particular correction is applied. the reference mesh, while smalle…
Figure 9
Figure 9. Figure 9: The mesh morphing method applied to a coarse subduction zone reference mesh for different values of α. Middle panel: Reference mesh using α = 1.75 × 10−3 = αref with cell diameter of ∼30 km. Top panel: α = 3.5 × 10−3 > αref. Bottom panel: α = 0.5 × 10−3 < αref. In the …
Figure 10
Figure 10. Figure 10: Bar plots of the mesh quality as α varies, measured by (a) the Aspect Ratio (AR), (b) the Scaled Jacobian (SJ), and (c) the Minimum Angle (MA) metrics. The ideal values for each metric is shown by the dotted green line, and the mesh quality for the reference (not mor￾…
Figure 11
Figure 11. Figure 11: Boundaries of the morphed meshes as α varies (solid lines), with the reference mesh boundaries shown in black and the exact slab interface points as scatter plots. parison between timings for mesh morphing and exact mesh generation to illustrate the computational feas…
Figure 12
Figure 12. Figure 12: Temperature vs. depth curves as α varies, with the morphed mesh results shown in solid lines and values from the exactly generated meshes shown as scatter plots. 4.3.4 Temperature Variability The slab interface temperatures in [PITH_FULL_IMAGE:figures/full_fig_p035_12.png]
Figure 13
Figure 13. Figure 13: Boundaries of the morphed meshes as β varies (solid lines), with the reference mesh boundaries shown in black and the exact slab interface points as scatter plots. 5 Reduced-Order Models for Dynamic Rupture Output with Geomet￾ric Variability A central requirement of t…
Figure 14
Figure 14. Figure 14: Time series of ground velocity at 5 of the TPV13-3D off-fault receivers for θ = 54◦ , with the simulated velocity on a morphed mesh shown in black and the ROM ap￾proximation shown in blue. Scatter points in orange show the solution for a simulation on an exact mesh wi…
Figure 15
Figure 15. Figure 15: Full order model (FOM) vs. reduced order model (ROM) approximations of the vertical ground velocity component uz for a fault dip of θ = 52.5 ◦ . The maximum error is re￾ported in blue text. –43– [PITH_FULL_IMAGE:figures/full_fig_p043_15.png]
Figure 16
Figure 16. Figure 16: Mean field, standard deviation, and maximum variability as dip varies, for vertical ground velocity uz at simulation time t = 8 seconds. erate geometrically varying meshes must be balanced against potential increases in nu￾merical simulation time and decreases in accu…
Figure 17
Figure 17. Figure 17: Mesh quality for a morphed mesh with θ = 13◦ , shown from (a) a side-on view with the fault in light green, and (b) an angled view with a summary of the mesh quality infor￾mation. tetrahedral cells with higher AR values. We note that a morph from 60◦ to 89◦ does not d…

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.