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arxiv: 2605.16717 · v1 · pith:2GMLTC4Dnew · submitted 2026-05-16 · ⚛️ physics.geo-ph · cs.SD

Radial-Component Predominant-Mode Inversion of Rayleigh Waves: Application to DAS-based Site Characterization

Mrinal Bhaumik , Brady R. Cox This is my paper

Pith reviewed 2026-05-19 20:06 UTC · model grok-4.3

classification ⚛️ physics.geo-ph cs.SD
keywords Rayleigh wavesDistributed Acoustic Sensingdispersion inversionsite characterizationshear wave velocitymodal participationradial componentnear-surface geophysics
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The pith

A radial-component predominant-mode inversion framework matches DAS radial dispersion data to the theoretical Rayleigh mode with highest radial participation, eliminating manual mode indexing for reliable shear-wave velocity profiles.

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

This paper presents a radial-component predominant-mode inversion framework for analyzing Rayleigh waves measured by Distributed Acoustic Sensing. DAS with vertical sources records only the radial component, which can exhibit different dispersion characteristics than vertical measurements, especially in layered ground with velocity changes. The framework identifies the dominant mode by its maximum participation in the radial component rather than relying on analyst interpretation of mode order. Tests on synthetic models with velocity contrasts and two field datasets show it produces shear-wave velocity profiles that align well with borehole measurements. This approach makes inversion less subjective and more suitable for DAS data in site characterization.

Core claim

The RCPM inversion framework is designed for DAS-based surface-wave analysis that explicitly accounts for source-receiver directivity and modal sensitivity of the Rayleigh-wave radial component. It matches measured dominant radial dispersion trends with the theoretical mode exhibiting the maximum modal participation. As a result, the RCPM framework eliminates the need for explicit modal indexing, provides a component-consistent interpretation of radial-component dispersion data, and substantially reduces reliance on subjective analyst-driven modal interpretations while yielding reliable Vs profiles on synthetic and field data.

What carries the argument

Radial-component predominant-mode (RCPM) inversion, which selects the theoretical Rayleigh mode with maximum modal participation in the radial component to represent observed dispersion trends.

If this is right

  • Modal energy distribution differs significantly between vertical and radial components in the presence of strong velocity contrasts and velocity reversals.
  • Conventional inversion approaches may misinterpret modal behavior, resulting in less accurate Vs profiles.
  • The RCPM method consistently captures the correct modal response and yields reliable Vs profiles on synthetic ground models.
  • Application to two field DAS datasets demonstrates good agreement between the inverted Vs profiles and independent invasive borehole measurements.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This component-specific selection could support automated processing pipelines for large-scale DAS deployments along infrastructure corridors.
  • The approach might be extended to hybrid datasets combining radial DAS with vertical geophone records to improve overall model constraints.
  • In geotechnical projects with limited access for drilling, the reduced subjectivity could increase confidence in non-invasive velocity mapping for foundation design.

Load-bearing premise

The theoretical mode with maximum modal participation in the radial component accurately represents the measured dominant radial dispersion trends, particularly under complex stratigraphic conditions with strong velocity contrasts or reversals.

What would settle it

A field site with documented strong velocity reversals where the RCPM-derived Vs profile shows large mismatches with borehole logs or other independent measurements would indicate failure to capture the correct modal response.

read the original abstract

Distributed Acoustic Sensing (DAS) has emerged as a transformative technology for near-surface site characterization. When a vertical source is activated along the fiber, DAS measures only the in-line (radial) component of Rayleigh-wave motion. Dispersion data extracted from radial-component waveforms may differ from those obtained from vertical-component measurements, particularly under complex stratigraphic conditions. Hence, a component-consistent forward problem is desired when inverting radial-component DAS dispersion data to retrieve accurate shear wave velocity (Vs) profiles. This study presents a radial-component predominant-mode (RCPM) inversion framework designed for DAS-based surface-wave analysis that explicitly accounts for source-receiver directivity and modal sensitivity of the Rayleigh-wave radial component. The proposed approach matches measured dominant radial dispersion trends with the theoretical mode exhibiting the maximum modal participation. As a result, the RCPM framework eliminates the need for explicit modal indexing, provides a component-consistent interpretation of radial-component dispersion data, and substantially reduces reliance on subjective analyst-driven modal interpretations. The RCPM approach is systematically evaluated using three synthetic ground models and two field DAS datasets. The synthetic results demonstrate that modal energy distribution differs significantly between vertical and radial components in the presence of strong velocity contrasts and velocity reversals, and that conventional inversion approaches may misinterpret modal behavior, resulting in less accurate Vs profiles. In contrast, the RCPM method consistently captures the correct modal response and yields reliable Vs profiles. Application to two field DAS datasets further demonstrates good agreement between the inverted Vs profiles and independent invasive borehole measurements.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a radial-component predominant-mode (RCPM) inversion framework for DAS-based Rayleigh-wave site characterization. It matches observed dominant radial dispersion trends to the theoretical Rayleigh mode with maximum radial-component modal participation, thereby avoiding explicit modal indexing and providing a component-consistent forward model. The approach is evaluated on three synthetic 1D models exhibiting velocity contrasts and reversals plus two field DAS datasets, with the claim that it produces more accurate Vs profiles than conventional methods and shows good agreement with independent borehole measurements.

Significance. If the core assumption holds under broader conditions, the RCPM method would reduce subjectivity in modal interpretation for radial-component data and improve near-surface Vs recovery in complex stratigraphy, where radial and vertical modal energy distributions diverge. The explicit accounting for source-receiver directivity and modal sensitivity is a practical strength for DAS applications.

major comments (2)
  1. [Abstract; synthetic results paragraph] Abstract and synthetic evaluation: the claim that RCPM 'consistently captures the correct modal response and yields reliable Vs profiles' rests on qualitative visual agreement; no quantitative metrics (e.g., RMS error or bias between inverted and true Vs, or depth-averaged misfit to borehole logs) are reported to substantiate superiority over conventional inversion.
  2. [RCPM framework description; field application paragraph] RCPM framework and field-data section: the assumption that the mode of maximum radial modal participation will dominate measured dispersion trends is demonstrated only for the three specific synthetic models. The manuscript does not test or bound the sensitivity of this choice to small perturbations in velocity structure, source directivity, or overlapping modes that can arise in real data with strong contrasts or reversals.
minor comments (2)
  1. [Abstract] The abstract states 'good agreement' with boreholes but does not specify the number of boreholes, their locations relative to the DAS line, or the depth range of comparison.
  2. [Methods / RCPM framework] Notation for modal participation factors and the exact definition of 'maximum modal participation' should be given explicitly (e.g., as an equation) rather than described only in prose.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments on our manuscript. We have addressed each major point below, with revisions incorporated where they strengthen the presentation of the RCPM framework without altering its core claims.

read point-by-point responses

  1. Referee: [Abstract; synthetic results paragraph] Abstract and synthetic evaluation: the claim that RCPM 'consistently captures the correct modal response and yields reliable Vs profiles' rests on qualitative visual agreement; no quantitative metrics (e.g., RMS error or bias between inverted and true Vs, or depth-averaged misfit to borehole logs) are reported to substantiate superiority over conventional inversion.

    Authors: We agree that quantitative support would make the synthetic evaluation more rigorous. In the revised manuscript we have added RMS error and mean bias metrics between the inverted and true Vs profiles for both RCPM and conventional inversions across all three synthetic models. These values are reported in a new table and briefly discussed in the text, confirming lower errors for RCPM especially in reversal layers. revision: yes

  2. Referee: [RCPM framework description; field application paragraph] RCPM framework and field-data section: the assumption that the mode of maximum radial modal participation will dominate measured dispersion trends is demonstrated only for the three specific synthetic models. The manuscript does not test or bound the sensitivity of this choice to small perturbations in velocity structure, source directivity, or overlapping modes that can arise in real data with strong contrasts or reversals.

    Authors: The RCPM selection is deterministic: at each frequency the mode with the largest radial-component participation factor (computed from the eigenfunctions and the known source-receiver geometry) is chosen. The three models were selected precisely because they contain the velocity contrasts and reversals where radial and vertical modal energy distributions diverge most strongly. We have added a short robustness subsection that includes one additional perturbed synthetic case and a brief discussion of the conditions under which overlapping modes could affect the dominant radial trend. A exhaustive sensitivity bound over all possible real-data perturbations lies outside the scope of the present study. revision: partial

Circularity Check

0 steps flagged

No significant circularity; RCPM derivation grounded in independent wave theory

full rationale

The paper's RCPM framework is constructed from standard Rayleigh-wave modal participation calculations and source-receiver directivity considerations drawn from established wave propagation theory. No derivation step reduces by construction to fitted parameters renamed as predictions, nor does any central claim rest on a self-citation chain that itself lacks external verification. The method is evaluated against synthetic models with known 1D properties and field data cross-checked against independent borehole measurements, providing falsifiable benchmarks outside the inversion itself. The assumption that the maximum-participation mode matches observed trends is presented as a modeling choice rather than a tautology, and the abstract and described evaluations contain no load-bearing self-referential loops.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The framework rests on standard Rayleigh-wave theory and modal participation concepts from prior literature; no new free parameters, axioms, or invented entities are introduced in the abstract.

axioms (1)
  • standard math Rayleigh-wave dispersion and modal energy distribution can be computed from 1D layered velocity models using standard forward modeling.
    Invoked implicitly when matching measured dominant radial dispersion trends to theoretical modes.

pith-pipeline@v0.9.0 · 5804 in / 1165 out tokens · 38437 ms · 2026-05-19T20:06:40.952309+00:00 · methodology

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Reference graph

Works this paper leans on

10 extracted references · 10 canonical work pages

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    Computation of the Radial-Component Predominant-Mode (RCPM) This section presents the methodology adopted to compute the radial-component predominant -mode of Rayleigh waves. Herein, we define the predominant mode as the mode with the highest theoretical energy/amplitude at the ground surface for any given frequency, and note that the predominant mode can...

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    Dispersion Behavior of Vertical and Radial Components of Rayleigh Waves In this section, the dispersion behavior of Rayleigh waves obtained from the vertical and radial components is examined. To investigate the modal energy distribution associated with these two components, three representative synthetic ground models are considered ( Figure 1): (i) Grou...

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    Inversion Framework: Synthetic Examples This section presents the implementation of the proposed RCPM inversion framework to the three synthetic ground models discussed above . The formulation of inversion targets and selection of inversion model parameters are first described, followed by the implementation of a differential evolution (DE)–based global o...

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    As dispersion data uncertainty from simulated waveforms tends to be under -predicted relative to actual field waveforms, a minimum coefficient of variation (COV) of 0.05 was adopted. Note that the dispersion data extracted from the simulated waveforms are consistent with the predominant energy trends of a radial- component and a vertical source, as shown ...

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    To demonstrate its effectiveness, the proposed approach is compared with CMM inversion strategies

    Inversion Results for Synthetic Examples This section evaluates the performance of the proposed RCPM inversion framework using the three synthetic ground models. To demonstrate its effectiveness, the proposed approach is compared with CMM inversion strategies. The CMM inversions were performed using the Dinver module in Geopsy (Wathelet 2008). In the CMM ...

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    The results are evaluated against available geologic information and invasive test results at each site to assess the reliability of the inverted subsurface 𝑉𝑠 profiles

    Application to Real Field DAS Data Sets Following the successful RCPM validation using synthetic ground models, the RCPM inversion framework was applied to two field DAS datasets : Site A and Site B, as described below . The results are evaluated against available geologic information and invasive test results at each site to assess the reliability of the...

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