REVIEW 2 major objections
Finite Difference Based Wave Simulation in Fractured Porous Rocks
T0 review · 2 major / 0 minor · reviewed 2026-05-24 · grok-4.3
Pith's one-line read Finite difference simulations in fractured porous rocks reproduce Biot's slow compressional wave and its conversion at boundaries.
desk verdict Standard FD implementation of Biot plus linear-slip fractures; shows expected slow wave but leaves the poroelastic fracture equivalence untested. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
Velocity-stress staggered-grid finite difference scheme combined with the linear-slip equivalent-medium model for fractures.
What would settle it
A run of the same finite-difference code on the described models in which the particle-velocity snapshots contain no slow compressional wave, or in which the slow wave does not convert at the interface, would show that the method fails to capture the claimed behavior.
Extended reading notes
Core claim
A fourth-order-in-space, second-order-in-time velocity-stress staggered-grid finite difference algorithm solves Biot's poroelastic equations in two dimensions. An equivalent-medium representation of fractures is obtained from the linear slip model and inserted into the grid. Particle-velocity snapshots from the resulting simulations contain the slow compressional wave predicted by Biot's theory; at the boundary of a layered model the slow P-wave converts into a P-wave that travels faster than the original slow wave.
Load-bearing premise
The linear slip model supplies an accurate equivalent-medium representation of fractures inside fluid-saturated porous rock without any need to resolve the fracture aperture or the fluid flow inside it.
Editorial extensions
If this is right
- The scheme produces the slow compressional wave required by Biot's theory inside fluid-saturated porous media.
- At a fractured interface the slow P-wave converts into a faster P-wave.
- The linear-slip model allows the fractures to be treated without explicitly resolving their aperture or internal flow.
- The fourth-order spatial, second-order temporal discretization is sufficient to propagate these waves on a two-dimensional grid.
Reading between the lines
- The same grid and equivalent-medium approach could be applied to three-dimensional reservoir models to examine how fracture orientation affects wave polarization.
- The documented conversion of the slow wave at boundaries supplies a possible signature that field seismologists could look for when interpreting data from fractured reservoirs.
- Direct comparison of the computed waveforms against laboratory tank experiments on porous samples with known fractures would test the accuracy of the equivalent-medium step.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript implements a 2D velocity-stress staggered-grid finite-difference scheme (fourth-order space, second-order time) for Biot poroelastic equations and derives an equivalent-medium representation of fractured fluid-saturated rock by combining those equations with the linear-slip model. Numerical experiments are reported that display a slow compressional wave in particle-velocity snapshots and its conversion to a faster P-wave at a fractured interface in a layered model.
Significance. If the numerical implementation and the equivalent-medium construction were shown to be accurate, the work would supply a practical tool for simulating poroelastic wavefields in fractured reservoirs. The absence of quantitative validation, however, prevents the results from being used with certainty for either code verification or physical interpretation of slow-wave behavior.
major comments (2)
- [Abstract / Results] Abstract and results section: the central observations (slow P-wave presence and mode conversion) are stated only qualitatively; no L2 error norms, phase-velocity comparisons against analytic Biot solutions, grid-convergence studies, or attenuation measurements are supplied, so the numerical support for the claims cannot be assessed.
- [Equivalent media model] Equivalent-media derivation (section describing the linear-slip extension): the model supplies displacement-discontinuity conditions but omits explicit poroelastic jump conditions for fluid-mass conservation and pressure continuity across the fracture aperture. Because the slow compressional wave is controlled by relative fluid-solid motion, this omission directly affects the predicted wave speed and conversion coefficients; no additional effective-permeability term or validation against a discrete-fracture reference solution is provided.
Simulated Author's Rebuttal
We thank the referee for the constructive comments on our manuscript. We address each major point below and indicate where revisions will be made to strengthen the work.
read point-by-point responses
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Referee: [Abstract / Results] Abstract and results section: the central observations (slow P-wave presence and mode conversion) are stated only qualitatively; no L2 error norms, phase-velocity comparisons against analytic Biot solutions, grid-convergence studies, or attenuation measurements are supplied, so the numerical support for the claims cannot be assessed.
Authors: We agree that quantitative validation is needed to support the claims. In the revised manuscript we will add L2 error norms computed against analytic Biot solutions for a homogeneous medium, phase-velocity dispersion curves extracted from the simulations, a grid-convergence study demonstrating fourth-order spatial accuracy, and basic attenuation estimates from the slow-wave snapshots. These additions will allow readers to assess the numerical fidelity directly. revision: yes
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Referee: [Equivalent media model] Equivalent-media derivation (section describing the linear-slip extension): the model supplies displacement-discontinuity conditions but omits explicit poroelastic jump conditions for fluid-mass conservation and pressure continuity across the fracture aperture. Because the slow compressional wave is controlled by relative fluid-solid motion, this omission directly affects the predicted wave speed and conversion coefficients; no additional effective-permeability term or validation against a discrete-fracture reference solution is provided.
Authors: The linear-slip model is introduced as an effective discontinuity in the solid displacement field while the underlying Biot equations govern the poroelastic fields. We acknowledge that explicit jump conditions enforcing fluid-mass conservation and pressure continuity across the fracture aperture are not stated separately; the formulation relies on the continuity already present in the staggered-grid discretization of the Biot system. This approximation may indeed influence slow-wave speed and conversion coefficients. In revision we will add an explicit discussion of this limitation, introduce an effective-permeability term to account for fluid flow across the fracture, and note the absence of a discrete-fracture benchmark as a direction for future validation. revision: partial
Circularity Check
No circularity: numerical results follow from external Biot theory and linear-slip model without self-referential reduction
full rationale
The paper implements a standard velocity-stress FD scheme for Biot poroelastic equations (fourth-order space, second-order time) and then applies the linear-slip model to obtain an equivalent-medium representation for fractures. The reported slow-P-wave observation and its mode conversion are explicitly attributed to Biot's theory as implemented in the scheme, not to any parameter fitted inside the paper or to a self-citation chain. No equation is shown to equal its own input by construction, no fitted quantity is relabeled as a prediction, and the linear-slip extension is presented as an external modeling choice rather than a uniqueness theorem imported from the authors' prior work. The derivation chain therefore remains self-contained against external benchmarks.
Assumptions & free parameters
assumptions (2)
- domain assumption Biot's equations of motion and constitutive relations hold for the fluid-saturated porous background medium.
- domain assumption The linear-slip model supplies an equivalent anisotropic medium that correctly represents the mechanical effect of fractures on wave propagation.
Cite this review
Pith. "Pith review of Finite Difference Based Wave Simulation in Fractured Porous Rocks." pith.science (2026). https://pith.science/paper/5PTXVKXT
@misc{pith2026190710833,
author = {Pith},
title = {Pith review of: Finite Difference Based Wave Simulation in Fractured Porous Rocks},
year = {2026},
howpublished = {\url{https://pith.science/paper/5PTXVKXT}},
note = {Machine review of arXiv:1907.10833}
}
read the original abstract
Biot's theory provides a framework for computing seismic wavefields in fluid saturated porous media. Here we implement a velocity-stress staggered grid 2D finite difference algorithm to model the wave-propagation in poroelastic media. The Biot's equation of motion are formulated using a finite difference algorithm with fourth order accuracy in space and second order accuracy in time. Seismic wave propagation in reservoir rocks is also strongly affected by fractures and faults. We next derive the equivalent media model for fractured porous rocks using the linear slip model and perform numerical simulations in the presence of fractured interfaces. As predicted by Biot's theory a slow compressional wave is observed in the particle velocity snapshots. In the layered model, at the boundary, the slow P-wave converts to a P-wave that travels faster than the slow P-wave. We finally conclude by commenting on the major details of our results.
Reviewed May 24, 2026 · model on record in the stance chip above.
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