DOI: 10.5061/dryad.47d7wm3mj
title: Acoustoelastic modeling and effective moduli of prestressed fractured rocks

description: This dataset contains experimental measurements, MATLAB scripts, and
 simulation results supporting the analysis of acoustoelastic and effective
 medium behavior in prestressed fractured rocks. The central file
 (0_HD-2-1-20230829-193251-Strength-data.xlsx) provides raw and processed
 data on P- and S-wave velocities, stress conditions, and derived elastic
 parameters from laboratory tests. Accompanying MATLAB code allows users to
 calculate Thomsen-style anisotropy parameters, phase velocities, and
 stress-dependent moduli using nonlinear acoustoelastic and crack-density
 models. The dataset also includes output results and figures in compressed
 form (results.zip), and an optional finite-difference simulation toolkit
 (RSG-FD.zip) for full waveform modeling in fractured media. This data
 package is designed to be reusable by researchers in geophysics, rock
 physics, and applied seismology for validating or extending acoustoelastic
 theory under varying fluid saturations and stress regimes. All data are
 original, and there are no legal or ethical restrictions associated with
 its use.
description: # Acoustoelastic modeling and effective moduli of prestressed fractured
 rocks This dataset supports the study of stress-dependent seismic velocity
 behavior in fractured rocks using acoustoelastic and effective medium
 theories. It includes experimental data, MATLAB code, and simulation
 results for computing Thomsen-type anisotropic parameters and phase
 velocities under varying crack densities and prestress conditions. The
 study combines theoretical modeling with experimental verification to
 characterize acoustoelastic signatures in fluid-saturated fractured
 media. All code files included in this submission are original and
 developed by the authors. Mentions of “Winkler” and “Liu” refer to
 referenced models or publications and do not indicate code reuse.
 Therefore, the code is fully compatible with the CC0 license and is
 released under that waiver. --- ## Description of the Data and File
 Structure This dataset contains both experimental and numerical components
 related to acoustoelastic wave propagation in fractured rocks. All files
 are organized by function: ### **Experimental Data** *
 `0_HD-2-1-20230829-193251-Strength-data.xlsx`: Contains raw and processed
 experimental measurements of wave velocities, strength parameters, and
 stress conditions on fractured rock specimens. * **Columns** include:
 axial stress (MPa), confining pressure (MPa), P-wave and S-wave velocities
 (km/s), and derived elastic parameters. * Units are provided in the first
 row. Missing data are indicated with `NaN`. ### **MATLAB Code** *
 `Thomsen_parameters`: Computes Thomsen-style anisotropic parameters (ε, γ,
 δ) based on nonlinear acoustoelastic theory. * `Effective_moduli.m`:
 Implements a crack-density-dependent effective medium model to estimate
 bulk and shear moduli under varying prestress. *
 `experimetal_data_verification.m`: Compares theoretical predictions with
 laboratory data, computes fitting errors and plots verification figures. *
 `Phase_velocities.m`: Simulates phase velocity dispersion curves in
 fractured rocks using the Acoustoelastic-Hudson-Crack Model (AHCM). ###
 **Results** * `results.zip`: Contains figure data used in the main
 manuscript. Subfolders include: * `/wavefield_outputs/`: Contains
 simulated wavefield snapshots and seismic gathers in `.dat` format. These
 outputs are generated under varying crack densities and confining
 pressures, and represent the key modeling results used for figure
 generation and quantitative analysis. Each `snap_xxxxx_component.dat` file
 represents a **wavefield snapshot** at time step `xxxxx` for a specific
 stress or velocity component (e.g., `txx`, `tzz`, `vx`). These snapshots
 have spatial dimensions of `807 × 807` grid points and are saved in
 single-precision binary format (`real*4`). Corresponding `.dat` waveform
 records such as `seistxx.dat` capture the **temporal evolution** of the
 same physical component at a specific receiver location. seisXXX.dat files
 record the temporal evolution of specific stress or particle velocity
 components (e.g., seistxx.dat for txx, seisvx.dat for vx, seistzz.dat for
 tzz, etc.) at one or more receiver locations. These files are stored in
 single-precision binary format (real*4) and contain 1D seismic traces
 sampled over time. Each file corresponds to the same physical quantity as
 represented in snap_xxxxx_XXX.dat snapshot files, which provide the
 spatial distribution of the wavefield component at selected time steps.
 Together, the seisXXX.dat and snap_xxxxx_XXX.dat files enable joint
 time-space analysis of wave propagation behavior under different loading
 and material conditions. * other scripts: **`snapshot.m`** This script
 reads and visualizes a 2D wavefield snapshot from binary data. 
 **Purpose:** Visual inspection of the spatial distribution of stress or
 velocity components in the wavefield, useful for analyzing wave
 propagation characteristics. **`ht.m`** This script loads a seismic trace
 `seistxx.dat` (representing the stress component txx over time) and the
 source wavelet `wlet.dat`, and compares them in both time and frequency
 domains.  **Purpose:** Estimate propagation velocity from arrival time
 differences and evaluate the waveform response in the
 σ<sub>xx</sub> component. **`htht.m`** This script functions
 similarly to `ht.m`, but focuses on the velocity component `seisvx.dat`
 (e.g., particle velocity in the x-direction).  **Purpose:** Analyze wave
 propagation and waveform features using the particle velocity component,
 enhancing the understanding of dynamic responses. **`open.m`** This is a
 multi-purpose script with several capabilities: **Seismic trace
 visualization (`seistzz.dat`)**; **Wavefield snapshots**; **Source wavelet
 analysis**; **Source dimension and directional energy analysis**. ###
 **Supplementary Finite-Difference Model** **RSG-FD: Finite-Difference
 Modeling of Wave Propagation in Anisotropic Media** #### Description: This
 dataset contains the input files, source code, and output needed to run 2D
 finite-difference wavefield simulations in anisotropic elastic media. The
 simulations are part of the RSG-FD (Rotated Staggered Grid Finite
 Difference) modeling framework for seismic wave propagation. #### Folder
 Structure and File Descriptions: | File Name | Description | |
 :------------ |
 :----------------------------------------------------------------------------- | | `a.out` | Compiled executable file for running the simulation (compiled from `RCPF.f90`) | | `RCPF.f90` | Fortran source code for the RSG-FD simulation program | | `c11.dat` | Stiffness coefficient C11 matrix (in Pa) for the anisotropic elastic model | | `c12.dat` | Stiffness coefficient C12 matrix | | `c13.dat` | Stiffness coefficient C13 matrix | | `c22.dat` | Stiffness coefficient C22 matrix | | `c23.dat` | Stiffness coefficient C23 matrix | | `c33.dat` | Stiffness coefficient C33 matrix | | `rho.dat` | Density model file (in kg/m³) | | `iso.wok` | Parameter file containing simulation settings (e.g., grid size, time step) | | `wavelet.dat` | Input source wavelet (e.g., Ricker wavelet) used for seismic excitation | | `wav.dat` | Another input source wavelet | | `wlet.dat` | Another input source wavelet | #### Usage Instructions: 1. Ensure that all `.dat` and `.wok` files are in the same directory as `a.out`. 2. To run the simulation, execute the binary: `./a.out` 3. The output wavefield snapshots and synthetic seismograms will be stored in generated subfolders or output files (not included here but typically saved during runtime). --- ## Sharing/Access Information This dataset is exclusively available via Dryad. All code files included in this submission are original and developed by the authors. Mentions of “Winkler” and “Liu” refer to referenced models or publications and do not indicate code reuse (Winkler, K. W., & Liu, X. (1996). Measurements of third‐order elastic constants in rocks. *The Journal of the Acoustical Society of America*, *100*(3), 1392-1398.). There are no access restrictions. All files are under open license for research and educational reuse. --- ## Code/Software All modeling scripts were written in **MATLAB R2022a**. Required toolboxes include: * Signal Processing Toolbox * Curve Fitting Toolbox * Optimization Toolbox (optional) To reproduce figures and results: 1. Load experimental data using `experimetal_data_verification.m` 2. Run `Effective_moduli` to compute nonlinear effective parameters 3. Use `Thomsen_parameters` to analyze anisotropy parameters 4. Use `Phase_velocities` to simulate directional velocities For large-scale wavefield simulation, unzip `RSG-FD.zip` and follow the instructions in the included `README_RSG.txt` file.