# Finite Difference Based Wave Simulation in Fractured Porous Rocks

## TL;DR

This paper develops a finite difference simulation method based on Biot's theory to model seismic wave propagation in fractured porous rocks, capturing complex wave interactions including slow P-waves.

## Contribution

It introduces a 2D finite difference algorithm with high accuracy for modeling wavefields in fractured poroelastic media, incorporating fracture effects via an equivalent media model.

## Key findings

- Observation of slow compressional waves consistent with Biot's theory
- Wave conversion at fractured interfaces from slow to fast P-waves
- Successful simulation of seismic wave propagation in layered fractured rocks

## 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.

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Source: https://tomesphere.com/paper/1907.10833