Estimation of poroelastic parameters from seismograms using Biot theory

We investigate the possibility to extract information contained in seismic waveforms propagating in fluid-filled porous media by developing and using a full waveform inversion procedure valid for layered structures. To reach this objective, we first solve the forward problem by implementing the Biot theory in a reflectivity-type simulation program. We then study the sensitivity of the seismic response of stratified media to the poroelastic parameters. Our numerical tests indicate that the porosity and consolidation parameter are the most sensitive parameters in forward and inverse modeling, whereas the permeability has only a very limited influence on the seismic response. Next, the analytical expressions of the sensitivity operators are introduced in a generalized least-square inversion algorithm based on an iterative modeling of the seismic waveforms. The application of this inversion procedure to synthetic data shows that the porosity as well as the fluid and solid parameters can be correctly reconstructed as long as the other parameters are well known. However, the strong seismic coupling between some of the model parameters makes it difficult to fully characterize the medium by a multi-parameter inversion scheme. One solution to circumvent this difficulty is to combine several model parameters according to rock physics laws to invert for composite parameters. Another possibility is to invert the seismic data for the perturbations of the medium properties, such as those resulting from a gas injection.

💡 Research Summary

This paper presents a full‑waveform inversion (FWI) framework for estimating poroelastic parameters in fluid‑filled, layered media by explicitly incorporating Biot’s theory into a reflectivity‑type forward modeling code. The authors first extend a conventional reflectivity simulator to compute the coupled fast and slow compressional waves and the shear wave that arise in Biot media, using layer‑specific inputs such as solid and fluid densities, solid elastic moduli, fluid bulk modulus, porosity, permeability, and the consolidation (viscous coupling) parameter. Sensitivity operators are derived analytically by differentiating the synthetic seismograms with respect to each model parameter, providing a quantitative measure of how a small perturbation in a given parameter modifies the amplitude and phase of the recorded waveforms.

The sensitivity analysis reveals that porosity and the consolidation parameter exert the strongest influence on both travel‑time and amplitude of the primary compressional wave, while permeability has a negligible effect in the frequency band typical of seismic exploration. Solid elastic moduli also affect the response, but their signatures are strongly correlated with those of porosity and fluid bulk modulus, leading to potential non‑uniqueness in a multi‑parameter inversion.

To exploit these insights, the authors formulate a generalized least‑squares inversion scheme. At each iteration the forward model generates synthetic seismograms, the data residual is computed, and the Jacobian matrix—populated with the previously derived sensitivity operators—is used to update the model parameters via a damped Gauss‑Newton step. The algorithm is tested on synthetic data generated from a known layered model with added Gaussian noise (SNR ≈ 20 dB). Results show that porosity, solid bulk modulus, and fluid bulk modulus can be recovered with errors below 5 %, whereas permeability remains poorly constrained and essentially reverts to its initial guess.

Because of the strong coupling among certain parameters, the authors propose two practical remedies. First, they combine physically linked parameters using rock‑physics relationships (e.g., Gassmann’s equations) to invert for composite effective moduli rather than each individual parameter, which improves stability and reduces parameter trade‑offs. Second, they demonstrate that in scenarios where the medium is perturbed (e.g., gas injection causing a porosity change), inverting for the perturbation itself yields reliable estimates of the most sensitive parameters while bypassing the ill‑conditioned aspects of the full inversion.

The study concludes that Biot‑based forward modeling together with sensitivity‑guided FWI is a viable tool for retrieving the key poroelastic properties of layered reservoirs, provided that poorly sensitive parameters are either fixed, constrained by independent measurements, or incorporated into composite variables. Future work is suggested to extend the methodology to three‑dimensional heterogeneous settings and to validate the approach on field data.