Poroelastic near-field inverse scattering

TL;DR

This paper develops a multiphysics data analytic platform for imaging poroelastic interfaces, such as hydraulic fractures, using non-iterative sampling methods and elastic waveforms or pore pressure data.

Contribution

It introduces a novel framework combining Biot equations, thin-layer approximation, and operator factorizations for poroelastic interface imaging, advancing non-iterative inverse scattering techniques.

Findings

Robust imaging indicators for poroelastic interfaces.

Mathematical analysis of scattering operator properties.

Application to hydraulic fracture network reconstruction.

Abstract

A multiphysics data analytic platform is established for imaging poroelastic interfaces of finite permeability (e.g., hydraulic fractures) from elastic waveforms and/or acoustic pore pressure measurements. This is accomplished through recent advances in design of non-iterative sampling methods to inverse scattering. The direct problem is formulated via the Biot equations in the frequency domain where a network of discontinuities is illuminated by a set of total body forces and fluid volumetric sources, while monitoring the induced (acoustic and elastic) scattered waves in an arbitrary near-field configuration. A thin-layer approximation is deployed to capture the rough and multiphase nature of interfaces whose spatially varying hydro-mechanical properties are a priori unknown. In this setting, the well-posedness analysis of the forward problem yields the admissibility conditions for the contact parameters. In light of which, the poroelastic scattering operator and its first and second factorizations are introduced and their mathematical properties are carefully examined. It is shown that the non-selfadjoint nature of the Biot system leads to an intrinsically asymmetric factorization of the scattering operator which may be symmetrized at certain limits. These results furnish a robust framework for systematic design of regularized and convex cost functionals whose minimizers underpin the multiphysics imaging indicators. The proposed solution is synthetically implemented with application to spatiotemporal reconstruction of hydraulic fracture networks via deep-well measurements.