Simultaneous density-velocity inversion by extended Gel'fand-Levitan-Marchenko solution in layered acoustic media for oblique incidence

TL;DR

This paper extends the Gel'fand-Levitan-Marchenko method to simultaneously invert for velocity and density in layered acoustic media at oblique incidence, incorporating reflection amplitude and traveltime data.

Contribution

It formulates a new GLM impedance solution for oblique incidence that accounts for boundary jumps and combines amplitude and traveltime information for joint inversion.

Findings

Successful recovery of velocity and density in numerical tests

Validation of the extended GLM approach for layered media

Demonstrated effectiveness of combined amplitude and traveltime data

Abstract

Original GLM (Gel'fand-Levitan-Marchenko) theory is for scattering potential recovery of Schr\"odinger equation. In this paper, we formulate the GLM impedance solution of oblique incidence for simultaneous inversion of velocity and density including boundary jumps based on acoustic wave equation. In addition to the use of reflection amplitude, traveltime information of reflection arrivals is also utilized for inversion based on the focusing principle. Numerical tests demonstrate the recovery of velocity and density, verified the validity of the theory and method. The theory of Schr\"odinger impedance inverse-scattering studied in this paper is closely related to the direct envelope inversion.