Target-oriented inversion using the patched Green’s function method

Abstract

We have designed a target-oriented methodology to perform full-waveform inversion (FWI) using a frequency-domain wave propagator based on the so-called patched Green’s function (PGF) technique. Originally developed in condensed matter physics to describe electronic waves in materials, the PGF technique is easily adaptable to the case of wave propagation in spatially variable media in general. By dividing the entire computational domain into two sections, namely the target area and the outside target area, we calculate the Green’s functions related to each section separately. The calculations related to the section outside the target are performed only once at the beginning of the inversion, whereas the calculations in the target area are performed repeatedly for each iteration of the inversion process. With the Green’s functions of the separate areas, we calculate the combined Green’s function of the two systems patched together through application of a recursive Dyson equation. The calculation is exact; that is, it is the same as the Green’s function calculated by directly solving the Helmholtz equation. By performing 2D and time-lapse experiments on the Marmousi and a Brazilian presalt velocity models, we determined that the target-oriented PGF reduces the computational time of the inversion without compromising accuracy. In fact, when compared with conventional FWI results, the PGF-based calculations are identical but done in a reduced time according to the target size.