Acoustic full waveform inversion of synthetic land and marine data in the Laplace domain

Abstract

A B S T R A C TElastic waves, such as Rayleigh and mode-converted waves, together with amplitude versus offset variations, serve as noise in full waveform inversion using the acoustic approximation. Heavy preprocessing must be applied to remove elastic effects to invert land or marine data using the acoustic inversion method in the time or frequency domains. Full waveform inversion using the elastic wave equation should be one alternative; however, multi-parameter inversion is expensive and sensitive to the starting velocity model. We implement full acoustic waveform inversion of synthetic land and marine data in the Laplace domain with minimum preprocessing (i.e., muting) to remove elastic effects. The damping in the Laplace transform can be thought of as an automatic time windowing. Numerical examples show that Laplace-domain acoustic inversion can yield correct smooth velocity models even with the noise originating from elastic waves. This offers the opportunity to develop an accurate smooth starting model for subsequent inversion in the frequency domain.

Smooth 2‐D ocean sound speed from Laplace and Laplace‐Fourier domain inversion of seismic oceanography data

“…The application of the Laplace and Laplace‐Fourier transforms to seismic inversion has been documented in numerous publications [e.g., Shin and Cha , , ; Ha et al , , ; Bae et al , ]. Here we provide a brief overview of the method and refer the reader to the cited works for more details.…”

“…Laplace and Laplace‐Fourier domain inversion (LDI), developed for seismic application by Changsoo Shin and colleagues [ Shin and Cha , , ; Ha et al , , ], are two promising means of obtaining starting models for FWI without the need for a priori information about the sound speed structure. These techniques apply concepts from electrical prospecting to seismic data by transforming the data to the Laplace domain in which the zero frequency component (Laplace domain) and low frequency components (Laplace‐Fourier domain) of the damped wavefield are examined to extract a smooth model of the speed of sound in the Earth.…”

Laplace-domain full-waveform inversion of seismic data lacking low-frequency information

“…Because the data were acquired on 3D elastic media, the elastic waves and the 3D geometric spreading of the amplitude can serve as the noise. However, it has been shown that the Laplace-domain inversion can yield an accurate large-scale velocity model from field data sets (Shin and Cha, 2008;Shin et al, 2010) and synthetic marine data with elastic waves (Ha et al, 2010b).…”

2-D acoustic Laplace-domain waveform inversion of marine field data

“…Because we used the acoustic approximation to simulate the marine environment, elastic waves including mode‐converted waves serve as a type of noise in the inversion. However, elastic waves do not need to be removed from the data (Ha et al 2010b). They usually appear at a later time, and their effect on the Laplace‐transform is limited.…”

“…Many processing techniques can be applied to compensate for the discrepancy (Operto et al 2004; Ravaut et al 2004; Brenders & Pratt 2007); however, we did not apply any pre‐processing to change the amplitude of the data to minimize the pre‐processing. Ha et al (2010b) showed that the acoustic Laplace‐domain inversion could be applied to synthetic marine data. We also ignored the directivity of the sources and the receivers.…”