A comparison between the behavior of objective functions for waveform inversion in the frequency and Laplace domains

Abstract

In the frequency domain, gradient-based local-optimization methods of waveform inversions have been unsuccessful at inverting subsurface parameters without an accurate starting model. Such methods could not correct automatically for poor starting models because multiple local minima made it difficult to approach the true global minimum. In this study, we compared the behavior of objective functions in the frequency and Laplace domains. Wavefields in the Laplace domain correspond to the zero-frequency component of a damped wavefield; thus, the Laplace-domain waveform inversion can image smooth velocity models. Objective functions in the Laplace-domain inversion have a smoother surface and fewer local minima than in the frequency-domain inversion. We applied the waveform inversion to a 2D slice of the acoustic SEG/EAGE salt model in the Laplace domain and recovered smooth velocity models from inaccurate initial velocity conditions. We also successfully imaged velocities of the salt, SEG overthrust, and Institut Francais du Petrole Marmousi models with the frequency-domain inversion method by using the inverted velocity model of the Laplacedomain inversion as the initial model.

An adaptive subspace trust-region method for frequency-domain seismic full waveform inversion

“…Global optimization algorithms such as simulated annealing (SA) (Sen and Stoffa, 1991), genetic algorithms (GA) (Tran and Hiltunen, 2012) and particle swarm optimization algorithm (PSO) (Zhu et al, 2011) have already been used in full waveform inversion. Global optimization schemes have advantages over local optimization approaches in that the former can utilize the nonlinear of the inversion problem to find the global minima (Shin and Ha, 2008). However, these global techniques are computationally practical only with small scale models or simple models because of their blindness search and enormous times of the forward modeling, hence unacceptable for large scale models.…”

Proof of the existence of both zero- and low-frequency information in a damped wavefield

“…Recently, Shin and Cha (2008) suggested a Laplace-domain waveform inversion technique that can recover large-scale velocity structures from seismic data that contain no low-frequency information. The largescale results of Laplace-domain inversions can be used as initial models for conventional full-waveform inversions (Shin and Ha, 2008). Shin and Cha (2009) and Ha et al (2010) showed that a damped seismic trace has both zero-and low-frequency components.…”

Full-waveform Velocity Inversion Based on the Acoustic Wave Equation

“…It is a powerful way in reconstructing complex velocity structures. The inversion can be performed in the time-space domain [1][2][3][4] or in the frequency-space domain [5][6][7][8][9]. The frequency-domain inversion approach is equivalent to the time-domain inversion approach if all of the frequency data components are used in the inversion process [9].…”