Velocity estimation via registration-guided least-squares inversion

Abstract

Least-squares (LS) acoustic-waveform inversion often suffers from a very narrow basin of attraction near the global minimum. To mitigate this problem, we evaluated an iterative inversion scheme in which the notion of proximity of two traces is not the usual LS distance, but instead it involves registration as in image processing. Observed data were matched to predicted waveforms via piecewise-polynomial warpings, obtained by solving a nonconvex optimization problem in a multiscale fashion from low to high frequencies. This multiscale process required defining lowfrequency augmented signals to seed the frequency sweep at zero frequency. Custom adjoint sources were then defined from the warped waveforms. The new method, referred to as registration-guided least-squares, was successfully applied to a few scenarios of model velocity estimation in the transmission setting. We determined that the new method can converge to the correct model in situations in which conventional LS inversion suffers from cycle skipping and converges to a spurious model.

A new objective function for full waveform inversion: Differential semblance in the data domain

“…Luo and Wu (2013) proposed and implemented envelope inversion to recover the large scale component of the model. Baek et al (2014) formulated registration-guided least-square inversion to mitigate the problem of the narrow basin of attraction near the global minimum in conventional FWI. These efforts were designed to make FWI less sensitive to initial models by using different objective functions.…”

Image registration guided wavefield tomography for shear-wave velocity model building

“…Recent developments in Hale (2013) and Baek et al (2014) provide efficient algorithms to solve similar problems for time warping with smooth constraints. The application of these methods for image warping is straightforward.…”

“…However, convergence is still not guaranteed. Baek et al (2014) propose an RGLS method to mitigate the cycle-skipping effects in FWI. In the cost function, fractionally warped synthetic data are used as the new observed data to make sure the phase differences between the synthetic waveforms and the new observed data are less than a half-wavelength.…”

“…In this study, we propose a new methodology to invert for S-wave velocities by combining IDWT (Yang et al, 2014a), dynamic image warping (DIW) (Hale, 2013), and the registration-guided leastsquares (RGLS) method (Baek et al, 2014). The paper is organized as follows: We first briefly describe the ERTM and DIW algorithms that are used to form and register P-S images, respectively.…”

“…Hale (2013) computes time shifts in a robust and efficient manner with an improvement of a dynamic warping method originally developed for speech recognition, which he applies to the registration of P-P and P-S time-migration images. Baek et al (2014) present a robust time/amplitude warping method with piecewise polynomials and low-frequency augmented signals, and they successfully use their method in waveform inversion to mitigate cycle skipping. All of these methods can potentially be applied for the registration of depth-migrated images.…”