Local-crosscorrelation elastic full-waveform inversion

Abstract

Full-waveform inversion (FWI) in its classic form is a method based on minimizing the [Formula: see text] norm of the difference between the observed and simulated seismic waveforms at the receiver locations. The objective is to find a subsurface model that reproduces the full waveform including the traveltimes and amplitudes of the observed seismic data. However, the widely used [Formula: see text]-norm-based FWI faces many issues in practice. The point-wise comparison of waveforms fails when the phase difference between the compared waveforms of the predicted and observed data is larger than a half-cycle. In addition, amplitude matching is impractical considering the simplified physics that we often use to describe the medium. To avoid these known problems, we have developed a novel elastic FWI algorithm using the local-similarity attribute. It compares two traces within a predefined local time extension; thus, is not limited by the half-cycle criterion. The algorithm strives to maximize the local similarities of the predicted and observed data by stretching/squeezing the observed data. Phases instead of amplitudes of the seismic data are used in the comparison. The algorithm compares two data sets locally; thus, it performs better than the global correlation in matching multiple arrivals. Instead of picking/calculating one stationary stretching/squeezing curve, we used a weighted integral to find all possible stationary curves. We also introduced a polynomial-type weighting function, which is determined only by the predefined maximum stretching/squeezing and is guaranteed to be smoothly varying within the extension range. Compared with the previously used Gaussian or linear weighting functions, our polynomial one has fewer parameters to play around with. A modified synthetic elastic Marmousi model and the North Sea field data are used to verify the effectiveness of the developed approach and also reveal some of its limitations.

Rayleigh Wave Dispersion Spectrum Inversion Across Scales

“…Besides, it is very hard to match the amplitudes in practice (non-reproducible noise, attenuation, and so on). Thus, we introduced local-similarity to measure the shape of different modes (Zhang & Alkhalifah, 2019a, 2019b. The local similarity, instead of global similarity, is more friendly to data with many arrivals (i.e., different modes).…”

“…The proposed objective function aims to match the slopes of arrivals, and it is insensitive to the polarity difference. We refer readers to two related publications for more details (Zhang & Alkhalifah, 2019a, 2019b.…”

“…Even if we ignore the waveform errors caused by incomplete physics, the L 2 norm-based objective functions may have more than one local minimum when the difference between the initially predicted and observed data is larger than a half cycle (Virieux & Operto, 2009). The local-similarity (i.e., local crosscorrelation) based objective function can be a replacement for the conventionally used L 2 norm one, especially for field data applications (Zhang & Alkhalifah, 2019a). It aims to maximize the similarity between the predicted and observed fv spectra and is less sensitive to the magnitude difference of the spectra (Zhang & Alkhalifah, 2019b;Zhang et al, 2020).…”

Convolution Coding and Amplitude Attenuation-Based Full Waveform Inversion

“…There are some ideas proposed by other researchers we can learn from to improve our method. Zhang and Alkhalifah [51]- [52] compared two traces within a predefined local time extension which is not limited by the half-cycle criterion. Leeuwen and Mulder [53] proposed a misfit criterion to measure the relative phase shift which is a weighted norm of the correlation and is less sensitive to differences in the amplitude spectra.…”

Shallow Ice‐Sheet Composite Structure Revealed by Seismic Imaging Near the West Antarctic Ice Sheet (WAIS) Divide Camp

“…(a) Rayleigh wave inversion centered at 8 Hz with a searching extension of 30% (Z.‐D. Zhang & Alkhalifah, 2019a). (b) Rayleigh wave inversion centered at 8 Hz with a searching extension of 10%.…”