Wave-equation Rayleigh-wave dispersion inversion using fundamental and higher modes

Abstract

Recorded surface waves often provide reasonable estimates of the S-wave velocity in the near surface. However, existing algorithms are mainly based on the 1D layered-model assumption and require picking the dispersion curves either automatically or manually. We have developed a wave-equation-based inversion algorithm that inverts for S-wave velocities using fundamental and higher mode Rayleigh waves without picking an explicit dispersion curve. Our method aims to maximize the similarity of the phase velocity spectrum ([Formula: see text]) of the observed and predicted surface waves with all Rayleigh-wave modes (if they exist) included in the inversion. The [Formula: see text] spectrum is calculated using the linear Radon transform applied to a local similarity-based objective function; thus, we do not need to pick velocities in spectrum plots. As a result, the best match between the predicted and observed [Formula: see text] spectrum provides the optimal estimation of the S-wave velocity. We derive S-wave velocity updates using the adjoint-state method and solve the optimization problem using a limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Our method excels in cases in which the S-wave velocity has vertical reversals and lateral variations because we used all-modes dispersion, and it can suppress the local minimum problem often associated with full-waveform inversion applications. Synthetic and field examples are used to verify the effectiveness of our method.

Rayleigh Wave Dispersion Spectrum Inversion Across Scales

“…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.…”

“…The picking of such dispersion curves either automatically or manually not only introduces uncertainty, but is also labor intensive (Cheng et al, 2019;Dai et al, 2020). Zhang and Alkhalifah (2019b) introduced a new wave equation dispersion spectrum inversion algorithm, which utilizes the dispersion spectra (e.g., phase velocity versus frequency) as the input data and does not require dispersion curves to be picked. The fundamental-and higher-modes are utilized naturally in the S-wave velocity estimation, where the utilization of higher-modes reduces the non-uniqueness associated with using the fundamental mode only (Beaty et al, 2002;Xia et al, 2003;Mi et al, 2018).…”

“…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). Similar to the non-zero lag crosscorrelation, the local similarity measurement also has an additional degree of freedom in the frequency axis.…”

A new mathematical model for dispersion of Rayleigh wave and a machine learning based inversion solver

“…Therefore, this type of methods often fails in the real world application. The heuristic global-optimization methods, such as the annealing simulation algorithm [30], the particle-swarm global optimization method [27], the genetic algorithm [9,20,36], and others [39,2,29,25], are usually derivative-free methods and the implementation is simple. Hence, during last decades, they have been widely used in the practice.…”

Wave‐Equation Migration Velocity Analysis Using Radon‐Domain Common‐Image Gathers

“…It is recognized that FWI is sensitive to inaccurate starting models and the lack of low‐frequency data due to the cycle‐skipping problem. To mitigate the problem of cycle‐skipping, substantial efforts have been made to establish a reliable starting model for FWI, such as emphasizing low‐wavenumber updates (Alkhalifah, ; Kazei & Alkhalifah, ; Wu & Alkhalifah, ; Xie, ; Yao et al, ), modulating low‐frequency components (Bharadwaj et al, ; Bozdağ et al, ; Chi et al, ; Liu et al, ; Shin & Cha, ), and building more effective objective functions (Leeuwen & Mulder, ; Yi et al, ; Zhang et al, ; Zhang & Alkhalifah, ).…”