Tackling cycle skipping in full-waveform inversion with intermediate data

Abstract

Full-waveform inversion (FWI) is a promising technique for recovering the earth models for exploration geophysics and global seismology. FWI is generally formulated as the minimization of an objective function, defined as the L2-norm of the data residuals. The nonconvex nature of this objective function is one of the main obstacles for the successful application of FWI. A key manifestation of this nonconvexity is cycle skipping, which happens if the predicted data are more than half a cycle away from the recorded data. We have developed the concept of intermediate data for tackling cycle skipping. This intermediate data set is created to sit between predicted and recorded data, and it is less than half a cycle away from the predicted data. Inverting the intermediate data rather than the cycle-skipped recorded data can then circumvent cycle skipping. We applied this concept to invert cycle-skipped first arrivals. First, we picked up the first breaks of the predicted data and the recorded data. Second, we linearly scaled down the time difference between the two first breaks of each shot into a series of time shifts, the maximum of which was less than half a cycle, for each trace in this shot. Third, we moved the predicted data with the corresponding time shifts to create the intermediate data. Finally, we inverted the intermediate data rather than the recorded data. Because the intermediate data are not cycle-skipped and contain the traveltime information of the recorded data, FWI with intermediate data updates the background velocity model in the correct direction. Thus, it produces a background velocity model accurate enough for carrying out conventional FWI to rebuild the intermediate- and short-wavelength components of the velocity model. Our numerical examples using synthetic data validate the intermediate-data concept for tackling cycle skipping and demonstrate its effectiveness for the application to first arrivals.

A review on reflection-waveform inversion

“…Currently, the most widely used method for retraveling the travel-time information is dynamic time/ image warping-DTW/DIW from the field of image processing (Hale 2013). Besides, there are some other methods, for example, intermediate data by Wang et al (2016) and Yao et al (2019b).…”

Inexact Newton-type methods based on Lanczos orthonormal method and application for full waveform inversion

“…For highly nonlinear optimization problems, such as the conventional minimization of FWI for a complex geological anomaly imaging, there may have many local extrema and deep narrow curved valleys [23][24][25][26][27][28]. When the Newton-type method applies and the current point m k belongs to a neighborhood of one local extremum, enforcing monotonicity may have twofold dangerous effects in the minimization of highly nonlinear functions.…”

Full waveform inversion using frequency shift envelope-based global correlation norm for ultrasound computed tomography

“…FWI is an imaging technique to construct high-precision sound speed images. However, FWI, being a nonlinear optimization problem, is prone to get trapped in local minima, resulting in 'cycle-skipping', which can be occured when the phase match between observed data and synthetic data is greater than half period (Yao et al 2019).…”