Waveform inversion combining one-way and two-way wave equation migration

Xin Fu, Sergio J. Romahn, Kristopher A. H. Innanen

Full waveform inversion (FWI), which considers dynamic and kinematic information of seismic wave simultaneously, helps to interpret detailed characteristics of the subsurface. Growing out from FWI, iterative modelling, migration, and inversion (IMMI) considers waveform inversion as a cyclical process of the migration and standard inversion. In IMMI, any type of depth migration is available, which gives greater convenience to waveform inversion. Much research has shown that IMMI with the control of well log data is an effective method for waveform inversion. However, how to perform IMMI in the absence of well log data has not systematically investigated. In this paper, we examine IMMI in the absence of well log data. we introduce how to choose impedance inversion algorithms in IMMI for different depth migration algorithms. And we suggest employing the trace integration algorithm in frequency domain for a one-way depth migration based on the one-way wave equation, and the impedance inversion algorithm without phase change for a two-way depth migration based on the two-way wave equation. In our research, the one-way depth migration algorithm used is phase shift plus interpolation (PSPI) migration, and the two-way depth migration algorithm used is reverse time migration (RTM). Built on this, we develop a combined IMMI method which uses the one-way depth migration and the two-way depth migration sequentially in IMMI. To do comparisons between FWI, IMMI using PSPI migration, IMMI using RTM, and the combined IMMI method, two numerical examples are used. The comparisons show that IMMI using RTM and using PSPI are better than FWI, and the best wave to implement waveform inversion in the absence of well log data is the combined IMMI method.