Benxin Chi

Full Waveform Inversion Based on Envelope Objective Function

Full waveform inversion has been a successful tool to build high resolution velocity models, but it suffers from local minima problem. We propose an envelope based method allowing the updating of long wavelength components of the velocity model. The gradient of the misfit function can be efficiently computed through adjoint-state technique. We use simple models to prove that the envelope objective function is more convex than the traditional FWI objective function and is not as sensitive to the frequency components of the data as traditional FWI. Finally we compare the new approach to the traditional FWI through an application on a simple 2D synthetic data set to illustrate our method can be a supplement to traditional FWI approach when initial model is far from the true model and low-frequency data is missing.

Correlation-based reflection waveform inversion by one-way wave equations: Correlation-based RWI by one-way wave equations

Reflection full waveform inversion can update subsurface velocity structure of the deeper part, but tends to get stuck in the local minima associated with the waveform misfit function. These local minima cause cycle skipping if the initial background velocity model is far from the true model. Since conventional reflection full waveform inversion using two-way wave equation in time domain is computationally expensive and consumes a large amount of memory, we implement a correlation-based reflection waveform inversion using one-way wave equations to retrieve the background velocity. In this method, one-way wave equations are used for the seismic wave forward modelling, migration/de-migration and the gradient computation of objective function in frequency domain. Compared with the method using two-way wave equation, the proposed method benefits from the lower computational cost of one-way wave equations without significant accuracy reduction in the cases without steep dips. It also largely reduces the memory requirement by an order of magnitude than implementation using two-way wave equation both for two- and three-dimensional situations. Through numerical analysis, we also find that one-way wave equations can better construct the low wavenumber reflection wavepath without producing high-amplitude short-wavelength components near the image points in the reflection full waveform inversion gradient. Synthetic test and real data application show that the proposed method efficiently updates the background velocity model.