Multiscale Seismic Inversion in the Data and Image Domains

(Ph.D. Dissertation)

Sanzong Zhang

King Abdullah University of Science and Technology

ABSTRACT

I present a general methodology for inverting seismic data in either the data or image domains. It partially overcomes one of the most serious problems with current waveform inversion methods, which is the tendency to converge to models far from the actual one. The key idea is to develop a multiscale misfit function that is composed of both a simplified version of the data and one associated with the complex part of the data. Misfit functions based on simple data are characterized by many fewer local minima so that a gradient optimization method can make quick progress in getting to the general vicinity of the actual model. Once we are near the actual model, we then use the gradient based on the more complex data. Below, we describe two implementations of this multiscale strategy: wave equation traveltime inversion in the data domain and generalized differential semblance optimization in the image domain.

• Wave Equation Traveltime Inversion in the Data Domain (WT): The main difficulty with iterative waveform inversion is that it tends to get stuck in local minima associated with the waveform misfit function. To mitigate this problem and avoid the need to fit amplitudes in the data, we present a wave-equation method that inverts the traveltimes of reflection events, and so is less prone to the local minima problem. Instead of a waveform misfit function, the penalty function is a crosscorrelation of the downgoing direct wave and the upgoing reflection wave at the trial image point. The time lag which maximizes the crosscorrelation amplitude represents the reflection-traveltime residual that is back-projected along the reflection wavepath to update the velocity. Shot- and angle-domain crosscorrelation functions are introduced to estimate the reflection-traveltime residual by semblance analysis and scanning. In theory, only the traveltime information is inverted and there is no need to precisely fit the amplitudes or assume a high-frequency approximation. Results with both synthetic data and field records reveal both the benefits and limitations of WT.
• Generalized Differental Semblance Optimization in the Image Domain (GDSO): We now extend the multiscale physics approach to differential semblance optimization (DSO) in the image domain. That is, we identify the space-lag offset H(x,z,h) in the subsurface-offset domain as an implicit function of velocity. It describes the smoothly varying moveout H(x,z,h) of the migration image m(x,z,h) in the subsurface-offset domain, which is analogous to the smoothly varying traveltime residual Δτ(x) of a reflection event in a shot gather. The velocity model is found that minimizes the objective function ∑_x, z, hH(x, z, h)²m(x, z, h)², where coherent noise is eliminated everywhere except along the picked curve H(x, z, h). This method is denoted as generalized DSO (GDSO) and mitigates the coherent noise problem with DSO. Numerical examples are presented that empirically demonstrate its effectiveness in providing more accurate velocity models compared to conventional DSO.