Correlation-based inversion of seismic data
T. van Leeuwen, dept. of Geotechnology, Delft University of Technology.
The aim of waveform inversion is to infer subsurface medium properties from seismic (reflection) data. Such an inverse problem may be posed as a PDE-constrained least-sqaures optimization problem. However, due to the band-limited nature of the data, the data depends very nonlinearly on the medium parameters that control the kinematics of the data. If a kinematically accurate initial guess is not provided, a gradient-based optimization algorithm will most likely get stuck in a local minimum of the least-squares objective functional. This calls for a reformulation of the inverse problem into a traveltime tomography problem. The basic idea is that the traveltimes of the data depend more linearly on the velocity than the waveforms themselves. A standard technique involves a correlation of the modeled and observed waveforms to extract the traveltime difference. We propose a novel way to measure the traveltime misfit from the correlation and show that this can be immediately used to define an alternative objective functional that mitigates the local minima that plague the least-squares approach. The proposed method can be adapted for both transmission and reflection tomography. We illustrate the workings on synthetic and real data examples.