Inversion of Crosswell Seismograms via Diierential Semblance Optimization

In crosswell seismic experiments, seismic sources are red in one well, and the waveeelds generated are measured in another well. The goal of the crosswell seismology is to nd physical parameters, especially the velocities, of the rocks between the wells from these measurements. This amounts to the mathematical problem of solving a coeecient inverse problem of the multidimensional acoustic wave equation. The two common inversion methods traveltime tomography and waveform inversion via output least squares have some unpleasant features from the viewpoint of numerical computations. We present a new waveform inversion method { diierential semblance optimization (DSO) { in this paper under the non-caustic assumption. The main result is that the objective function is smooth and a critical point is kinematically close to the true velocity model if the noise level is low enough, the source wavelet is oscillatory enough, and the DSO parameter is small enough.