On Crosswell Traveltime Tomography

In this paper, we give a theoretical analysis of the crosswell traveltime tomography. In the single arrival case, we prove that the objective function is smooth, and every critical point is a kinematically correct velocity model. A numerical example is presented to demonstrate the properties we prove and the difference between traveltime tomography and waveform inversion via the output least squares. These results are extended to a local formulation of traveltime tomography in the presence of multiple arrivals. 1 Introduction In crosswell seismic experiments, seismic sources are fired in one well, and the wavefields generated are measured in another well. The goal of the crosswell seismology is to find physical parameters, especially the velocities, of the rocks between the wells from these measurements. This amounts to the mathematical problem of solving a coefficient inverse problem of the multidimensional acoustic wave equation. Crosswell inverse problems are important in reservoir..