Elastic wavefield tomography with physical model constraints

We propose elastic isotropic wavefield tomography formulated with the misfit of observed and recorded data as the objective function. The adjoint-state method enables efficient calculation of the gradient of this data misfit function. We solve this optimization problem with the gradient-descent method in order to update the model parameters iteratively. Using the elastic isotropic wave-equation formulated for slowly varying media, we invert for the squared velocities of compressional (P) and shear (S) modes. Physical relationships between Pand S-velocities, which are assumed to be generally linear, can be derived from laboratory measurements, well logs, and seismic data. Poor illumination of Pand S-waves often prevents reliable update of the model parameters, while preserving their intrinsic physical relationships. Thus, we introduce a model constraint term in the objective function, which sets the ratio of Pand S-wave velocities to a chosen range, assumed to be generally linear as suggested by laboratory measurements or well logs. Examples demonstrate that this constraint yields models that are more physically plausible than models obtained using only the data misfit as the objective function.