Inversion of CMP Gathers for P and S Velocity
, by Peter Mora
A method for inverting common midpoint gather data for the parameters P-velocity, S-velocity, density, quality, factor, and source waveform is described. The method uses as iterative nonlinear least-squares formulation for overdetermined problems. Therefore, an efficient modeling theory is required to enable the required iterations of parameters to be carried out within a reasonable amount of time. The iterations proceed until a solution is located which minimizes the square error between the modeled and real data. The practical limitations are the ability of the modeling theory to simulate the real data, and the sizes of the data and parameter spaces which determine matrix dimensions and hence speed of the algorithm. A simple ray tracing scheme for horizontal layers is used as the modeling theory, and an inversion for P and S velocities in a 16 layer model is performed for synthetic data generated by the same modeling theory. The P and S velocities resulting from the inversion are in reasonably close agreement with the true vales.
STANFORD