Tomographic determination of velocity and depth in laterally varying media

Abstract

Estimation of reflector depth and seismic velocity from seismic reflection data can be formulated as a general inverse problem. The method used to solve this problem is similar to tomographic techniques in medical diagnosis and we refer to it as seismic reflection tomography. Seismic tomography is formulated as an iterative Gauss‐Newton algorithm that produces a velocity‐depth model which minimizes the difference between traveltimes generated by tracing rays through the model and traveltimes measured from the data. The input to the process consists of traveltimes measured from selected events on unstacked seismic data and a first‐guess velocity‐depth model. Usually this first‐guess model has velocities which are laterally constant and is usually based on nearby well information and/or an analysis of the stacked section. The final model generated by the tomographic method yields traveltimes from ray tracing which differ from the measured values in recorded data by approximately 5 ms root‐mean‐square. The indeterminancy of the inversion and the associated nonuniqueness of the output model are both analyzed theoretically and tested numerically. It is found that certain aspects of the velocity field are poorly determined or undetermined. This technique is applied to an example using real data where the presence of permafrost causes a near‐surface lateral change in velocity. The permafrost is successfully imaged in the model output from tomography. In addition, depth estimates at the intersection of two lines differ by a significantly smaller amount than the corresponding estimates derived from conventional processing.