Tomographic determination of velocity and depth in laterally varying media

Abstract

INTRODUCTIONEstimation 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 velocitydepth 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 non uniqueness 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 nearsurface 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.Estimation of velocity and depth is often an important step in prospect evaluation in areas where lithology and structure undergo significant lateral change. Depth estimation is usually accomplished by converting zero-offset traveltimes, interpreted from a stacked section, to depth using a velocity field obtained from a normal-movement (NMO) analysis. In areas with complex lateral changes, a depth migration technique may be necessary to obtain the correct depth estimate (Lamer et aI., 1981). Both of these methods require an accurate representation of the root-mean-square (rms) velocity field. However, the stacking velocities used for such analyses can deviate significantly from rms velocities because analysis of stacking velocities assumes that the medium is laterally invariant and that traveltime trajectories for reflection events in CDP gathers are hyperbolic.Media vary laterally due to either reflector dip or curvature, or due to lateral velocity variations, or both. A large portion of the effect of reflector dip or curvature on the stacking velocity can be removed approximately by first migrating commonoffset panels with a first-guess velocity function, and then recalculating the stacking velocity in the migrated common-depthpoint (CDP) gathers (Doherty and Claerbout, 1976). The influence of lateral variations in velocity on the stacking velocity cannot be corrected this way. For lateral vari...

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