Automatic data extrapolation to zero offset along local slope

Velocity-independent seismic data processing requires information about the local slope in the data. From estimates of local time and space derivatives of the data, a total least-squares algorithm gives an estimate of the local slope at each data point. Total least squares minimizes the orthogonal distance from the data points (the local time and space derivatives) to the fitted straight line defining the local slope. This gives a more consistent estimate of the local slope than standard least squares because it takes into account uncertainty in the temporal and spatial derivatives. The total least-squares slope estimate is the same as the one obtained from using the structure tensor with a rectangular window function. The estimate of the local slope field is used to extrapolate all traces in a seismic gather to the smallest recorded offset without using velocity information. Extrapolation to zero offset is done using a hyperbolic traveltime function in which slope information replaces the knowledge of the normal moveout (NMO) velocity. The new data processing method requires no velocity analysis and there is little stretch effect. All major reflections and diffractions that are present at zero offset will be reproduced in the output zero-offset section. Therefore, if multiple reflections are undesired in the output, they should be removed before data extrapolation to zero offset. The automatic method is sensitive to noise, so for poor signal-to-noise ratios, standard NMO velocities for primary reflections can be used to compute the slope field. Synthetic and field data examples indicate that compared with standard seismic data processing (velocity analysis, mute, NMO correction, and stack), our method provides an improved zero-offset section in complex data areas.