Depth Transform of Seismic Data by Use of Equi-traveltime Planes

The present paper proposes a new algorithm for the three-dimensional depth transform of the surface reflection, the cross-well reflection and VSP data by use of equi-traveltime planes. The equation of equi-traveltime planes of waves which travel from source to receiver through reflection point on reflector is derived. The derived equation shows the equation of ellipsoid of which foci are source and receiver. This means that a reflection point on reflector is located on ellipsoid. Ellipsoids are drawn for each pair of source and receiver. Consequently, reflector is determined by drawing a common tangent plane to these ellipsoids. The procedure of depth transform is as follows. 1) The velocity distribution within survey area is assumed. 2) The ellipsoids for each sample time in seismograms for each pair of source and receiver are drawn. 3) Reflector is determined as the common tangent plane to these ellipsoids. Here, reflector is automatical1y drawn as follows. 1) Survey area is divided into cubic cells of appropriate size. 2) An ellipsoid is drawn from seismogram for each pair of source and receiver by changing with one sampling interval from the designated time after the travel time of first break. 3) The intersecting points of the ellipsoid with the vertical lines of cells are shifted to the nearest cell corners. 4) Amplitudes for the corresponding sample times on seismograms are stacked on these cell corners. The amplitudes on the cell corners where the common tangent plane of ellipsoids passes are amplified by summation with in-phase. However, the amplitude on the other grid cell corners would be canceled because of the summation with out-phase. Judging from the model studies, it was clarified that this algorithm reconstructed the structure with good accuracy, the short calculation time and the small requirement for core memory.