Depth Transform of Seismic Data by Use of Equi-Travel Time Planes

The present paper proposes an algorithm for the three-dimensional depth transform of the surface reflection, the cross-well reflection and VSP data by use of equi-travel time planes.

The equation of equi-travel time planes of waves which travel from source to receiver through a reflection point on the reflector is derived. The derived equation shows an ellipsoid of which foci are source and receiver. This means that a reflection point on the reflector is located on the ellipsoid. Ellipsoids are drawn for each pair of source and receiver. Consequently, the 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 the survey area is assumed.

2) The ellipsoids for each sample time in seismograms for each pair of source and receiver are drawn.

3) The reflector is determined as the common tangent plane to these ellipsoids.

Here, the reflector is automatically drawn as follows.

1) The survey area is divided into cubic cells of appropriate size.

2) An ellipsoid is drawn from the seismogram for each pair of source and receiver by changing by one sampling interval from the designated time after the travel time of the 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 pass are amplified by summation with in-phase. However, the amplitude on the other grid cell corners would be cancelled because of the summation with out-of-phase.

Judging from the model studies, it was determined that this algorithm reconstructed the structure with good accuracy, short calculation time, and small requirement for core memory.