Kirchhoff PSTM

Kirchhoff Prestack Time Imaging (PreSTM)

Kirchhoff prestack time migration is typically applied after the input data has be compensated for fold. During the migration stage, the code keeps track of the illumination strength as a smooth function of space, offset and time; after stacking, the migrated gathers are compensated based on this illumination volume.

True amplitude Kirchhoff prestack time migration, Yu Zhang’s weighting function (2000) is used to handle the true amplitude weight. It includes compensation for the geometrical spreading in Bjorn Ursin (1990), and the “directional illumination” (so called Beylkin determinant, the Jacobian of the transformation from subsurface coordinates to surface coordinates, Beylkin, 1990, linearized inverse scattering problems in acoustics and elasticity).

For antialiasing, each input trace is low-pass filtered with a predetermined set of filters to form a number of frequency bands. A maximum nonaliasing frequency is computed based on the spatial coordinates of the migrated trace at some control time samples and a low-pass trace is used for the migration based on the maximum frequency. Based on these limits the appropriate frequency bands are selected and summed together to form the output sample.


Beylkin, G. and R. Burridge, 1990, Linearized Inverse Scattering Problems in Acoustics and Elasticity, Wave Motion, 12 (1), 15-52.

Ursin, B., 1990, Offset‐dependent geometrical spreading in a layered medium: GEOPHYSICS, 55(4), 492-496.

Zhang, Y., S. Gray, and J. Young, 2000, Exact and approximate weights for Kirchhoff migration: 70th Annual International Meeting, SEG, Expanded Abstracts.