Kirchhoff integral applied to two-dimensional seismic modeling of a growth fault in the Niger delta region

Abstract

Over seventy percent of the oil and gas fields found in the delta region is associated with growth faults. Recognition of this type of fault system therefore will play an important role in future petroleum exploration and development in the Niger delta region and any other region where growth faults are found. A model of the influence of growth faults on the accumulation and distribution of hydrocarbons has been presented in this study. It is shown that they constitute some of the migration route of hydrocarbons from the shales of the Akata Formation into the paralic sand layers of Agbada Formation. A two-dimensional model analysis of the growth fault is presented seismically. To generate the two-dimensional seismic model response, application is made of the solution of the wave equation known as Kirchhoff Integral. This solution has been derived by making use of Green functions. A computational form of the Kirchhoff integral has been presented. Using this solution, a computer program is written which generates the seismic responses and plots them on a versatec plotter. The plots reveal that the reflection-diffraction amplitude at the very edge of each model is approximately one-half the reflection magnitude. This leads to the suggestion that marking the half amplitude point of a flat event, the horizontal extent of the boundary can be mapped. A mathematical relationship between retarded potential (wave equation solution) and potential theory equation (solution of Poisson's equation) has been derived.