Uniform asymptotic conversion of Helmholtz data from 3D to 2D

Abstract The conversion of a three-dimensional acoustic data set into an equivalent two-dimensional acoustic data set is essential for seismic interpretation where the amplitude is a key issue. The transfer function for such a transformation should be estimated and we propose the construction of such a transfer function via the computation of the pressure field when considering the Helmholtz equation. Ray theory is used in order to improve the homogeneous transfer function that is typically applied to three-dimensional data to obtain the input two-dimensional data set used in many inversion algorithms. The improved transfer function uses a uniform expansion that directly includes the source singularity. The entire useful frequency bandwidth is more accurately preserved by using the uniform expansion. A synthetic example is presented for the Helmholtz equation for the bore-hole geometry encountered in cross-well radar experiments.

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