Arrays of synthetic acoustic well logging waveforms: Computation and source design

Arrays of synthetic acoustic well logging waveforms are useful in the initial development of signal processing methods, as an aid in understanding actual well logging data, and in an analysis-by-synthesis approach to data inversion. In this paper, we present a fast and accurate method for the numerical evaluation of arrays of synthetic acoustic well logging waveforms associated with a homogeneous solid formation model. The method evaluates the two-dimensional Fourier transform of the modal coefficient which is expressed in terms of the cylindrical wave reflection coefficient and cylindrical wave impedances. A table look-up and interpolation scheme for the evaluation of ratios of Hankel functions for complex-valued arguments is responsible for a factor of three reduction in the overall computation time required to generate synthetic data, relative to the evaluation of these ratios using a Hankel function evaluation algorithm. This substantial savings easily outweighs the modest increase in storage which is required for the table. A low frequency constraint on the temporal response of the source is presented to ensure that the synthetic waveforms tend to zero for large time.