FINITE-DIFFERENCE AND FREQUENCY-WAVE-NUMBER MODELING OF SEISMIC MONOPOLE SOURCES AND RECEIVERS IN FLUID-FILLED BOREHOLES

In borehole seismic experiments the presence of the borehole has a significant effect on observations. Unfortunately, including boreholes explicitly in modeling schemes excludes the use of some methods (e.g., frequency-wavenumber) and adds prohibitively to the cost of others (e.g., finite difference). To overcome this problem, we use the concept of an effective source/receiver array to replace the explicit representation of the borehole by a distributed seismic source/receiver. This method mimics the presence of the borehole at seismic frequencies under a wide variety of conditions without adding a significant computational cost. It includes the effects of dispersive and attenuative tube wave propagation, the generation of secondary sources at interfaces and caliper changes, and the generation of conical waves in low-velocity layers. Comparison with a finite-difference scheme with an explicit borehole representation validates the approach. The modeling method applied to a continuity logging geometry demonstrates that the presence of guided waves does not uniquely imply bed connectivity. Results for a single-well imaging geometry emphasize the dominance of the tube wave in the hydrophone synthetics and demonstrates the necessity of using clamped geophones for single-well experiments. The concept of an effective source/receiver array is an efficient way of including borehole phenomena in seismic modeling methods at minimal extra computational cost.