Low‐ and high‐frequency radiation from seismic sources in cased boreholes

Abstract

An accurate characterization of borehole seismic sources is necessary to model and interpret waveforms observed in crosshole and reverse vertical seismic profiling (VSP) surveys, since the radiation pattern of a source will directly influence the amplitudes of elastic wave arrivals at receiver locations. Any attempt to study these data or perform inversions of amplitude data without incorporating the borehole effects will have serious limitations. Most previous studies of borehole seismic source radiation patterns have applied low‐frequency approximations to develop expressions for the radiation patterns of volume injection or stress sources (Heelan, 1953; White, 1960; White and Senghush, 1963; Lee and Balch, 1982; Lee, 1986; Kurkjian, 1986; Meredith, 1990; Winbow, 1991; Ben‐Menahem and Kostek, 1991). For example, Lee and Balch (1982) used this approach, along with a steepest descent solution, to derive closed‐form analytic expressions for the asymptotic far‐field radiation from sources located in uncased boreholes. Meredith (1990) applied the same methodology to study the radiation patterns of a variety of types of sources, though he also computed full waveform synthetic seismograms using the discrete wavenumber method. Likewise, Greenfield (1978) used full waveform numerical solutions to compute seismograms for force sources applied to the wall of a cylindrical cavity.