Seismogram Synthesis and Recompression of Dispersive In‐seam Seismic Multimode Data Using a Normal‐mode Superposition Approach

Abstract

BREITZKE, M. 1992. Seismogram synthesis and recompression of dispersive in-seam seismic multimode data using a normal-mode superposition approach. Geophysical Prospecting 40, In spite of a geometrical rotation into radial and transverse parts, two-or threecomponent in-seam seismic data used for underground fault detection often suffer from the problem of overmoding ' noise '. Special recompression filters are required to remove this multimode dispersion so that conventional reflection seismic data processing methods, e.g. CMP stacking techniques, can be applied afterwards.A normal-mode superposition approach is used to design such multimode recompression filters. Based on the determination of the Green's function in the far-field, the normal-mode superposition approach is usually used for the computation of synthetic single-and multimode (transmission) seismograms for vertically layered media. From the filter theory's point of view these Green's functions can be considered as dispersion filters which are convolved with a source wavelet to produce the synthetic seismograms. Thus, the design of multimode recompression filters can be reduced to a determination of the inverse of the Green's function. Two methods are introduced to derive these inverse filters. The first operates in the frequency domain and is based on the amplitude and phase spectrum of the Green's function. The second starts with the Green's function in the time domain and calculates two-sided recursive filters.To test the performance of the normal-mode superposition approach for in-seam seismic problems, it is first compared and applied to synthetic finite-difference seismograms of the Love-type which include a complete solution of the wave equation. It becomes obvious that in the case of one and two superposing normal modes, the synthetic Love seam-wave seismograms based on the normal-mode superposition approach agree exactly with the finitedifference data if the travel distance exceeds two dominant wavelengths. Similarly, the application of the one-and two-mode recompression filters to the finite-difference data results 31-70. 31 32 M O N I K A BREITZKE in an almost perfect reconstruction of the source wavelet already two dominant wavelengths away from the source.Subsequently, based on the dispersion analysis of an in-seam seismic transmission survey, the normal-mode superposition approach is used both to compute one-and multimode synthetic seismograms and to apply one-and multimode recompression filters to the field data. The comparison of the one-and two-mode synthetic seismograms with the in-seam seismic transmission data reveals that arrival times, duration and shape of the wavegroups and their relative excitation strengths could well be modelled by the normal-mode superposition approach. The one-mode recompressions of the transmission seismograms result in non-dispersive wavelets whose temporal resolution and signal-to-noise ratio could clearly be improved. The simultaneous two-mode recompressions of the underground transmission data show th...

Elimination of higher modes in dispersive in‐seam multimode Love waves

“…The computation of multimode synthetic seismograms is based on the determination of Green's function for a vertically layered medium subject to a unidirectional unit impulse in the 2D case (Breitzke 1992). In this case the mathematical approach is based on the reciprocity and representation theorem and leads to a far-field expression of the Love-wave terms of Green's function (Aki and Richards 1980).…”

“…with r(z) denoting the density. Obviously, the amplitude spectrum |S n (x,z,q)| depends on (Breitzke 1992): -the value of the eigenfunction or spectral amplitude-depth distribution curve l(q,k n ,Z) at depths Z = z and Z = h; -the group-velocity dispersion curve u n (q); -the energy integral I L1 (q,k n ) which mainly integrates the amplitude-depth distribution curves from minus to plus infinity (equation (7)).…”

“…In addition, the principle of the NMS method is used to explain the PPSF procedure. An inverse of Green's function has been used as a filter to remove the dispersion in the seismogram (Breitzke 1992).…”

“…The energy integral (7) describes the total energy trapped in the complete layer sequence. Thus, the single-mode amplitude spectra of the Green's function provide information on the relative excitation strength of each single mode depending on the source and receiver positions (Breitzke 1992). For the symmetric layer sequence, rock-coal-rock, and a source and receiver positioned in the centre of the coal-seam, Fig.…”

“…This 'mode separation' can be achieved to the degree to which we know a priori the characteristics of the individual modes that compose the seismogram (Aki and Richards 1980). In contrast to seismology, very few modes need to be considered in in-seam seismic exploration to simulate synthetic multimode data (Breitzke 1992).…”