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Finite‐difference modelling for tunnel seismology
Author(s) -
Kneib Guido,
Leykam Alice
Publication year - 2004
Publication title -
near surface geophysics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.639
H-Index - 39
eISSN - 1873-0604
pISSN - 1569-4445
DOI - 10.3997/1873-0604.2004005
Subject(s) - classification of discontinuities , finite difference , seismogram , geology , finite difference method , seismic wave , diagonal , point (geometry) , seismology , geometry , mathematical analysis , mathematics
The diagonal differencing algorithm, which takes spatial derivatives along the diagonals of the finite‐difference grid, is well suited to solve the elastodynamic equations for tunnel seismic modelling because it is accurate and stable at strong low‐order discontinuities of the elastic medium. Spatial high‐order finite‐difference operators increase the accuracy and efficiency of the algorithm except at steps in the elastic properties, where these operators fail. A solution is to use high‐order finite differences in most of the grid but to employ two‐point second‐order operators at low‐order discontinuities. This keeps memory requirements and computational effort on a level that allows 3D simulations on moderately priced PC hardware. Measurements with the commercial tunnel seismic prediction method yield complex seismic common‐receiver gathers with long direct‐wave pulses. Finite‐difference simulations in two and three dimensions reveal that these long pulses are due to P‐wave reverberations in and around the water‐filled shothole. Direct S‐waves originate close to the detonation point by conversion at the shothole–rock boundary. A dispersive, low‐frequency guided wave reverberates with the average S‐wave velocity inside the excavation damaged zone around the tunnel. The guided wave creates multiple body waves inside the undisturbed rock as it reverberates. It carries useful information about the degree and depth of the rock excavation damage but the guided wave often overlaps tunnel surface‐wave modes and may be difficult to extract from seismograms. Receivers should be buried deeper than the extent of the excavation damaged zone so that the guided waves and tunnel surface waves, which circulate around the tunnel, do not dominate seismic records and hide direct S‐waves, reflections or other late arrivals.