Levinson Inversion of Earthquake Geometry Sh-Transmission Seismograms in the Presence of Noise*
F. Scherbaum, 2008. "Levinson Inversion of Earthquake Geometry Sh-Transmission Seismograms in the Presence of Noise ", Seismic Interferometry: History and Present Status, Kees Wapenaar, Deyan Draganov, Johan O.A. Robertsson
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Scherbaum, F. 1987, Levinson Inversion of Earthquake Geometry SH-Transmission Seismograms in the Presence of Noise, Geophysical Prospecting 35, 787-802.
The Kunetz-Claerbout equation for the acoustic transmission problem in a layered medium in its original form establishes the relation between the transmission-and the reflection response for P-waves in an horizontally layered medium and with vertical incidence. It states that the reflection seismogram due to an impulsive source at the surface,is one side of the autocorrelation of the seismogram due to an impulsive source at depth and a surface receiver.
By adapting Claerbout’s formulation to the transmission of SH-waves, the Kunetz-Claerbout equation also holds for reflection and transmission coefficients dependent on the incident angle. Thus, earthquake geometry SH-transmission seismograms can be used to calculate corresponding pseudoreflection seismograms which, in turn, can be inverted for the impedance structure using the Levinson algorithm. If the average incidence angle is known, a geometrical correction on the resulting impedance model can improve the resolution oflayer thicknesses.
In contrast to the inversion of reflection seismograms, the Levinson algorithm is shown to yield stable results for the inversion of transmission seismograms even in the presence of additive noise. This noise stabilization is inherent to the Kunetz-Claerbout equation.
Results of inverted SH-wave microearthquake seismograms from the Swabian Jura, SW Germany, seismic zone obtained at recording site Hausen im Tal have been compared with sonic-log data from nearby exploration drilling at Trochtelfingen. The agreement of the main structural elements is fair to a depth of several hundred metres.