A Time‐domain Approach to the Normal‐incidence Inverse Problem*

Mendel, Jerry M.

doi:10.1111/j.1365-2478.1981.tb00707.x

Cited by 10 publications

(1 citation statement)

References 19 publications

(18 reference statements)

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“…For noisy data, major problems with the instability of the Levinson recursion algorithm are reported with the inversion of ' real ' reflection seismograms (Mendel and Habibi-Ashrafi 1980;Mendel 1981 ;Bamberger, Chavent, Hermon and Lailly 1982;Ferber 1985). Cybenko (1980) showed that where instabilities occur the underlying Toeplitz matrix is ill-conditioned.…”

Section: The Inversion O F Pseudoreflection Seismogramsmentioning

confidence: 99%

Levinson Inversion of Earthquake Geometry Sh‐transmission Seismograms in the Presence of Noise*

Scherbaum

1987

Geophysical Prospecting

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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 of layer 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.

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Section: The Inversion O F Pseudoreflection Seismogramsmentioning

confidence: 99%

Levinson Inversion of Earthquake Geometry Sh‐transmission Seismograms in the Presence of Noise*

Scherbaum

1987

Geophysical Prospecting

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Higher‐Order Statistics

Hadjileontiadis

Panas

Rekanos

2006

Wiley Encyclopedia of Biomedical Engineering

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In the past 15 years, we have witnessed an expansion of higher‐order statistics (spectra) (HOS)‐based techniques, which have been applied to a wide range of signal processing and system theory problems. This expansion is a direct result of the advantageous properties of HOS, which make them favorable in problems where nonGaussianity, nonminimum phase, colored noise, or nonlinearities are important and must be accounted for. To this end, HOS have been applied to the design of advanced communications, sonar, radar, speech, biomedical, geophysical, and imaging systems. The purpose of the present study is to review the main aspects of the application of HOS in the biomedical engineering field by presenting biomedical application problems that can directly benefit from the use of HOS, in order to aid the reader in grasping the utility of HOS‐based techniques within the biomedical signal processing framework. Fundamental definitions and properties of HOS are initially presented, pointing out the general reasons that are behind the use of HOS in signal processing (i.e., extraction of information because of deviations from normality, estimation of the phase of parametric signals, and detection and characterization of the properties of nonlinear mechanisms that generate time series). Next, a variety of HOS‐based biomedical applications are described, referring to detection of nonlinearities (e.g., quadratic phase‐coupling), denoising‐signal estimation, system identification, classification, and compression issues, and involving analysis of electroencephalogram, electrocardiogram, surface electromyogram, electroneurogram, bioacoustic signals (lung, heart, bowel sounds), tremor, and tissue signatures. Finally, an extensive list of references in the area is provided as a companion aid to the reader for further exploitation of HOS.

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Some Representation, Measurement, Estimation, and Validation Problems in Reflection Seismology

Mendel

1985

IFAC Proceedings Volumes

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A Time‐domain Approach to the Normal‐incidence Inverse Problem*

Cited by 10 publications

References 19 publications

Levinson Inversion of Earthquake Geometry Sh‐transmission Seismograms in the Presence of Noise*

Levinson Inversion of Earthquake Geometry Sh‐transmission Seismograms in the Presence of Noise*

Higher‐Order Statistics

Some Representation, Measurement, Estimation, and Validation Problems in Reflection Seismology

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