Finding a Velocity Profile from a Love Wave Dispersion Curve: Problems of Uniqueness

Gerver, M. L.; Kazhdan, David

doi:10.1007/978-1-4684-8815-9_20

Cited by 5 publications

(5 citation statements)

References 1 publication

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“…13, one can see that the fit after inversion is almost perfect, although the true model and the reconstructed f a t a v t 7fteyi:vefsiy Al-;>Y , , I , I , I ~ I , I , model are quite different. This shows a practical non-uniqueness that, given the fact that group velocities are a derivative property of phase velocities may well be related to the theoretical non-uniqueness Gerver & Kazhdan (1972) found for fundamental-mode phase velocities. For the B models the results of inversions of group velocities with the data set indicated in Fig.…”

Section: Group Velocitiesmentioning

confidence: 86%

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Resolving a low-velocity zone with surface-wave data

Heijst

Snieder

Nowack

1994

Geophysical Journal International

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SUMMARY The main purpose of seismic inversion is the retrieval of seismic velocities and densities in the earth. Inversion of body‐wave traveltimes cannot uniquely determine the seismic velocities as a function of depth when a low‐velocity layer is present. It is generally assumed that surface waves do not suffer from the same non‐uniqueness. The issue is addressed whether it is possible to remove the non‐uniqueness of traveltime inversions with a realistic set of surface‐wave data. This requires the exact determination of the velocity distribution within and around the low‐velocity zone. Waveforms, phase velocities as well as group velocities are investigated qualitatively. Synthetic Love‐wave phase and group velocities are actually inverted. Waveforms are shown to be sensitive to the exact velocity distribution of a low‐velocity layer, but it is concluded that the removal of the non‐uniqueness with the use of waveforms is difficult because the differences of the waveforms are generally small and because complications such as lateral heterogeneity and poorly known source parameters reduce the accuracy of waveform inversions. The inversions of Love phase and group velocities indicate that it is difficult to determine the velocity distribution of a low‐velocity layer in a statistically significant way with a realistic set of dispersion data. Group velocities are shown to be more sensitive to the low‐velocity structure than phase velocities. Unfortunately, group‐velocity data suffers from a practical non‐uniqueness because in general only fundamental‐mode group velocities can be measured. It is concluded that the non‐uniqueness in the detailed structure caused by a low‐velocity layer cannot readily be resolved by using surface‐wave dispersion data.

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Section: Group Velocitiesmentioning

confidence: 86%

“…The first rigorous attempt to establish uniqueness in the case of the inverse Love-wave dispersion problem was performed by Gerver & Kazhdan (1972). They showed that the S velocity as a function of depth cannot be derived uniquely from only fundamental-mode phase velocities.…”

Section: Introductionmentioning

confidence: 99%

Resolving a low-velocity zone with surface-wave data

Heijst

Snieder

Nowack

1994

Geophysical Journal International

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“…The spherical approximations devised by Alterman, Jarosch & Pakeris (1961) and Bolt & Dorman (1961) were used for these calculations. The results for Love waves were checked subsequently against those obtained by the exact transformation presented by Biswas & Knopoff (1970), and Gerver & Khazdan (1968). Both sets of calculations were concordant in the period range of interest.…”

Section: Multi-mode Crustal Surface Wave Dispersion Observed At Intermentioning

confidence: 90%

Theory for Errors, Resolution, and Separation of Unknown Variables in Inverse Problems, with Application to the Mantle and the Crust in Southern Africa and Scandinavia

Der

Landisman²

1972

Geophysical Journal International

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The geophysical inverse problem, the determination of the properties of the subsurface from a limited set of measurements, is basically non-unique. Separation of the unknown variables, the depth resolution, and the accuracy of the parameter estimates are three competing objectives which are reciprocally related.The investigation of a set of free oscillation measurements having errors based upon those given by Derr revealed that the addition of overtones with low radial order numbers to the set of fundamental mode observations does not greatly improve the shear velocity depth resolution but does facilitate the separation of shear velocity from density.Two sets of multi-mode surface wave dispersion measurements were inverted: the surface wave observations for Southern African reported by Bloch, Hales & Landisman, and a set of data for central Scandinavia as reported by Noponen, Porkka, Pirhonen and Luosto, and Crampin. Several models were obtained for each data set by varying the constraints used in the inversion process. The errors of the dispersion measurements were propagated into estimates of the accuracy of the inverted crustal models for the first time. Inclusion of shear and compressional velocity refraction measurements as a constraint on the inversion process leads to models for Scandinavia having some indication of velocity inversions at the base of the sialic portion of the crust at the base of the crust and in the first few tens of kilometres of the uppermost mantle. 137

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“…3 were used for this purpose. For Love waves it is possible to apply a suitable transformation to the plane-layered earth model to simulate the effects of sphericity (Gerver and Kazhdan, 1968;Biswas and Knopoff, 1970). For Rayleigh waves, however, a similar trans-* formation is difficult to achieve and an empirical correction must be applied.…”

Section: Corrections To the Observed Datamentioning

confidence: 99%

Propagation Path Effects for Rayleigh and Love Waves (Surface Wave Studies of the Bering Sea and Alaska Area)

Herrin¹,

Goforth²,

Jin³

1979

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The area of the Bering Sea and Alaska has been studied in terms of shear-velocity, density and compressional-velocity structure by applying a generalized linear inversion method to fundamental-mode Rayleigh-wave group-velocity dispersion relationships in the period range from 10 to 100 sec.Group velocity dispersion relationships in the area have been obtained by applying the phase-matched filtering technique (He-rrin and Goforth, 1977) to digitally recorded surface-wave data.Corrections for instrument response and the sphericity of the Earth were applied to the dispersion observations. A new exact analytical method for the computation of Rayleigh-wave phase-velocity partial derivatives with respect to Earth parameters hias been formulated. With the phase-velocity partial derivatives determined, the group velocity partial derivatives were computed by use of the fast and accurate method of Rodi e-t-al. (1975), and were successfully incorporated into a generalized linear inversion method. ivThe study area has been found to ccnsist of three physiographic provinces and the structure of the three

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Finding a Velocity Profile from a Love Wave Dispersion Curve: Problems of Uniqueness

Cited by 5 publications

References 1 publication

Resolving a low-velocity zone with surface-wave data

Resolving a low-velocity zone with surface-wave data

Theory for Errors, Resolution, and Separation of Unknown Variables in Inverse Problems, with Application to the Mantle and the Crust in Southern Africa and Scandinavia

Propagation Path Effects for Rayleigh and Love Waves (Surface Wave Studies of the Bering Sea and Alaska Area)

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