Computation of analytical partial derivatives of phase and group velocities for Rayleigh waves with respect to structural parameters

Urban, L.; Cichowicz, Artur; Vaccari, Franco

doi:10.1007/bf01613919

Cited by 36 publications

(26 citation statements)

References 4 publications

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“…A model is considered acceptable if the objective function is less than 0.04 km/s. The period range of the dispersion curves used for inversion varies from 4 s to 30 s. The partial derivatives of the group velocity of Rayleigh wave (Rodi et al, 1975;Urban et al, 1993;Fang et al, 2010) show that the dispersion curve in this period range is sensitive to shear wave velocity structure from the near surface to about 50 km of depth, and insensitive to the shear wave velocity structure below 150 km (see also Panza, 1981). So we construct a starting model of 150 km thick.…”

Section: Parameterization and Priori Constraintsmentioning

confidence: 99%

Crustal velocity structures beneath North China revealed by ambient noise tomography

Fang

Ding

et al. 2010

Earthq Sci

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We collected continuous noise waveform data from January 2007 to February 2008 recorded by 190 broadband and 10 very broadband stations of the North China Seismic Array. The study region is divided into grid with interval 0.25°×0.25°, and group velocity distribution maps between 4 s and 30 s are obtained using ambient noise tomography method. The lateral resolution is estimated to be 20−50 km for most of the study area. We construct a 3-D S wave velocity model by inverting the pure path dispersion curve at each grid using a genetic algorithm with smoothing constraint. The crustal struc- ture observed in the model includes sedimentary basins such as North China basin, Yanqing-Huailai basin and Datong basin. A well-defined low velocity zone is observed in the Beijing-Tianjin-Tangshan region in 22−30 km depth range, which may be related to the upwelling of hot mantle material. The high velocity zone near Datong, Shuozhou and Qingshuihe within the depth range of 1−23 km reveals stable characteristics of Ordos block. The Taihangshan front fault extends to 12 km depth at least

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Section: Parameterization and Priori Constraintsmentioning

confidence: 99%

Crustal velocity structures beneath North China revealed by ambient noise tomography

Fang

Ding

et al. 2010

Earthq Sci

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“…However, his formulae are based on the Thomson-Haskell matrices, which are numerically unstable at short periods (see below). Urban et al (1993) described the analytical computation of partial derivatives of phase and group velocities of Rayleigh waves using Knopoff's formulation of the dispersion equation (see Schwab and Knopoff, 1972). This approach avoids loss-of-precision problems at short periods, but leads to very complicated expressions.…”

Section: Introductionmentioning

confidence: 99%

Analytical partial derivatives of the phase- and group velocities for Rayleigh waves propagating in a layer on a half-space

2005

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The dispersion relation for Rayleigh waves in a layer on a half-space is modified by introducing the quadratic wave number instead of the phase velocity. The implicit function theorem is then used to derive analytical formulae for the group velocity and for the phase-and group velocity partial derivatives with respect to the parameters of the medium. As two examples, the method is applied to the interpretation of dispersion curves for short-period Rayleigh waves observed in a sedimentary basin of the WestCarpathians, and in the Moravo-Silesian region, Czech Republic.

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“…Similar conclusions are given in Peter et al (2008): in the absence of an accurate crustal model, the retrieved upper mantle structure is dubious to about 200 km of depth. Accordingly with the values of the partial derivatives of the group and phase velocities for Rayleigh waves with respect to structural parameters (Urban et al 1993), the assembled cellular dispersion data in the period ranges from 5 to 150 s for group velocity and from 15 to 150 s for phase velocity allow us to obtain reliable velocity structure in the depth range from 3-15 to about 350 km. In each cell, the Earth structure is modelled by 19 layers down to the depths of about 600 km: the uppermost five layers have properties fixed a priori, using independent literature information specific for each cell; the following five layers have variable Vs, Vp, thicknesses and, if necessary, density; in the 11th layer Vp, Vs, and density are fixed while the thickness varies in such a way that the whole stack of 11 layers has a total thickness, H, equal to 350 km; below 350 km of depth there are eight layers, of Poissonian material, with constant properties common to all cells.…”

Section: Methods and Datamentioning

confidence: 99%

The shear-wave velocity structure of the lithosphere–asthenosphere system in the Iberian area and surroundings

Raykova

Panza

2010

Rend. Fis. Acc. Lincei

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The S-wave velocity model, to the depth of 300 km for the Iberian area and surroundings, is obtained with the non-linear inversion of Rayleigh wave tomographic data in the period range from 5 to 150 s. The three-dimensional model of the region is assembled from 74 juxtaposed one-dimensional cellular structures, sized 1°9 1°, by means of a local smoothing optimisation. The S-wave velocity model shows the almost constant velocity (*4.40 km/s) in the upper mantle beneath the Iberian Massif, the welldeveloped low-velocity zones in the Valencia Trough and under northwest Africa, and specific features of the upper mantle layering in the zone of the Iberian range. The thickness of the crust varies between 25 and 35 km with exceptions in the zones of the Valencia Trough (11-18 km) and Pyrenees (35-45 km). Our Vs models are well correlated with the geological structure along Transmed I and evidence several features of the lithosphere-asthenosphere system in the Betic-Rif domain: quite distinct Iberian, Alboran and Meseta crustal domains; relatively thin, well-developed lithosphere under the Rif system; and clearly defined boundary between the upper and lower asthenosphere. The cellular velocity model of the Betics, where ultrapotassic lamproitic magmatism is observed, has features similar to those of other three areas in the western Mediterranean where ultrapotassic lamproitic magmatism of different age is observed. The crust and upper mantle models in these four areas can be correlated with the age of the magmatism and the local heat flow, and outline how, starting from a naturally quite undifferentiated mantle where magma genesis is currently in progress, the differentiation in lithosphere and asthenosphere can take place in time.

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Computation of analytical partial derivatives of phase and group velocities for Rayleigh waves with respect to structural parameters

Cited by 36 publications

References 4 publications

Crustal velocity structures beneath North China revealed by ambient noise tomography

Crustal velocity structures beneath North China revealed by ambient noise tomography

Analytical partial derivatives of the phase- and group velocities for Rayleigh waves propagating in a layer on a half-space

The shear-wave velocity structure of the lithosphere–asthenosphere system in the Iberian area and surroundings

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