scholarly journals A MATLAB Package for Calculating Partial Derivatives of Surface-Wave Dispersion Curves by a Reduced Delta Matrix Method

2019 ◽  
Vol 9 (23) ◽  
pp. 5214 ◽  
Author(s):  
Wu ◽  
Wang ◽  
Su ◽  
Zhang
Keyword(s):  
Surface Wave ◽  
Group Velocity ◽  
Love Wave ◽  
Wave Dispersion ◽  
Dispersion Curves ◽  
Wave Group ◽  
Surface Wave Dispersion ◽  
Partial Derivatives ◽  
Matlab Package ◽  
Derivatives Of

Various surface-wave exploration methods have become increasingly important tools in investigating the properties of subsurface structures. Inversion of the experimental dispersion curves is generally an indispensable component of these methods. Accurate and reliable calculation of partial derivatives of surface-wave dispersion curves with respect to parameters of subsurface layers is critical to the success of these approaches if the linearized inversion strategies are adopted. Here we present an open-source MATLAB package, named SWPD (Surface Wave Partial Derivative), for modeling surface-wave (both Rayleigh- and Love-wave) dispersion curves (both phase and group velocity) and particularly for computing their partial derivatives with high precision. The package is able to compute partial derivatives of phase velocity and of Love-wave group velocity analytically based on the combined use of the reduced delta matrix theory and the implicit function theorem. For partial derivatives of Rayleigh-wave group velocity, a hemi-analytical method is presented, which analytically calculates all the first-order partial differentiations and approximates the mixed second-order partial differentiation term with a central difference scheme. We provide examples to demonstrate the effectiveness of this package, and demo scripts are also provided for users to reproduce all results of this paper and thus to become familiar with the package as quickly as possible.

scholarly journals A perturbation scheme for obtaining partial derivatives of Love-wave group-velocity dispersion

1975 ◽  
Vol 65 (6) ◽  
pp. 1753-1760
Author(s):  
Dan Kosloff
Keyword(s):  
Group Velocity ◽  
Love Wave ◽  
Group Velocity Dispersion ◽  
Second Order ◽  
Wave Number ◽  
Perturbation Scheme ◽  
Wave Group ◽  
Partial Derivatives ◽  
Velocity Spectra ◽  
Derivatives Of

abstract A method is derived for obtaining partial derivatives of Love-wave group-velocity spectra for a layered medium using a second-order perturbation theory. These partials are a prerequisite for systematic inversion of group-velocity spectra but they are helpful as well in trial and error methods. Mathematically the equation of motion and boundary conditions for Love waves are a singular Sturm Liouville type eigenvalue problem. In the case of a fixed wave number, the eigenvalues are the negative of the square of the frequencies. Thus, by expressing the first- and second-order perturbations of the eigenvalues in terms of partial derivatives of the frequency with respect to the wave number and material parameters of the medium, one can relate these perturbations to group-velocity partials. The scheme should be relatively economical and easy to incorporate in Love-wave dispersion codes.

scholarly journals A Feasibility Study on Monitoring Crustal Structure Variations by Direct Comparison of Surface Wave Dispersion Curves from Ambient Seismic Noise

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
K. Muhumuza
Keyword(s):  
Surface Wave ◽  
Rayleigh Wave ◽  
Crustal Structure ◽  
Upper Mantle ◽  
Ambient Noise ◽  
Seismic Velocity ◽  
Wave Dispersion ◽  
Dispersion Curves ◽  
Wave Group ◽  
Surface Wave Dispersion

This work assesses the feasibility of the direct use of surface-wave dispersion curves from seismic ambient noise to gain insight into the crustal structure of Bransfield Strait and detect seasonal seismic velocity changes. We cross-correlated four years of vertical component ambient noise data recorded by a seismic array in West Antarctica. To estimate fundamental mode Rayleigh wave Green’s functions, the correlations are computed in 4-hr segments, stacked over 1-year time windows and moving windows of 3 months. Rayleigh wave group dispersion curves are then measured on two spectral bands—primary (10–30 s) and secondary (5–10 s) microseisms—using frequency-time analysis. We analyze the temporal evolution of seismic velocity by comparing dispersion curves for the successive annual and 3-month correlation stacks. Our main assumption was that the Green’s functions from the cross-correlations, and thus the dispersion curves, remain invariant if the crustal structure remains unchanged. Maximum amplitudes of secondary microseisms were observed during local winter when the Southern Ocean experiences winter storms. The Rayleigh wave group velocity ranges between 2.1 and 3.7 km/s, considering our period range studied. Interannual velocity variations are not much evident. We observe a slight velocity decrease in summer and increase in winter, which could be attributed to the pressure melting of ice and an increase in ice mass, respectively. The velocity anomalies observed within the crust and upper mantle structure correlate with the major crustal and upper mantle features known from previous studies in the area. Our results demonstrate that the direct comparison of surface wave dispersion curves extracted from ambient noise might be a useful tool in monitoring crustal structure variations.

P- and S-wave velocity models from surface wave dispersion curves data transform

2017 ◽  
Author(s):  
Valentina Socco ◽  
Farbod Khosro Anjom ◽  
Cesare Comina ◽  
Daniela Teodor
Keyword(s):  
Surface Wave ◽  
Wave Velocity ◽  
Wave Dispersion ◽  
Dispersion Curves ◽  
S Wave ◽  
Surface Wave Dispersion ◽  
Velocity Models

A model study of elastic waves in a layered sphere

1967 ◽  
Vol 57 (5) ◽  
pp. 959-981
Author(s):  
Victor Gregson
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Elastic Waves ◽  
Wave Dispersion ◽  
Flat Space ◽  
Dispersion Curves ◽  
Body Waves ◽  
Surface Wave Dispersion ◽  
Steel Sphere ◽  
Long Wave

abstract Elastic waves produced by an impact were recorded at the surface of a solid 12.0 inch diameter steel sphere coated with a 0.3 inch copper layer. Conventional modeling techniques employing both compressional and shear piezoelectric transducers were used to record elastic waves for one millisecond at various points around the great circle of the sphere. Body, PL, and surface waves were observed. Density, layer thickness, compressional and shear-wave velocities were measured so that accurate surface-wave dispersion curves could be computed. Surface-wave dispersion was measured as well as computed. Measured PL mode dispersion compared favorably with theoretical computations. In addition, dispersion curves for Rayleigh, Stoneley, and Love modes were computed. Measured surface-wave dispersion showed Rayleigh and Love modes were observed but not Stoneley modes. Measured dispersion compared favorably with theoretical computations. The curvature correction applied to dispersion calculations in a flat space has been estimated to correct dispersion values at long-wave lengths to about one per cent of correct dispersion in a spherical model. Measured dispersion compared with such flat space dispersion corrected for curvature proved accurate within one per cent at long wave lengths. Two sets of surface waves were observed. One set was associated with body waves radiating outward from impact. The other set was associated with body waves reflecting at the pole opposite impact. For each set of surface waves, measured dispersion compared favorably with computed dispersion.

scholarly journals A fast, convenient program for computation of surface-wave dispersion curves in multilayered media

1961 ◽  
Vol 51 (4) ◽  
pp. 495-502
Author(s):  
Frank Press ◽  
David Harkrider ◽  
C. A. Seafeldt
Keyword(s):  
Surface Wave ◽  
Rayleigh Waves ◽  
High Speed ◽  
Wave Dispersion ◽  
Dispersion Curves ◽  
Mail Order ◽  
Mantle Structure ◽  
Wave Analysis ◽  
Multilayered Media ◽  
Surface Wave Dispersion

Abstract Surface wave analysis has become an important tool for exploration of crustal and mantle structure. The need exists for fast, convenient digital computer programs for computing theoretical dispersion curves and displacements for Rayleigh waves and Love waves. One such program for an IBM 7090 computer is described and made available to the scientific community. Among the conveniences are mail-order service, high speed, and choice of many options.

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