Propagation Path Effects for Rayleigh and Love Waves

1978 ◽  
Author(s):  
E. Herrin ◽  
T. Goforth
Keyword(s):  
Love Waves ◽  
Propagation Path ◽  
Rayleigh And Love Waves

scholarly journals Surface waves in multilayered elastic media I. Rayleigh and Love waves from buried sources in a multilayered elastic half-space

1964 ◽  
Vol 54 (2) ◽  
pp. 627-679
Author(s):  
David G. Harkrider
Keyword(s):  
Surface Waves ◽  
Frequency Domain ◽  
Half Space ◽  
Rayleigh Waves ◽  
Elastic Half Space ◽  
Love Waves ◽  
Displacement Fields ◽  
Matrix Formulation ◽  
Total Displacement ◽  
Rayleigh And Love Waves

ABSTRACT A matrix formulation is used to derive integral expressions for the time transformed displacement fields produced by simple sources at any depth in a multilayered elastic isotropic solid half-space. The integrals are evaluated for their residue contribution to obtain surface wave displacements in the frequency domain. The solutions are then generalized to include the effect of a surface liquid layer. The theory includes the effect of layering and source depth for the following: (1) Rayleigh waves from an explosive source, (2) Rayleigh waves from a vertical point force, (3) Rayleigh and Love waves from a vertical strike slip fault model. The latter source also includes the effect of fault dimensions and rupture velocity. From these results we are able to show certain reciprocity relations for surface waves which had been previously proved for the total displacement field. The theory presented here lays the ground work for later papers in which theoretical seismograms are compared with observations in both the time and frequency domain.

Microtremor surveys based on rotational seismology: theoretical analysis with focus on separation of Rayleigh and Love waves in general wavefield of microtremors

2021 ◽  
Vol 228 (1) ◽  
pp. 589-603
Author(s):  
I Cho ◽  
K Yoshida ◽  
H Uebayashi
Keyword(s):  
Wavelength Range ◽  
Process Model ◽  
Spatial Differentiation ◽  
Love Waves ◽  
Rotational Seismology ◽  
Finite Differencing ◽  
Rayleigh And Love Waves ◽  
Rotational Method ◽  
Incoherent Noise ◽  
Array Geometry

SUMMARY The applicability of rotational seismology to the general wavefield of microtremors is theoretically demonstrated based on a random process model of a 2-D wavefield. We show the effectiveness of taking the rotations (i.e. spatial differentiation) of microtremor waveforms in separating the Rayleigh and Love waves in a wavefield where waves are simultaneously arriving from various directions with different intensities. This means that a method based on rotational seismology (a rotational method) is capable of separating Rayleigh and Love waves without adopting a specific array geometry or imposing a specific assumption on the microtremor wavefield. This is an important feature of a rotational method because the spatial autocorrelation (SPAC) method, a conventional approach for determining phase velocities in microtremor array surveys, requires either the use of a circular array or the assumption of an isotropic wavefield (i.e. azimuthal averaging of correlations is required). Derivatives of the SPAC method additionally require the assumption that Rayleigh and Love waves are uncorrelated. We also show that it is possible to apply a rotational method to determine the characteristics of Love waves based on a simple three-point microtremor array that consists of translational (i.e. ordinary) three-component sensors. In later sections, we assume realistic data processing for microtremor arrays with translational sensors to construct a theoretical model to evaluate the effects of approximating spatial differentiation via finite differencing (i.e. array-derived rotation, ADR) and the effects of incoherent noise on analysis results. Using this model, it is shown that in a short-wavelength range compared to the distance for finite differencing (e.g. $\lambda < 3h$, where $\lambda $ and $h$ are the wavelength and distance for finite differencing, respectively), the leakage of unwanted wave components can determine the analysis limit. It is also shown that in a long-wavelength range (e.g. $\lambda > 3h$), the signal intensity gradually decreases, and thus the effects of incoherent noise increase (i.e. the signal-to-noise ratio, SNR decreases) and determine the analysis limit. We derive the relation between the SNR and wavelength. Although the analysis results quantitatively depend on the array geometry used for finite differencing, the qualitative understanding supported by mathematical expressions with a physically clear meaning can serve as a guideline for the treatment of data obtained from ADR.

Surface waves in homogenous visco-elastic media of higher order under the influence of surface stresses

2013 ◽  
Vol 22 (5-6) ◽  
pp. 185-191 ◽  
Author(s):  
Munish Sethi ◽  
K.C. Gupta ◽  
Monika Rani ◽  
A. Vasudeva
Keyword(s):  
Surface Waves ◽  
Solid Medium ◽  
Elastic Solid ◽  
Higher Order ◽  
Love Waves ◽  
Elastic Media ◽  
Time Rate ◽  
Surface Stresses ◽  
Rayleigh And Love Waves

AbstractThe aim of the present paper is to investigate the surface waves in a homogeneous, isotropic, visco-elastic solid medium of nth order, including time rate of strain under the influence of surface stresses. The theory of generalized surface waves is developed to investigate particular cases of waves such as the Stoneley, Rayleigh, and Love waves. Corresponding equations have been obtained for different cases. These are reduced to classical results, when the effects of surface stresses and viscosity are ignored.

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