Errors Introduced in Estimation of Surface Wave Phase and Group Velocities Due to Wrong Assumptions: An Assessment Using a Simple Model For Love Wave

2021 ◽  
Author(s):  
Akash Kharita ◽  
Sagarika Mukhopadhyay
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Love Wave ◽  
Arrival Time ◽  
Epicentral Distance ◽  
Horizontal Distance ◽  
Wave Analysis ◽  
Time Period ◽  
Phase And Group Velocities ◽  
Group Velocities

<p>The surface wave phase and group velocities are estimated by dividing the epicentral distance by phase and group travel times respectively in all the available methods, this is based on the assumptions that (1) surface waves originate at the epicentre and (2) the travel time of the particular group or phase of the surface wave is equal to its arrival time to the station minus the origin time of the causative earthquake; However, both assumptions are wrong since surface waves generate at some horizontal distance away from the epicentre. We calculated the actual horizontal distance from the focus at which they generate and assessed the errors caused in the estimation of group and phase velocities by the aforementioned assumptions in a simple isotropic single layered homogeneous half space crustal model using the example of the fundamental mode Love wave. We took the receiver locations in the epicentral distance range of 100-1000 km, as used in the regional surface wave analysis, varied the source depth from 0 to 35 Km with a step size of 5 km and did the forward modelling to calculate the arrival time of Love wave phases at each receiver location. The phase and group velocities are then estimated using the above assumptions and are compared with the actual values of the velocities given by Love wave dispersion equation. We observed that the velocities are underestimated and the errors are found to be; decreasing linearly with focal depth, decreasing inversely with the epicentral distance and increasing parabolically with the time period. We also derived empirical formulas using MATLAB curve fitting toolbox that will give percentage errors for any realistic combination of epicentral distance, time period and depths of earthquake and thickness of layer in this model. The errors are found to be more than 5% for all epicentral distances lesser than 500 km, for all focal depths and time periods indicating that it is not safe to do regional surface wave analysis for epicentral distances lesser than 500 km without incurring significant errors. To the best of our knowledge, the study is first of its kind in assessing such errors.</p>

scholarly journals Automated detection and association of surface waves

1994 ◽  
Vol 37 (3) ◽  
Author(s):  
R. G. North ◽  
C. R. D. Woodgold
Keyword(s):  
Surface Waves ◽  
Group Velocity ◽  
Rayleigh Waves ◽  
Arrival Time ◽  
Narrow Band ◽  
Broad Band ◽  
Detection Algorithm ◽  
Automated Detection ◽  
Short Period ◽  
Group Velocities

An algorithm for the automatic detection and association of surface waves has been developed and tested over an 18 month interval on broad band data from the Yellowknife array (YKA). The detection algorithm uses a conventional STA/LTA scheme on data that have been narrow band filtered at 20 s periods and a test is then applied to identify dispersion. An average of 9 surface waves are detected daily using this technique. Beamforming is applied to determine the arrival azimuth; at a nonarray station this could be provided by poIarization analysis. The detected surface waves are associated daily with the events located by the short period array at Yellowknife, and later with the events listed in the USGS NEIC Monthly Summaries. Association requires matching both arrival time and azimuth of the Rayleigh waves. Regional calibration of group velocity and azimuth is required. . Large variations in both group velocity and azimuth corrections were found, as an example, signals from events in Fiji Tonga arrive with apparent group velocities of 2.9 3.5 krn/s and azimuths from 5 to + 40 degrees clockwise from true (great circle) azimuth, whereas signals from Kuriles Kamchatka have velocities of 2.4 2.9 km/s and azimuths off by 35 to 0 degrees. After applying the regional corrections, surface waves are considered associated if the arrival time matches to within 0.25 km/s in apparent group velocity and the azimuth is within 30 degrees of the median expected. Over the 18 month period studied, 32% of the automatically detected surface waves were associated with events located by the Yellowknife short period array, and 34% (1591) with NEIC events; there is about 70% overlap between the two sets of events. Had the automatic detections been reported to the USGS, YKA would have ranked second (after LZH) in terms of numbers of associated surface waves for the study period of April 1991 to September 1992.

The dispersion of surface waves on multilayered media*

1953 ◽  
Vol 43 (1) ◽  
pp. 17-34 ◽  
Author(s):  
N. A. Haskell
Keyword(s):  
Surface Waves ◽  
Rayleigh Waves ◽  
Matrix Formalism ◽  
Multilayered Media ◽  
Solid Media ◽  
Phase Velocity Dispersion ◽  
Phase And Group Velocities ◽  
Horizontal Heterogeneity ◽  
The Difference ◽  
Group Velocities

abstract A matrix formalism developed by W. T. Thomson is used to obtain the phase velocity dispersion equations for elastic surface waves of Rayleigh and Love type on multilayered solid media. The method is used to compute phase and group velocities of Rayleigh waves for two assumed three-layer models and one two-layer model of the earth's crust in the continents. The computed group velocity curves are compared with published values of the group velocities at various frequencies of Rayleigh waves over continental paths. The scatter of the observed values is larger than the difference between the three computed curves. It is believed that not all of this scatter is due to observational errors, but probably represents a real horizontal heterogeneity of the continental crusts.

Measurement of interstation phase and group velocities and Q using Wiener filtering

1982 ◽  
Vol 72 (1) ◽  
pp. 73-91
Author(s):  
Steven R. Taylor ◽  
M. Nafi Toksöz
Keyword(s):  
Surface Wave ◽  
Green’S Function ◽  
Green's Function ◽  
Amplitude Spectrum ◽  
Wiener Filter ◽  
Wave Path ◽  
Phase And Group Velocities ◽  
Filtering Technique ◽  
Surface Wave Data ◽  
Group Velocities

abstract A method for calculating interstation phase and group velocities and attenuation coefficients using a Wiener (least-squares) filtering technique is presented. The interstation Green's (or transfer) function is estimated from surface wave data from two stations laying along the same great circle path. The estimate is obtained from a Wiener filter which is constructed to estimate the signal recorded at the station further from the source from the signal recorded at the nearer station. The interstation group velocity is obtained by applying the multiple-filtering technique to the Green's function, and the interstation phase velocity from the phase spectrum of the Green's function. The amplitude spectrum of the Green's function is used to calculate average attenuation between the two stations. Using synthetic seismograms contaminated by noise, it is shown that the Q values calculated from the Green's function are significantly more stable and accurate than those obtained by taking spectral ratios. The method is particularly useful for paths involving short station separations and is applied to a surface wave path crossing the Iranian Plateau.

Monochromatic surface waves at the interface between poroelastic and fluid halfspaces

2005 ◽  
Vol 462 (2067) ◽  
pp. 701-723 ◽  
Author(s):  
Bettina Albers
Keyword(s):  
Surface Waves ◽  
Full Range ◽  
Limited Range ◽  
Open Boundary ◽  
Stoneley Wave ◽  
Poroelastic Media ◽  
Phase And Group Velocities ◽  
Leaky Rayleigh Wave ◽  
Surface Permeability ◽  
Group Velocities

The topic of the previous work of Albers and Wilmanski was the study of monochromatic surface waves at the boundary between a porous medium and a vacuum. This article is an extension of this research to the propagation of surface waves on the interface between a porous halfspace and a fluid halfspace. Results for phase and group velocities and attenuations are shown in dependence on both the frequency and the surface permeability. In contrast to classical papers on surface waves where only the limits of the frequency ω →0, ω →∞ and the limits of the surface permeability (fully sealed and fully open boundary) were studied, we investigate the problem in the full range of both parameters. For the analysis we use the ‘simple mixture model’ which is a simplification of the classical Biot model for poroelastic media. The construction of a solution is shown and the dispersion relation solved numerically. There exist three surface waves for this boundary: a leaky Rayleigh wave and both a true and a leaky Stoneley wave. The true Stoneley wave exists only in a limited range of the surface permeability.

The October 6, 1974 Acapulco earthquake: An example of the importance of short-period surface waves in strong ground motion

1978 ◽  
Vol 68 (6) ◽  
pp. 1663-1677
Author(s):  
Stephen H. Hartzell ◽  
James N. Brune ◽  
Jorge Prince
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Epicentral Distance ◽  
Source Region ◽  
Crystalline Rock ◽  
Body Waves ◽  
Wave Number ◽  
Source Depth ◽  
Moment Estimate ◽  
Short Period

abstract The Acapulco earthquake of October 6, 1974 (mb = 5.0, Ms = 4.75) resulted in 0.5 g accelerations in Acapulco at an epicentral distance of about 35 km. Extrapolation of the peak acceleration to the source region gives a near source acceleration of at least 1.0 g. If the teleseismically estimated source depth of 51 km is assumed, the Acapulco accelerogram must be interpreted as composed of primarily body waves. This assumption yields a moment estimate of 3.3 ×1023 dyne-cm and a stress drop of 1.5 kbar. However, strong evidence indicates that the source depth is only about 1.0 km and that the record is composed mainly of high frequency (1.0 to 4.0 Hz) surface waves. The character of the record is that of a normally dispersed surface wave. The relatively simple form and high acceleration may be attributed to the high rigidity, crystalline rock types in the region. The three component record is fitted by summing the fundamental and first higher mode Rayleigh and Love waves using a model consisting of a single layer over a homogeneous half-space. The results are also checked using a direct wave-number integration program developed by Apsel and Luco. The moment estimate from the surface-wave synthetics is 2.0 ×1023 dyne-cm.

Experimental investigation of PL modes in a single layer

1962 ◽  
Vol 52 (1) ◽  
pp. 59-66
Author(s):  
Freeman Gilbert ◽  
Stanley J. Laster
Keyword(s):  
Half Space ◽  
Arrival Time ◽  
Single Layer ◽  
Good Resolution ◽  
P Waves ◽  
Small Phase ◽  
Shear Modes ◽  
Phase And Group Velocities ◽  
Set Up ◽  
Group Velocities

Abstract A two dimensional seismic model has been set up to simulate the problem of elastic wave propagation in a single layer overlying a uniform half space. Both the source and the receiver are mounted on the free surface of the layer. Seismograms are presented as a funciton of range. In addition to the Rayleigh and shear modes, PL modes are observed. Experimentally determined phase and group velocities compare fairly well with theoretical curves. The decay factor for PL is maximum at the arrival time of P waves in the half-space. There is also a secondary maximum at the arrival time of P waves in the layer. Although the decay of PL is small, phase equalization of PL does not yield the initial pulse shape because the mode embraces an insufficient frequency band to permit good resolution.

scholarly journals Local Coupling and Conversion of Surface Waves due to Earth’s Rotation. Part 2: Numerical Examples

2020 ◽  
Author(s):  
Christoph Sens-Schönfelder ◽  
Ebru Bozdağ ◽  
Roel Snieder
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Normal Mode ◽  
Coriolis Force ◽  
Rayleigh Waves ◽  
Love Wave ◽  
Resonant Coupling ◽  
Phase Velocities ◽  
Rayleigh And Love Waves ◽  
Similar Phase

Summary Rotation of the Earth affects the propagation of seismic waves. The global coupling of spheroidal and toroidal modes by the Coriolis force over time is described by normal-mode theory. The local action of the Coriolis force on the propagation of surface waves can be described by coefficients for the coupling between propagating Rayleigh and Love waves as derived by (Landau & Lifshitz 1959). Using global wavefield simulations we show how the Coriolis force leads to coupling and conversion between both surface wave types depending on latitude, propagation direction, frequency, and local velocity structure. Surface wave coupling is most efficient for periods where the modes have similar phase velocities, a condition that is equivalent to the selection rules of the angular degree in the normal-mode framework, a phenomenon that we refer to as resonant coupling. In the time-domain, resonant coupling gradually converts energy from one wave type–Rayleigh waves or Love wave–into the other, which then propagates independently. Due to the lateral heterogeneity, the condition of equal phase velocity renders the rotational coupling location-dependent. East-west oriented ray path segments and segments at high latitudes (across the Poles) only weakly couple the fundamental mode Rayleigh and Love waves while coupling is strongest for propagation along the meridians across the equator. At 250 s period, where Love and Rayleigh waves have similar phase velocities, the net energy transfer from Rayleigh to Love wave reaches about 10% for one orbit.

Adaptive wavelets for analyzing dispersive seismic waves

Geophysics ◽  
2007 ◽  
Vol 72 (1) ◽  
pp. V1-V11 ◽  
Author(s):  
A. Kritski ◽  
A. P. Vincent ◽  
D. A. Yuen ◽  
T. Carlsen
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Shear Wave ◽  
Primary Objective ◽  
Sediment Surface ◽  
Horizontal Distance ◽  
Time Frequency ◽  
Interface Waves ◽  
Adaptive Wavelets ◽  
Wave Modes

Our primary objective is to develop an efficient and accurate method for analyzing time series with a multiscale character. Our motivation stems from the studies of the physical properties of marine sediment (stiffness and density) derived from seismic acoustic records of surface/interface waves along the water-seabed boundary. These studies depend on the dispersive characteristics of water-sediment surface waves. To obtain a reliable retrieval of the shear-wave velocities, we need a very accurate time-frequency record of the surface waves. Such a time-frequency analysis is best carried out by a wavelet-transform of the seismic records. We have employed the wavelet crosscorrelation technique for estimating the shear-wave propagational parameters as a function of depth and horizontal distance. For achieving a greatly improved resolution in time-frequency space, we have developed a new set of adaptive wavelets, which are driven by the data. This approach is based on a Karhunen-Loeve (KL) decomposition of the seismograms. This KL decomposition allows us to obtain a set of wavelet functions that are naturally adapted to the scales of the surface-wave modes. We demonstrate the superiority of these adaptive wavelets over standard wavelets in their ability to simultaneously discriminate the different surface-wave modes. The results can also be useful for imaging and statistical data analysis in exploration geophysics and in other disciplines in the environmental sciences.

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