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.

THE EMPIRICAL GREEN’S FUNCTION TECHNIQUE MODIFICATION FOR ACCELEROGRAM SYNTHESIS IN LOWSEISMICITY REGIONS

2018 ◽  
Vol 12 (5-6) ◽  
pp. 72-80
Author(s):  
A. A. Krylov
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Main Shock ◽  
Amplitude Spectrum ◽  
Strong Motion ◽  
Function Technique ◽  
Focal Region ◽  
Empirical Green’S Function ◽  
Epicentral Zone ◽  
Empirical Green's Function

In the absence of strong motion records at the future construction sites, different theoretical and semi-empirical approaches are used to estimate the initial seismic vibrations of the soil. If there are records of weak earthquakes on the site and the parameters of the fault that generates the calculated earthquake are known, then the empirical Green’s function can be used. Initially, the empirical Green’s function method in the formulation of Irikura was applied for main shock record modelling using its aftershocks under the following conditions: the magnitude of the weak event is only 1–2 units smaller than the magnitude of the main shock; the focus of the weak event is localized in the focal region of a strong event, hearth, and it should be the same for both events. However, short-termed local instrumental seismological investigation, especially on seafloor, results usually with weak microearthquakes recordings. The magnitude of the observed micro-earthquakes is much lower than of the modeling event (more than 2). To test whether the method of the empirical Green’s function can be applied under these conditions, the accelerograms of the main shock of the earthquake in L'Aquila (6.04.09) with a magnitude Mw = 6.3 were modelled. The microearthquake with ML = 3,3 (21.05.2011) and unknown origin mechanism located in mainshock’s epicentral zone was used as the empirical Green’s function. It was concluded that the empirical Green’s function is to be preprocessed. The complex Fourier spectrum smoothing by moving average was suggested. After the smoothing the inverses Fourier transform results with new Green’s function. Thus, not only the amplitude spectrum is smoothed out, but also the phase spectrum. After such preliminary processing, the spectra of the calculated accelerograms and recorded correspond to each other much better. The modelling demonstrate good results within frequency range 0,1–10 Hz, considered usually for engineering seismological studies.

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 Wiener estimation of the Green’s function

Geophysics ◽  
2013 ◽  
Vol 78 (5) ◽  
pp. W31-W44 ◽  
Author(s):  
Anton Ziolkowski
Keyword(s):  
Green’S Function ◽  
Impulse Response ◽  
Green's Function ◽  
Seismic Data ◽  
Wiener Filter ◽  
Electromagnetic Data ◽  
Transient Electromagnetic ◽  
Marine Seismic ◽  
Measured Response

I consider the problem of finding the impulse response, or Green’s function, from a measured response including noise, given an estimate of the source time function. This process is usually known as signature deconvolution. Classical signature deconvolution provides no measure of the quality of the result and does not separate signal from noise. Recovery of the earth impulse response is here formulated as the calculation of a Wiener filter in which the estimated source signature is the input and the measured response is the desired output. Convolution of this filter with the estimated source signature is the part of the measured response that is correlated with the estimated signature. Subtraction of the correlated part from the measured response yields the estimated noise, or the uncorrelated part. The fraction of energy not contained in this uncorrelated component is defined as the quality of the filter. If the estimated source signature contains errors, the estimated earth impulse response is incomplete, and the estimated noise contains signal, recognizable as trace-to-trace correlation. The method can be applied to many types of geophysical data, including earthquake seismic data, exploration seismic data, and controlled source electromagnetic data; it is illustrated here with examples of marine seismic and marine transient electromagnetic data.

Retrieving 2D structures from surface-wave data by means of space-varying spatial windowing

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. EN39-EN51 ◽  
Author(s):  
Paolo Bergamo ◽  
Daniele Boiero ◽  
Laura Valentina Socco
Keyword(s):  
Surface Wave ◽  
Real Data ◽  
Processing Technique ◽  
Dispersion Curves ◽  
Data Sets ◽  
Local Dispersion ◽  
Wave Data ◽  
Survey Line ◽  
Wave Path ◽  
Surface Wave Data

Surface-wave techniques are mainly used to retrieve 1D subsurface models. However, in 2D environments, the 1D approach usually neglects the presence of lateral variations and because the surface-wave path crosses different materials, the resulting model is a simplified or misleading description of the site. We tested a processing technique to retrieve 2D structures from surface-wave data acquired with a limited number of receivers. Our technique was based on a two-step process. First, we extracted several local dispersion curves along the survey line using a spatial windowing based on a set of Gaussian windows with different shapes; the window maxima span the survey line so that we were able to extract a dispersion curve from the seismic record for every window. This provided a set of local dispersion curves each of them referring to a different subsurface portion. This space varying spatial windowing provided a good compromise between wavenumber resolution and the lateral resolution of the obtained local dispersion curves. In the second step, we inverted the retrieved set of dispersion curves using a laterally constrained inversion scheme. We applied this procedure to the processing of synthetic and real data sets and the method proved to be successful in reconstructing even complex 2D structures in the subsurface.

scholarly journals Reflection images from ambient seismic noise

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. A63-A67 ◽  
Author(s):  
Deyan Draganov ◽  
Xander Campman ◽  
Jan Thorbecke ◽  
Arie Verdel ◽  
Kees Wapenaar
Keyword(s):  
Surface Wave ◽  
Green’S Function ◽  
Green's Function ◽  
Seismic Noise ◽  
Seismic Exploration ◽  
Ambient Seismic Noise ◽  
Reflection Data ◽  
Parallel Lines ◽  
Reflection Image ◽  
Sirte Basin

One application of seismic interferometry is to retrieve the impulse response (Green’s function) from crosscorrelation of ambient seismic noise. Various researchers show results for retrieving the surface-wave part of the Green’s function. However, reflection retrieval has proven more challenging. We crosscorrelate ambient seismic noise, recorded along eight parallel lines in the Sirte basin east of Ajdabeya, Libya, to obtain shot gathers that contain reflections. We take advantage of geophone groups to suppress part of the undesired surface-wave noise and apply frequency-wavenumber filtering before crosscorrelation to suppress surface waves further. After comparing the retrieved results with data from an active seismic exploration survey along the same lines, we use the retrieved reflection data to obtain a migrated reflection image of the subsurface.

Testing an Empirical Green’s Function Method for Determining the Rupture Parameters of the 24 April 2014 Vancouver Island Earthquake

2020 ◽  
Author(s):  
Collin Paul ◽  
John F. Cassidy ◽  
Stan E. Dosso ◽  
Jesse Hutchinson
Keyword(s):  
Surface Wave ◽  
Green’S Function ◽  
Green's Function ◽  
Signal To Noise Ratio ◽  
Moment Tensor ◽  
Vancouver Island ◽  
Double Difference ◽  
Empirical Green’S Function ◽  
Centroid Moment Tensor ◽  
Empirical Green's Function

ABSTRACT In this article, we examine the 24 April 2014 Mw 6.4 earthquake offshore Vancouver Island using a surface-wave empirical Green’s function (EGF) deconvolution method and compare the results with SeaJade II double-difference aftershock locations. The 24 April event was well recorded and provides the first opportunity to evaluate the suitability of surface-wave EGF deconvolution to constrain rupture details for moderate-sized earthquakes in areas lacking dense seismic arrays. Our surface-wave EGF deconvolution results agree with the aftershock distribution and previously determined centroid moment tensor results. This agreement suggests that this technique is valid for events of this magnitude in a sparsely networked region. We used an Mw 5.3 earthquake about 21 km from the 24 April epicenter as the primary EGF source event and applied stacking to improve the signal-to-noise ratio. Our analysis used broadband seismic data from 105 regional and teleseismic stations. Given the small magnitudes of these events, an aftershock (Mw 4.8) was considered a secondary EGF source to verify key observations. The relative source time functions obtained from this study reveal an overall rupture direction of 143°±6°, extent of 28±2  km, and duration of 16.7±0.3  s. We also determined that the rupture occurred in multiple, distinct subevents, but the deconvolution was unable to determine the subevent parameters. Double-difference aftershock relocations using both onshore and offshore seismometers indicate a 32±2  km unilateral rupture with strike of 146°±2°. These independently determined rupture parameters agree with previously determined centroid moment tensor results with a nodal plane striking 150°±6°.

Green’s functions extraction and surface-wave tomography from microseisms in southern California

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. SI23-SI31 ◽  
Author(s):  
Peter Gerstoft ◽  
Karim G. Sabra ◽  
Philippe Roux ◽  
W. A. Kuperman ◽  
Michael C. Fehler
Keyword(s):  
Surface Wave ◽  
Green’S Function ◽  
Wave Velocity ◽  
Green's Function ◽  
Green's Functions ◽  
Southern California ◽  
Green’S Functions ◽  
Square Root ◽  
Tomographic Inversion ◽  
Surface Wave Velocity

We use crosscorrelations of seismic noise data from 151 stations in southern California to extract the group velocities of surface waves between the station pairs for the purpose of determining the surface-wave velocity structure. We developed an automated procedure for estimating the Green’s functions and subsequent tomographic inversion from the 11,325 station pairs based on the characteristics of the noise field. We eliminate specific events by a procedure that does not introduce any spurious spectral distortion in the band of interest, 0.05–[Formula: see text]. Further, we only used the emerging arrival structure above a threshold signal-to-noise ratio. The result is that mostly station pairs with their axes oriented toward the sea are used, consistent with the noise having a microseism origin. Finally, it is the time derivative of the correlation function that is actually related to the Green’s function. The emergence of the time-domain Green’s function is proportional to the square root of the recording time and inversely proportional to the square root of the distance between stations. The tomographic inversion yields a surface-wave velocity map that compares favorably with more conventional and elaborate experimental procedures.

scholarly journals Tutorial on seismic interferometry: Part 1 — Basic principles and applications

Geophysics ◽  
2010 ◽  
Vol 75 (5) ◽  
pp. 75A195-75A209 ◽  
Author(s):  
Kees Wapenaar ◽  
Deyan Draganov ◽  
Roel Snieder ◽  
Xander Campman ◽  
Arie Verdel
Keyword(s):  
Surface Wave ◽  
Plane Wave ◽  
Green’S Function ◽  
Green's Function ◽  
Ambient Noise ◽  
Source Function ◽  
Stationary Points ◽  
Seismic Interferometry ◽  
Direct Wave ◽  
Reflected Wave

Seismic interferometry involves the crosscorrelation of responses at different receivers to obtain the Green’s function between these receivers. For the simple situation of an impulsive plane wave propagating along the [Formula: see text]-axis, the crosscorrelation of the responses at two receivers along the [Formula: see text]-axis gives the Green’s function of the direct wave between these receivers. When the source function of the plane wave is a transient (as in exploration seismology) or a noise signal (as in passive seismology), then the crosscorrelation gives the Green’s function, convolved with the autocorrelation of the source function. Direct-wave interferometry also holds for 2D and 3D situations, assuming the receivers are surrounded by a uniform distribution of sources. In this case, the main contributions to the retrieved direct wave between the receivers come from sources in Fresnel zones around stationary points. The main application of direct-wave interferometry is theretrieval of seismic surface-wave responses from ambient noise and the subsequent tomographic determination of the surface-wave velocity distribution of the subsurface. Seismic interferometry is not restricted to retrieving direct waves between receivers. In a classic paper, Claerbout shows that the autocorrelation of the transmission response of a layered medium gives the plane-wave reflection response of that medium. This is essentially 1D reflected-wave interferometry. Similarly, the crosscorrelation of the transmission responses, observed at two receivers, of an arbitrary inhomogeneous medium gives the 3D reflection response of that medium. One of the main applications of reflected-wave interferometry is retrieving the seismic reflection response from ambient noise and imaging of the reflectors in the subsurface. A common aspect of direct- and reflected-wave interferometry is that virtual sources are created at positions where there are only receivers without requiring knowledge of the subsurface medium parameters or of the positions of the actual sources.

Interactive processing to obtain interstation surface-wave dispersion

1991 ◽  
Vol 81 (3) ◽  
pp. 931-947
Author(s):  
E. A. Dean ◽  
G. R. Keller
Keyword(s):  
Surface Wave ◽  
Green’S Function ◽  
Least Squares ◽  
Group Velocity ◽  
Green's Function ◽  
Wave Dispersion ◽  
Standard Errors ◽  
Phase Matching ◽  
Surface Wave Dispersion ◽  
Processing Scheme

Abstract A processing scheme for the analysis of surface-wave dispersion is presented. This scheme involves preprocessing seismograms, computing the interstation Green's function, and determining the self-consistent phase and group dispersion with standard errors for one or more events for a two-station path. Time-variable filtering is employed, based on group velocity that is computer-selected by the multiple filter technique and refined by phase matching iteration. The interstation Green's function is frequency filtered to remove spikes from the spectrum. The interstation group velocity, perturbed by standard errors and refined by phase matching, is used to determine phase velocity and its uncertainty. Self-consistency between phase and group velocity is obtained by a simultaneous least-squares method, which ensures the correct functional relation for the two dispersed velocities. The uncertainty in dispersion is computed from the covariance matrix of the simultaneous least-squares solution. The technique is evaluated by comparing the analyzed dispersion for a path along the Andean Cordillera with results employing other techniques.

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