Geometrical spreading and Q of Pn waves: An investigative study in eastern Canada

1991 ◽  
Vol 81 (3) ◽  
pp. 882-896 ◽  
Author(s):  
Tianfei Zhu ◽  
Kin-Yip Chun ◽  
Gordon F. West
Keyword(s):  
Velocity Gradient ◽  
Geometrical Spreading ◽  
Eastern Canada ◽  
Frequency Dependent ◽  
Study Region ◽  
Amplitude Data ◽  
Short Period ◽  
Head Waves ◽  
Geometric Spreading ◽  
Spreading Function

Abstract Station site effects, uncertainties in seismic source spectrum, and instrument response errors are among the well-known frequency-dependent contaminating factors that limit the reliability of short-period Q measurements of regional phases. For the Pn wave, a regional phase of importance for both magnitude determination and nuclear test ban verification, the problem is made worse by the added uncertainty of its geometric spreading function. For realistic earth models, the Pn geometric spreading function is likely to depart drastically from that expected of canonical head waves. The extent of this departure is sensitively dependent upon the regional crust/mantle structure, making geometric spreading assumption a conspicuous source of disagreement among the published Pn attenuation (QPn) estimates. We describe a technique, referred to here as the extended reversed two-station method (RTSM), for simultaneous determination of QPn and geometrical spreading function. The formulation, being designed to bring about direct cancellation of the contaminating source, station and instrument effects, is a reliable tool for mapping the Pn propagation characteristics over continental paths, long and short. The extended RTSM has been tested using Pn spectral amplitude data derived from seismic records of the Eastern Canada Telemetered Network (ECTN). We find the spreading rate coefficient n in the power-law representation of the geometric spreading (d−n, d being epicentral distance) to be frequency dependent, increasing from 1.11 at 1 Hz to 1.77 at 20 Hz. Our QPn model in eastern Canada takes the form of QPn = 189f0.87. The results from eastern Canada suggest that: (a) there exists a significant positive velocity gradient in the uppermost mantle (≧ 0.0037 sec−1); (b) the regionally recorded Pn waves are dominated by the superposition of a series of interfering diving waves bent by the velocity gradient and internally reflected at the underside of the Moho discontinuity; and (c) the very strong frequency-dependence of QPn we found in this study region may not be unique among low-attenuating shield and platform regions.

High-frequency Pn attenuation in the Canadian shield

1989 ◽  
Vol 79 (4) ◽  
pp. 1039-1053
Author(s):  
Kin-Yip Chun ◽  
Richard J. Kokoski ◽  
Gordon F. West
Keyword(s):  
Velocity Structure ◽  
Epicentral Distance ◽  
Spectral Amplitude ◽  
Common Source ◽  
Spatial Decay ◽  
Geometrical Spreading ◽  
Eastern Canada ◽  
Frequency Dependent ◽  
Low Frequencies ◽  
Head Waves

Abstract Frequency-dependent spatial attenuation of Pn waves, incorporating the combined effects of geometrical spreading and anelastic dissipation, is investigated in eastern Canada between 3 and 15 Hz. Measurement of this total attenuation, instead of the two separate effects, circumvents the usual need for making a priori assumptions regarding the Pn geometrical spreading rate. The data consist of 77 Pn spectra, all amplitude-normalized using a set of previously measured spectral ratios of eastern Canadian earthquake sources. The normalization procedure eliminates the need for explicit source spectral assumptions, another common source of error in Pn attenuation measurements. An unconventional technique is introduced to account for differences in observed Pn spectra, which arise from geological site effects and instrument response error, both of which are frequency-dependent phenomena. We conclude that, at each frequency, the Pn amplitude falls off with distance according to: Δ−n, where Δ is epicentral distance. The exponent n is weakly frequency-dependent and takes the form: 2.2 + 0.02f. A unique interpretation of the behavior of the Pn spectral amplitude decay is unattainable, owing to the difficulty in separating the effects due to anelastic dissipation and the velocity structure in the uppermost mantle. It is interesting to note, however, that the spatial decay of pure elastic head waves follows the classical Δ−1/2L−3/2 relation, where L is the distance the waves travel in the mantle refractor. For the distance range of our interest (260-1087 km), this amounts to Δ−2.2. This indicates that towards low frequencies our n approaches a value which is consistent with the spatial decay rate expected of pure elastic head waves.

Geometrical spreading function for short-period S and coda waves recorded in southern Spain

1993 ◽  
Vol 80 (1-2) ◽  
pp. 25-36 ◽  
Author(s):  
J.M. Ibáñez ◽  
E. Del Pezzo ◽  
G. Alguacil ◽  
F. De Miguel ◽  
J. Morales ◽  
...  
Keyword(s):  
Southern Spain ◽  
Coda Waves ◽  
Geometrical Spreading ◽  
Short Period ◽  
Spreading Function

Attenuation and excitation of three-component ground motion in southern California

1999 ◽  
Vol 89 (4) ◽  
pp. 888-902 ◽  
Author(s):  
M. Raoof ◽  
R. B. Herrmann ◽  
L. Malagnini
Keyword(s):  
Ground Motion ◽  
Southern California ◽  
Vertical Component ◽  
Stochastic Simulations ◽  
Geometrical Spreading ◽  
Data Set ◽  
Frequency Dependent ◽  
Ground Motion Attenuation ◽  
Spreading Function ◽  
Velocity Spectra

Abstract Ground motion attenuation with distance and the variation of excitation with magnitude are parameterized using three-component, 0.25 to 5.0-Hz earthquake ground motions recorded in the distance range of 15-500 km for southern California to define a consistent model that describes both peak ground motion and Fourier spectra observations. The data set consists of 820 three-component TERRAscope recordings from 140 earthquakes, recorded at 17 stations, with moment magnitudes between 3.1 and 6.7. Regression analysis uses a simple model to relate the logarithm of measured ground motion to excitation, site, and propagation effects. The peak motions are Fourier velocity spectra and peak velocities in selected narrow bandpass-filtered frequency ranges. Regression results for Fourier amplitude spectra and peak velocities are used to define a piecewise continuous geometrical spreading function, frequency dependent Q(f), and a distance dependent duration that can be used with random vibration theory (RVT) or stochastic simulations to predict other characteristics of the ground motion. The duration results indicate that both the variation of the duration data with distance and its scattering decrease with increasing frequency. The ratio of horizontal to vertical component site terms is about √2 for all frequencies. However, this ratio is near unity for rock sites and is larger for soil sites. Simple modeling indicates that the Fourier velocity spectra are best fit by bilinear geometrical spreading of r−1 for r < 40 km and r−1/2 for r > 40 km. The frequency-dependent quality factor is Q(f) = 180f0.45 for each of the three components and also for the combined three-component data sets. The T5%-75% duration window provides good agreement between observed and RVT predicted peak values.

Upper-mantle discontinuity from amplitude data of P′P′ and its precursors

1973 ◽  
Vol 63 (2) ◽  
pp. 587-597
Author(s):  
Ta-Liang Teng ◽  
James P. Tung
Keyword(s):  
Upper Mantle ◽  
Body Waves ◽  
P Wave ◽  
Specific Reference ◽  
Amplitude Data ◽  
Surface Displacements ◽  
Short Period ◽  
Mantle Velocity ◽  
Mantle Discontinuity ◽  
Upper Mantle Discontinuity

abstract Recent observations of P′P′ and its precursors, identified as reflections from within the Earth's upper mantle, are used to examine the structure of the uppermantle discontinuities with specific reference to the density, the S velocity, and the Q variations. The Haskell-Thomson matrix method is used to generate the complex reflection spectrum, which is then Fourier synthesized for a variety of upper-mantle velocity-density and Q models. Surface displacements are obtained for the appropriate recording instrument, permitting a direct comparison with the actual seismograms. If the identifications of the P′P′ precursors are correct, our proposed method yields the following: (1) a structure of Gutenberg-Bullen A type is not likely to produce observable P′P′ upper-mantle reflections, (2) in order that a P′P′ upper-mantle reflection is strong enough to be observed, first-order density and S-velocity discontinuities together with a P-wave discontinuity are needed at a depth of about 650 km, and (3) corresponding to a given uppermantle velocity-density model, an estimate can be made of the Q in the upper mantle for short-period seismic body waves.

Robust Empirical Time–Frequency Relations for Seismic Spectral Amplitudes, Part 2: Model Uncertainty and Optimal Parameterization

2020 ◽  
Author(s):  
Maryam Safarshahi ◽  
Igor B. Morozov
Keyword(s):  
Measurement Errors ◽  
Nonparametric Model ◽  
Model Parameters ◽  
Geometrical Spreading ◽  
Model Quality ◽  
Frequency Dependent ◽  
Time Frequency ◽  
Trade Offs ◽  
Frequency Independent ◽  
Seismic Amplitudes

ABSTRACT In a companion article, Safarshahi and Morozov (2020) argued that construction of distance- and frequency-dependent models for seismic-wave amplitudes should include four general elements: (1) a sufficiently detailed (parametric or nonparametric) model of frequency-independent spreading, capturing all essential features of observations; (2) model parameters with well-defined and nonoverlapping physical meanings; (3) joint inversion for multiple parameters, including the geometrical spreading, Q, κ, and source and receiver couplings; and (4) the use of additional dataset-specific criteria of model quality, while fitting the logarithms of seismic amplitudes. Some of these elements are present in existing models, but, taken together, they are poorly understood and require an integrated approach. Such an approach was illustrated by detailed analysis of an S-wave amplitude dataset from southern Iran. The resulting model is based on a frequency-independent Q, and matches the data closer than conventional models and across the entire epicentral-distance range. Here, we complete the analysis of this model by evaluating the uncertainties and trade-offs of its parameters. Two types of trade-offs are differentiated: one caused by a (possibly) limited model parameterization and the second due to statistical data errors. Data bootstrapping shows that with adequate parameterization, attenuation properties Q, κ, and geometrical spreading parameters are resolved well and show moderate trade-offs due to measurement errors. Using the principal component analysis of these trade-offs, an optimal (trade-off free) parameterization of seismic amplitudes is obtained. By contrast, when assuming theoretical values for certain model parameters and using multistep inversion procedures (as commonly done), parameter trade-offs increase dramatically and become difficult to assess. In particular, the frequency-dependent Q correlates with the distribution of the source and receiver-site factors, and also with biases in the resulting median data residuals. In the new model, these trade-offs are removed using an improved parameterization of geometrical spreading, constant Q, and model quality constraints.

Processing of anisotropic data in the τ‐p domain: I—Geometric spreading and moveout corrections

Geophysics ◽  
2004 ◽  
Vol 69 (3) ◽  
pp. 719-730 ◽  
Author(s):  
Mirko van der Baan
Keyword(s):  
Plane Waves ◽  
Vertical Axis ◽  
Pure Mode ◽  
Spherical Waves ◽  
Time Migration ◽  
Head Waves ◽  
Geometric Spreading ◽  
Isotropic Media ◽  
P Domain ◽  
Time Offset

Stacking of seismic data is conventionally done in the time‐offset domain. This has the disadvantage that geometric spreading must be removed before true‐amplitude processing can be attempted. This inconvenience arises since wave motion in the time‐offset domain is determined by spherical waves. Plane waves in layered media, on the other hand, are not subject to geometric spreading. Hence, processing of both isotropic and anisotropic data in such media benefits from first applying a plane‐wave decomposition such as a proper τ‐p transform. The resulting τ‐p gathers can be flattened and stacked over slowness. Subsequent time differentiation is needed to counter the loss of high frequencies during stacking. This approach has the advantage that the geometric spreading is removed without prior knowledge of the actual (an)isotropic velocity field and without any need to pick traveltimes or moveout velocities. Subsequent moveout corrections naturally require knowledge of the velocityfield. The proposed methodology is exact for 3D data volumes and arbitrary anisotropy in laterally homogeneous media or for 2D acquisition lines over 1D, isotropic media or over 1D, transversely isotropic media with vertical axis of symmetry (VTI). It relies on the same principles as more conventional geometric spreading corrections and time‐offset stacking. In many respects, it is even more flexible. For instance, geometric spreading has been correctly removed for all present wave modes and types simultaneously (primary, multiple, pure‐mode, and converted waves), and nonhyperbolic moveout resulting from isotropic layering is also taken into account. In addition, head waves may now contribute constructively to the stacked section. Moreover, both multiple elimination and predictive deconvolution are straightforward and known to yield very good results in the τ‐p domain. The resulting stacked section can then be used for any poststack processing such as time migration.

scholarly journals Development of A Methodology For Predicting Landslide Hazards At A Regional Scale

2021 ◽  
Author(s):  
Blanche Richer ◽  
Ali Saeidi ◽  
Maxime Boivin ◽  
Alain Rouleau
Keyword(s):  
Stability Analysis ◽  
3D Model ◽  
Regional Scale ◽  
Back Analysis ◽  
Initial Step ◽  
Landslide Risk ◽  
Target Area ◽  
Eastern Canada ◽  
Study Region ◽  
Electric Induction

Abstract Landslide risk analysis is a common geotechnical evaluation and aims to protect life and infrastructure. In the case of sensitive clay zones, landslides can affect large areas and are difficult to predict. Here we propose a methodology to determine the landslide hazard across a large territory, and we apply our approach to the Saint-Jean-Vianney area, Quebec, Canada. The initial step consists of creating a 3D model of the surficial deposits of the target area. After creating a chart of the material electrical resistivity adapted for eastern Canada, we applied electric induction to interpret the regional soil. We collected samples from the main lithologies and estimated selected soil geotechnical parameters in laboratory tests. We transposed parameter values obtained from the samples to a larger scale that of a slope using the results of a back analysis undertaken on an earlier, smaller slide within the same area. The regional 3D model of deposits is then used to develop a zonation map of at-risk slopes and their respective constraint areas with the study region. This approach allowed us to target specific areas where a more precise stability analysis would be required. Our methodology offers an effective tool for stability analysis in territories characterized by the presence of sensitive clays.

scholarly journals Inversion of the body waves from the Borrego Mountain earthquake to the source mechanism

1976 ◽  
Vol 66 (5) ◽  
pp. 1485-1499 ◽  
Author(s):  
L. J. Burdick ◽  
George R. Mellman
Keyword(s):  
Body Wave ◽  
High Stress ◽  
Time Function ◽  
The Body ◽  
Body Waves ◽  
Polarization Angle ◽  
Long Period ◽  
Amplitude Data ◽  
Short Period ◽  
Wide Range

abstract The generalized linear inverse technique has been adapted to the problem of determining an earthquake source model from body-wave data. The technique has been successfully applied to the Borrego Mountain earthquake of April 9, 1968. Synthetic seismograms computed from the resulting model match in close detail the first 25 sec of long-period seismograms from a wide range of azimuths. The main shock source-time function has been determined by a new simultaneous short period-long period deconvolution technique as well as by the inversion technique. The duration and shape of this time function indicate that most of the body-wave energy was radiated from a surface with effective radius of only 8 km. This is much smaller than the total surface rupture length or the length of the aftershock zone. Along with the moment determination of Mo = 11.2 ×1025 dyne-cm, this radius implies a high stress drop of about 96 bars. Evidence in the amplitude data indicates that the polarization angle of shear waves is very sensitive to lateral structure.

Anisotropic frequency-dependent spreading of seismic waves from first-arrival vertical seismic profile data analysis

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. C41-C52 ◽  
Author(s):  
Amin Baharvand Ahmadi ◽  
Igor Morozov
Keyword(s):  
Seismic Waves ◽  
Seismic Profile ◽  
Anisotropic Scattering ◽  
Profile Data ◽  
Vertical Seismic Profile ◽  
Data Set ◽  
Frequency Dependent ◽  
Geometric Spreading ◽  
First Arrival ◽  
Viscoelastic Modeling

A model of first-arrival amplitude decay combining geometric spreading, scattering, and inelastic dissipation is derived from a multioffset, 3D vertical seismic profile data set. Unlike the traditional approaches, the model is formulated in terms of path integrals over the rays and without relying on the quality factor ([Formula: see text]) for rocks. The inversion reveals variations of geometric attenuation (wavefront curvatures and scattering, [Formula: see text]) and the effective attenuation parameter ([Formula: see text]) with depth. Both of these properties are also found to be anisotropic. Scattering and geometric spreading (focusing and defocusing) significantly affect seismic amplitudes at lower frequencies and shallower depths. Statistical analysis of model uncertainties quantitatively measures the significance of these results. The model correctly predicts the observed frequency-dependent first-arrival amplitudes at all frequencies. This and similar models can be applied to other types of waves and should be useful for true-amplitude studies, including inversion, inverse [Formula: see text]-filtering, and amplitude variations with offset analysis. With further development of petrophysical models of internal friction and elastic scattering, attenuation parameters [Formula: see text] and [Formula: see text] should lead to constraints on local heterogeneity and intrinsic physical properties of the rock. These parameters can also be used to build models of the traditional frequency-dependent [Formula: see text] for forward and inverse numerical viscoelastic modeling.

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