Frequency‐dependent anisotropy of seismic waves in a randomly layered 1‐D acoustic medium

1993 ◽  
Author(s):  
S. A. Shapiro ◽  
H. Zien ◽  
P. Hubral
Keyword(s):  
Seismic Waves ◽  
Acoustic Medium ◽  
Frequency Dependent

An investigation into the fundamental relationships between attenuation, phase dispersion, and frequency using seismic refraction profiles over sedimentary structures

Geophysics ◽  
1987 ◽  
Vol 52 (1) ◽  
pp. 72-87 ◽  
Author(s):  
R. S. Jacobson
Keyword(s):  
Frequency Dependence ◽  
Seismic Waves ◽  
Velocity Dispersion ◽  
Seismic Refraction ◽  
Systematic Investigation ◽  
Data Sets ◽  
Frequency Dependent ◽  
Frequency Independent ◽  
Apparent Attenuation ◽  
Seismic Refraction Data

Despite many attenuation measurements which indicate a linear functional frequency dependence of absorption or constant [Formula: see text] in sediments, several theories predict no such linear dependence. The primary justification for rejecting a first‐power frequency dependence of attenuation is that it implies that seismic waves cannot propagate causally. Seismic waves must also travel with some velocity dispersion to satisfy causality, yet there is a lack of velocity dispersion measurements in sediments. In‐situ attenuation is caused by two distinct mechanisms: anelastic heating, and scattering due to interbed multiples. Apparent, or scattering, attenuation can produce both frequency‐dependent and non‐frequency‐dependent effects. Accurate measurements of attenuation and velocity dispersion are difficult; it is not surprising that a systematic investigation into the frequency dependence of absorption and velocity has not been made. A reinvestigation into two seismic refraction data sets collected over thickly stratified deep‐sea fans indicates that [Formula: see text] should not be assumed to be independent of frequency. Further, significant frequency‐independent absorption is present, indicating a high degree of apparent attenuation. Phase, or velocity, dispersion was also measured, but the results are more ambiguous than those for attenuation, due to inherent limitations of digital signals. Nevertheless, the absorption and velocity dispersion results are largely compatible, suggesting that if apparent attenuation is observed, then the scattered waves propagate causally.

Inversion for Biot-consistent material properties in subresonant oscillation experiments with fluid-saturated porous rock

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. MR67-MR79 ◽  
Author(s):  
Igor B. Morozov ◽  
Wubing Deng
Keyword(s):  
Traveling Wave ◽  
Seismic Waves ◽  
Rock Specimen ◽  
Low Frequency ◽  
P Wave ◽  
Axial Deformation ◽  
Porous Rock ◽  
Frequency Dependent ◽  
Shear Moduli ◽  
Young’S Moduli

To quantitatively interpret the results of a subresonant laboratory or numerical experiment with wet porous rock, it is insufficient to merely state the measured frequency-dependent viscoelastic moduli and [Formula: see text]-factors. The measured properties are apparent, i.e., dependent on the experimental setup such as the length of the sample and boundary conditions for pore flows. To reveal the true properties of the material, all experimental factors need to be accurately modeled and corrected for. Here, such correction is performed by developing an effective Biot’s model for the material and using it to predict driven oscillations of a cylindrical rock specimen. The model explicitly describes elastic and inertial effects, Biot’s flows, and viscous internal friction within the solid frame and pore fluid, and it approximates squirt and other wave-induced flow effects. The model predicts the dynamic permeability of the specimen, fast (traveling) and slow (diffusive) P- and axial-deformation waves, and it allows accurate modeling of any other ultrasonic or seismic-frequency experiments with the same rock. To illustrate the approach, attenuation and dispersion data from two laboratory and numerical experiments with sandstones are inverted for effective, frequency-dependent moduli of drained sandstone. Several observations from this inversion may be useful for interpreting experiments with porous rock. First, Young’s moduli measured in a short rock cylinder differ from those in a traveling wave within an infinite rod. In particular, for the modeled 8 cm long rock specimen, modulus dispersion and attenuation ([Formula: see text]) are approximately 10 times greater than for a traveling wave. Second, P-wave moduli cannot be derived from the measured Young’s and shear moduli by using conventional (visco)elastic relations. Third, because of wavelengths comparable with the size of the specimen, slow waves contribute to its quasistatic and low-frequency behaviors. Similar observations should also apply to seismic waves traveling through approximately 10 cm layering in the field.

APPARENT ATTENUATION DUE TO INTRABED MULTIPLES, II

Geophysics ◽  
1978 ◽  
Vol 43 (4) ◽  
pp. 730-737 ◽  
Author(s):  
M. Schoenberger ◽  
F. K. Levin
Keyword(s):  
Seismic Data ◽  
Field Data ◽  
Seismic Waves ◽  
Synthetic Seismograms ◽  
Frequency Dependent ◽  
Total Attenuation ◽  
The World ◽  
Apparent Attenuation

In a paper with the same title published in Geophysics (June 1974), we showed that synthetic seismograms from two wells gave a frequency‐dependent attenuation due to intrabed multiples of about 0.06 dB/wavelength. This loss was 1/3 to 1/2 of the total attenuation found for field data on lines near the wells. Our data sufficed to confirm the conclusion of O’Doherty and Anstey that attenuation caused by intrabed multiples may be appreciable, but the number of wells was insufficient to establish the magnitude of that attenuation in general. To get a better feel for intrabed multiple‐generated attenuation, we have computed losses for 31 additional wells from basins all over the world. Sonic and, where available, density logs were digitized every foot and converted into synthetic seismograms with 50 orders of intrabed multiples. Using the technique of the 1974 paper of extending the logs and placing an isolated reflector 2000 ft below the bottom of the wells, we computed attenuation constants for plane seismic waves that had traveled down and back through the subsurfaces defined by the logs. Computed constants varied from 0.01 dB/wavelength to 0.22 dB/wavelength. Total traveltimes ranged from 0.7 to 2.7 sec; the average was 1.9 sec. Attenuation constants computed from surface seismic data near four of the 31 wells gave values 1.3 to 7 times the corresponding intrabed constants. Thus, attenuation due to intrabed multiples accounts for an appreciable fraction of the observed attenuation but by no means all of it.

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.

scholarly journals Noise Reduction Evaluation of Multi-Layered Viscoelastic Infinite Cylinder under Acoustical Wave Excitation

2008 ◽  
Vol 15 (5) ◽  
pp. 551-572 ◽  
Author(s):  
M.R. Mofakhami ◽  
H. Hosseini Toudeshky ◽  
Sh. Hosseini Hashemi
Keyword(s):  
Noise Reduction ◽  
Viscoelastic Material ◽  
Viscoelastic Properties ◽  
Separation Of Variables ◽  
Theory Of Elasticity ◽  
Acoustic Medium ◽  
Viscoelastic Layer ◽  
Infinite Cylinder ◽  
Frequency Dependent ◽  
Uniform Noise

In this paper sound transmission through the multilayered viscoelastic air filled cylinders subjected to the incident acoustic wave is studied using the technique of separation of variables on the basis of linear three dimensional theory of elasticity. The effect of interior acoustic medium on the mode maps (frequency vs geometry) and noise reduction is investigated. The effects of internal absorption and external moving medium on noise reduction are also evaluated. The dynamic viscoelastic properties of the structure are rigorously taken into account with a power law technique that models the viscoelastic damping of the cylinder. A parametric study is also performed for the two layered infinite cylinders to obtain the effect of viscoelastic layer characteristics such as thickness, material type and frequency dependency of viscoelastic properties on the noise reduction. It is shown that using constant and frequency dependent viscoelastic material with high loss factor leads to the uniform noise reduction in the frequency domain. It is also shown that the noise reduction obtained for constant viscoelastic material property is subjected to some errors in the low frequency range with respect to those obtained for the frequency dependent viscoelastic material.Noise reduction analyses are also performed for the infinite cylinder subjected to the periodic incident wave with uniform and piecewise form.

The physics and simulation of wave propagation at the ocean bottom

Geophysics ◽  
2004 ◽  
Vol 69 (3) ◽  
pp. 825-839 ◽  
Author(s):  
José M. Carcione ◽  
Hans B. Helle
Keyword(s):  
Wave Propagation ◽  
Seismic Waves ◽  
Differential Operators ◽  
Plane Boundary ◽  
Acoustic Medium ◽  
Frequency Domain Method ◽  
Ocean Bottom ◽  
Interface Waves ◽  
Physical Phenomena ◽  
Modeling Algorithm

We investigate some aspects of the physics of wave propagation at the ocean bottom (ranging from soft sediments to crustal rocks). Most of the phenomena are associated to the presence of attenuation. The analysis requires the use of an anelastic stress‐strain relation and a highly accurate modeling algorithm. Special attention is given to modeling the boundary conditions at the ocean‐bottom interface and the related physical phenomena. For this purpose, we further develop and test the pseudospectral modeling algorithm for wave propagation at fluid‐anelastic solid interfaces. The method is based on a domain‐decomposition technique (one grid for the fluid part and another grid for the solid part) and the Fourier and Chebyshev differential operators. We consider the reflection, transmission, and propagation of seismic waves at the ocean bottom, modeled as a plane boundary separating an acoustic medium (ocean) and a viscoelastic solid (sediment). The main physical phenomena associated with this interface are illustrated, namely, amplitude variations with offset, the Rayleigh window, and the propagation of Scholte and leaky Rayleigh waves. Modeling anelasticity is essential to describe these effects, in particular, amplitude variations near and beyond the critical angle, the Rayleigh window, and the dissipation of the fundamental interface mode. The physics of wave propagation is investigated by means of a plane‐wave analysis and the novel modeling algorithm. A wavenumber–frequency domain method is used to compute the reflection coefficient and phase angle from the synthetic seismograms. This method serves to verify the algorithm, which is shown to model with high accuracy the Rayleigh‐window phenomenon and the propagation of interface waves. The modeling is further verified by comparisons with the analytical solution for a fluid‐solid interface in lossless media, with source and receivers away from and at the ocean bottom. Using the pseudospectral modeling code, which allows general material variability, a complete and accurate characterization of the seismic response of the ocean bottom can be obtained. An example illustrates the effects of attenuation on the propagation of dispersive Scholte waves at the bottom of the North Sea.

scholarly journals Azimuth-, angle- and frequency-dependent seismic velocities of cracked rocks due to squirt flow

2019 ◽  
Author(s):  
Yury Alkhimenkov ◽  
Eva Caspari ◽  
Simon Lissa ◽  
Beatriz Quintal
Keyword(s):  
Seismic Wave ◽  
Seismic Waves ◽  
Numerical Study ◽  
Azimuth Angle ◽  
Hydrocarbon Exploration ◽  
Three Dimensions ◽  
Pore Scale ◽  
Frequency Dependent ◽  
Dependent Behavior ◽  
The Impact

Abstract. Understanding the properties of cracked rocks is of great importance in scenarios involving CO2 geological sequestration, nuclear waste disposal, geothermal energy, and hydrocarbon exploration and production. Developing non-invasive detecting and monitoring methods for such geological formations is crucial. Many studies show that seismic waves exhibit strong dispersion and attenuation across a broad frequency range due to fluid flow at the pore scale known as squirt flow. Nevertheless, how and to what extent squirt flow affects seismic waves is still a matter of investigation. To fully understand its angle- and frequency-dependent behavior for specific geometries appropriate numerical simulations are needed. We perform a three-dimensional numerical study of the fluid-solid deformation at the pore scale based on coupled Lame-Navier and Navier-Stokes linear quasistatic equations. We show that seismic wave velocities exhibit strong azimuth-, angle- and frequency-dependent behavior due to squirt flow between interconnected cracks. We show that the overall anisotropy of a medium mainly increases due to squirt flow but in some specific planes the anisotropy can locally decrease. We analyze the Thomsen-type anisotropic parameters and adopt another scalar parameter which can be used to measure the anisotropy strength of a model with any elastic symmetry. This work significantly clarifies the impact of squirt flow on seismic wave anisotropy in three dimensions and can potentially be used to improve the geophysical monitoring and surveying of fluid-filled cracked porous zones in the subsurface.

Amplification of seismic body waves by low-velocity surface layers

1971 ◽  
Vol 61 (1) ◽  
pp. 109-145 ◽  
Author(s):  
J. R. Murphy ◽  
A. H. Davis ◽  
N. L. Weaver
Keyword(s):  
Seismic Waves ◽  
Dynamic Range ◽  
Repeated Measurements ◽  
Body Waves ◽  
Recording Site ◽  
Low Velocity ◽  
Frequency Dependent ◽  
Near Surface ◽  
Wide Range ◽  
Analytic Models

abstract Frequency-dependent amplification of seismic waves by near-surface low-velocity layers is a well-known phenomenon. This phenomenon was examined from both the analytic and experimental viewpoints for body waves (P, SV, SH). Groundmotion data, recorded in conjunction with the underground nuclear testing program at the Nevada Test Site, are used to provide experimental validation of the analytic models. Experimental amplification factors are derived from these data for a variety of recording-site near-surface geological configurations (alluvium, mine tailings, fill) and a wide dynamic range of ground-motion intensity (10−5 to 100 g). The variability in the mean amplification observed at a site for repeated measurements is described statistically. This analysis shows that, although the amplification at a given site varies on the average by a factor of about 1.4 across the frequency band of interest, from detonation to detonation, the frequency and magnitude of the dominant amplification are fairly consistent. The quality of the comparisons of the observed and calculated amplification indicates that the available linear analytic models are capable of describing the major features of the frequency-dependent amplification observed for this wide range of groundmotion intensity and recording-site geology.

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