The effects of near-source heterogeneity on shear-wave evolution

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. T233-T241 ◽  
Author(s):  
Christopher S. Sherman ◽  
James Rector ◽  
Steven Glaser
Keyword(s):  
Wave Propagation ◽  
Wave Energy ◽  
Mode Conversion ◽  
Near Field ◽  
Seismic Source ◽  
Elastic Half Space ◽  
P Wave ◽  
S Wave ◽  
Rytov Approximation ◽  
Model Features

The Born and Rytov approximation, radiative transfer theory, and other related techniques are commonly used to model features of wave propagation through heterogeneous geologic media such as scattering, attenuation, and pulse-broadening. However, due to the underlying assumptions about the scattering direction and the reference Green’s function, these methods overlook important features of the wavefield such as mode conversion and near-field term coupling. These effects are particularly important within the predicted S-wave nodes of a seismic source, so we analyzed the problem of wave propagation beneath a vertical-point force on the surface of a heterogeneous, elastic half space. To do this, we generated a suite of 3D synthetic heterogeneous geologic models using fractal statistics and simulated the wave propagation using the finite-difference method. We derived an estimate for the effective source radiation patterns, and we used these to compare the results of the models. Our numerical results showed that, due to a combination of mode conversion and near-source coupling effects, S-wave energy on the order of 10% of the P-wave energy is generated within the shear-radiation node. In some cases, this S-wave energy may occur as a coherent pulse and may be used to enhance seismic imaging.

Mode Conversion Technique Employed in Shear Wave Velocity Studies of Rock Samples Under Axial and Uniform Compression

1967 ◽  
Vol 7 (02) ◽  
pp. 136-148 ◽  
Author(s):  
A.R. Gregory
Keyword(s):  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Wave Energy ◽  
Pressure Range ◽  
Mode Conversion ◽  
P Wave ◽  
S Wave ◽  
Rock Samples ◽  
Mode Converters

Abstract A shear wave velocity laboratory apparatus and techniques for testing rock samples under simulated subsurface conditions have been developed. In the apparatus, two electromechanical transducers operating in the frequency range 0.5 to 5.0 megahertz (MHz: megacycles per second) are mounted in contact with each end of the sample. Liquid-solid interfaces of Drakeol-aluminum are used as mode converters. In the generator transducer, there is total mode conversion from P-wave energy to plain S-wave energy, S-wave energy is converted back to P-wave energy in the motor transducer. Similar transducers without mode converters are used to measure P-wave velocities. The apparatus is designed for testing rock samples under axial or uniform loading in the pressure range 0 to 12,000 psi. The transducers have certain advantages over those used by King,1 and the measurement techniques are influenced less by subjective elements than other methods previously reported. An electronic counter-timer having a resolution of 10 nanoseconds measures the transit time of ultrasonic pulses through the sample; elastic wave velocities of most homogeneous materials can be measured with errors of less than 1 percent. S- and P-wave velocity measurements on Bandera sandstone and Solenhofen limestone are reported for the axial pressure range 0 to 6,000 psi and for the uniform pressure range 0 to 10,000 psi. The influence of liquid pore saturants on P- and S-wave velocity is investigated and found to be in broad agreement with Biot's theory. In specific areas, the measurements do not conform to theory. Velocities of samples measured under axial and uniform loading are compared and, in general, velocities measured under uniform stress are higher than those measured under axial stress. Liquid pore fluids cause increases in Poisson's ratio and the bulk modulus but reduce the rigidity modulus, Young's modulus and the bulk compressibility. INTRODUCTION Ultrasonic pulse methods for measuring the shear wave velocity of rock samples in the laboratory have been gradually improved during the last few years. Early experimental pulse techniques reported by Hughes et al.2, and by Gregory3 were beset by uncertainties in determining the first arrival of the shear wave (S-wave) energy. Much of this ambiguity was caused by the multiple modes propagated by piezoelectric crystals and by boundary conversions in the rock specimens. Shear wave velocity data obtained from the critical angle method, described by Schneider and Burton4 and used later by King and Fatt5 and by Gregory,3,6 are of limited accuracy, and interpreting results is too complicated for routine laboratory work. The mode conversion method described by Jamieson and Hoskins7 was recently used by King1 for measuring the S-wave velocities of dry and liquid-saturated rock samples. Glass-air interfaces acted as mode converters in the apparatus, and much of the compressional (P-wave) energy apparently was eliminated from the desired pure shear mode. A more detailed discussion of the current status of laboratory pulse methods applied to geological specimens is given in a review by Simmons.8

scholarly journals A new acoustic assumption for orthorhombic media

2020 ◽  
Vol 223 (2) ◽  
pp. 1118-1129
Author(s):  
Mohammad Mahdi Abedi ◽  
Alexey Stovas
Keyword(s):  
Wave Propagation ◽  
Conventional Approach ◽  
P Wave ◽  
Model Parameters ◽  
Governing Equations ◽  
S Wave ◽  
S Waves ◽  
Exploration Seismology ◽  
And Inversion ◽  
Approximate Equations

SUMMARY In exploration seismology, the acquisition, processing and inversion of P-wave data is a routine. However, in orthorhombic anisotropic media, the governing equations that describe the P-wave propagation are coupled with two S waves that are considered as redundant noise. The main approach to free the P-wave signal from the S-wave noise is the acoustic assumption on the wave propagation. The conventional acoustic assumption for orthorhombic media zeros out the S-wave velocities along three orthogonal axes, but leaves significant S-wave artefacts in all other directions. The new acoustic assumption that we propose mitigates the S-wave artefacts by zeroing out their velocities along the three orthogonal symmetry planes of orthorhombic media. Similar to the conventional approach, our method reduces the number of required model parameters from nine to six. As numerical experiments on multiple orthorhombic models show, the accuracy of the new acoustic assumption also compares well to the conventional approach. On the other hand, while the conventional acoustic assumption simplifies the governing equations, the new acoustic assumption further complicates them—an issue that emphasizes the necessity of simple approximate equations. Accordingly, we also propose simpler rational approximate phase-velocity and eikonal equations for the new acoustic orthorhombic media. We show a simple ray tracing example and find out that the proposed approximate equations are still highly accurate.

Guidelines for building a detailed elastic depth model

Geophysics ◽  
2000 ◽  
Vol 65 (1) ◽  
pp. 35-45
Author(s):  
Jarrod C. Dunne ◽  
Greg Beresford ◽  
Brian L. N Kennett
Keyword(s):  
Wave Velocity ◽  
Mode Conversion ◽  
Poisson Ratio ◽  
Velocity Model ◽  
P Wave ◽  
Time Interval ◽  
S Wave ◽  
Sea Floor ◽  
P Wave Velocity ◽  
Inelastic Attenuation

We developed guidelines for building a detailed elastic depth model by using an elastic synthetic seismogram that matched both prestack and stacked marine seismic data from the Gippsland Basin (Australia). Recomputing this synthetic for systematic variations upon the depth model provided insight into how each part of the model affected the synthetic. This led to the identification of parameters in the depth model that have only a minor influence upon the synthetic and suggested methods for estimating the parameters that are important. The depth coverage of the logging run is of prime importance because highly reflective layering in the overburden can generate noise events that interfere with deeper events. A depth sampling interval of 1 m for the P-wave velocity model is a useful lower limit for modeling the transmission response and thus maintaining accuracy in the tie over a large time interval. The sea‐floor model has a strong influence on mode conversion and surface multiples and can be built using a checkshot survey or by testing different trend curves. When an S-wave velocity log is unavailable, it can be replaced using the P-wave velocity model and estimates of the Poisson ratio for each significant geological formation. Missing densities can be replaced using Gardner’s equation, although separate substitutions are required for layers known to have exceptionally high or low densities. Linear events in the elastic synthetic are sensitive to the choice of inelastic attenuation values in the water layer and sea‐floor sediments, while a simple inelastic attenuation model for the consolidated sediments is often adequate. The usefulness of a 1-D depth model is limited by misties resulting from complex 3-D structures and the validity of the measurements obtained in the logging run. The importance of such mis‐ties can be judged, and allowed for in an interpretation, by recomputing the elastic synthetic after perturbing the depth model to simulate the key uncertainties. Taking the next step beyond using simplistic modeling techniques requires extra effort to achieve a satisfactory tie to each part of a prestack seismic record. This is rewarded by the greater confidence that can then be held in the stacked synthetic tie and applications such as noise identification, data processing benchmarking, AVO analysis, and inversion.

scholarly journals Downhole distributed acoustic seismic profiling at Skytrain Ice Rise, West Antarctica

2021 ◽  
Author(s):  
Alex Brisbourne ◽  
Mike Kendall ◽  
Sofia Kufner ◽  
Thomas Hudson ◽  
Andrew Smith
Keyword(s):  
Wave Energy ◽  
Drilling Fluid ◽  
Ice Sheet ◽  
Seismic Profile ◽  
Seismic Attenuation ◽  
Weddell Sea ◽  
P Wave ◽  
West Antarctica ◽  
S Wave ◽  
Ice Flow

<p>Antarctic ice sheet history is imprinted in the structure and fabric of the ice column. At ice rises, the signature of ice flow history is preserved due to the low strain rates inherent at these independent ice flow centres. We present results from a distributed acoustic sensing (DAS) experiment at Skytrain Ice Rise in the Weddell Sea Sector of West Antarctica, aimed at delineating the englacial fabric to improve our understanding of ice sheet history in the region. This pilot experiment demonstrates the feasibility of an innovative technique to delineate ice rise structure. Both direct and reflected P- and S-wave energy, as well as surface wave energy, are observed using a range of source offsets, i.e., a walkaway vertical seismic profile (VSP), recorded using fibre optic cable. Significant noise, which results from the cable hanging untethered in the borehole, is modelled and suppressed at the processing stage. At greater depth, where the cable is suspended in drilling fluid, seismic interval velocities and attenuation are measured. Vertical P-wave velocities are high (V<sub>INT</sub> = 4029 ± 244 m s<sup>-1</sup>) and consistent with a strong vertical cluster fabric. Seismic attenuation is high (Q<sub>INT </sub>= 75 ± 12) and contrary to observations in ice sheets over this temperature range. The signal level is too low, and the noise level too high, to undertake analysis of englacial fabric variability. However, modelling of P- and S-wave traveltimes and amplitudes with a range of fabric geometries, combined with these measurements, demonstrates the capacity of the DAS method to discriminate englacial fabric distribution. From this pilot study we make a number of recommendations for future experiments aimed at quantifying englacial fabric to improve our understanding of recent ice sheet history.</p><p> </p>

The effects of pore‐fluid salinity on ultrasonic wave propagation in sandstones

Geophysics ◽  
1998 ◽  
Vol 63 (3) ◽  
pp. 928-934 ◽  
Author(s):  
Simon M. Jones ◽  
Clive McCann ◽  
Timothy R. Astin ◽  
Jeremy Sothcott
Keyword(s):  
Wave Propagation ◽  
Ultrasonic Wave ◽  
Wave Attenuation ◽  
Clay Content ◽  
Seismic Wave Propagation ◽  
Ultrasonic Pulse ◽  
Pore Fluid ◽  
P Wave ◽  
S Wave ◽  
Shear Moduli

Petrophysical interpretation of increasingly refined seismic data from subsurface formations requires a more fundamental understanding of seismic wave propagation in sedimentary rocks. We consider the variation of ultrasonic wave velocity and attenuation in sandstones with pore‐fluid salinity and show that wave propagation is modified in proportion to the clay content of the rock and the salinity of the pore fluid. Using an ultrasonic pulse reflection technique (590–890 kHz), we have measured the P-wave and S-wave velocities and attenuations of 15 saturated sandstones with variable effective pressure (5–60 MPa) and pore‐fluid salinity (0.0–3.4 M). In clean sandstones, there was close agreement between experimental and Biot model values of [Formula: see text], but they diverged progressively in rocks containing more than 5% clay. However, this effect is small: [Formula: see text] changed by only 0.6% per molar change in salinity for a rock with a clay content of 29%. The variation of [Formula: see text] with brine molarity exhibited Biot behavior in some samples but not in others; there was no obvious relationship with clay content. P-wave attenuation was independent of pore‐fluid salinity, while S-wave attenuation was weakly dependent. The velocity data suggest the frame bulk and shear moduli of sandstones are altered by changes in the pore‐fluid salinity. One possible mechanism is the formation damage caused by clay swelling and migration of fines in low‐molarity electrolytes. The absence of variation between the attenuation in water‐saturated and brine‐saturated samples indicates the attenuation mechanism is relatively unaffected by changes in the frame moduli.

Automatic Classification of Impact-Echo Spectra II

2011 ◽  
pp. 199-205
Author(s):  
Addisson Salazar ◽  
Arturo Serrano
Keyword(s):  
Neural Networks ◽  
Wave Propagation ◽  
Propagation Velocity ◽  
Sampling Frequency ◽  
P Wave ◽  
Material Surface ◽  
S Wave ◽  
Wave Propagation Velocity ◽  
Impact Echo

We study the application of artificial neural networks (ANNs) to the classification of spectra from impact-echo signals. In this paper we focus on analyses from experiments. Simulation results are covered in paper I. Impact-echo is a procedure from Non-Destructive Evaluation where a material is excited by a hammer impact which produces a response from the material microstructure. This response is sensed by a set of transducers located on material surface. Measured signals contain backscattering from grain microstructure and information of flaws in the material inspected (Sansalone & Street, 1997). The physical phenomenon of impact-echo corresponds to wave propagation in solids. When a disturbance (stress or displacement) is applied suddenly at a point on the surface of a solid, such as by impact, the disturbance propagates through the solid as three different types of stress waves: a P-wave, an S-wave, and an R-wave. The P-wave is associated with the propagation of normal stress and the S-wave is associated with shear stress, both of them propagate into the solid along spherical wave fronts. In addition, a surface wave, or Rayleigh wave (R-wave) travels throughout a circular wave front along the material surface (Carino, 2001). After a transient period where the first waves arrive, wave propagation becomes stationary in resonant modes of the material that vary depending on the defects inside the material. In defective materials propagated waves have to surround the defects and their energy decreases, and multiple reflections and diffraction with the defect borders become reflected waves (Sansalone, Carino, & Hsu, 1998). Depending on the observation time and the sampling frequency used in the experiments we may be interested in analyzing the transient or the stationary stage of the wave propagation in impact- echo tests. Usually with high resolution in time, analyzes of wave propagation velocity can give useful information, for instance, to build a tomography of a material inspected from different locations. Considering the sampling frequency that we used in the experiments (100 kHz), a feature extracted from the signal as the wave propagation velocity is not accurate enough to discern between homogeneous and different kind of defective materials. The data set for this research consists of sonic and ultrasonic impact-echo signal (1-27 kHz) spectra obtained from 84 parallelepiped-shape (7x5x22cm. width, height and length) lab specimens of aluminium alloy series 2000. These spectra, along with a categorization of the quality of materials among homogeneous, one-defect and multiple-defect classes were used to develop supervised neural network classifiers. We show that neural networks yield good classifications (

The partition of radiated energy between P and S waves

1984 ◽  
Vol 74 (2) ◽  
pp. 361-376
Author(s):  
John Boatwright ◽  
Jon B. Fletcher
Keyword(s):  
Wave Energy ◽  
Body Wave ◽  
Focal Mechanisms ◽  
The Body ◽  
Body Waves ◽  
P Wave ◽  
Corner Frequency ◽  
S Wave ◽  
S Waves ◽  
Radiated Energy

Abstract Seventy-three digitally recorded body waves from nine multiply recorded small earthquakes in Monticello, South Carolina, are analyzed to estimate the energy radiated in P and S waves. Assuming Qα = Qβ = 300, the body-wave spectra are corrected for attenuation in the frequency domain, and the velocity power spectra are integrated over frequency to estimate the radiated energy flux. Focal mechanisms determined for the events by fitting the observed displacement pulse areas are used to correct for the radiation patterns. Averaging the results from the nine events gives 27.3 ± 3.3 for the ratio of the S-wave energy to the P-wave energy using 0.5 〈Fi〉 as a lower bound for the radiation pattern corrections, and 23.7 ± 3.0 using no correction for the focal mechanisms. The average shift between the P-wave corner frequency and the S-wave corner frequency, 1.24 ± 0.22, gives the ratio 13.7 ± 7.3. The substantially higher values obtained from the integral technique implies that the P waves in this data set are depleted in energy relative to the S waves. Cursory inspection of the body-wave arrivals suggests that this enervation results from an anomalous site response at two of the stations. Using the ratio of the P-wave moments to the S-wave moments to correct the two integral estimates gives 16.7 and 14.4 for the ratio of the S-wave energy to the P-wave energy.

Theory of scattered P- and S-wave energy in a random isotropic scattering medium

1993 ◽  
Vol 83 (4) ◽  
pp. 1264-1276 ◽  
Author(s):  
Yuehua Zeng
Keyword(s):  
Elastic Wave ◽  
Wave Field ◽  
Wave Energy ◽  
Wave Scattering ◽  
Energy Equation ◽  
P Wave ◽  
Isotropic Scattering ◽  
Scattering Medium ◽  
S Wave ◽  
Elastic Wave Energy

Abstract A new theory is presented to study the scattered elastic wave energy propagation in a random isotropic scattering medium. It is based on a scattered elastic wave energy equation that extends the work of Zeng et al. (1991) on multiple scattering by considering S to P and P to S wave scattering conversions. We obtain a complete solution of the scattered elastic wave energy equation by solving the equation in the frequency/wave-number domain. Using a discrete wave-number sum technique combined with a modified repeated averaging and the FFT method, we compute numerically the complete solution. By considering that the scattering conversion from P- to S-wave energy is about (α/β)4 times greater than that from S to P waves (Aki, 1992), we found that the P-wave scattering field was converted quickly to the S-wave scattering field, leading to the conclusion that coda waves generated from both P- and S-wave sources are actually dominated by scattered S waves. We also compared our result with that obtained under the acoustic wave assumption. The acoustic wave assumption for seismic coda works quite well for the scattered S-wave field but fails for the scattered P-wave field. Our scattered elastic wave energy equation provides a theoretical foundation for studying the scattered wave field generated by a P-wave source such as an explosion. The scattered elastic wave energy equation can be easily generalized to an inhomogeneous random scattering medium by considering variable scattering and absorption coefficients and elastic wave velocities in the earth.

Approximation of pure acoustic seismic wave propagation in TTI media

Geophysics ◽  
2011 ◽  
Vol 76 (5) ◽  
pp. WB97-WB107 ◽  
Author(s):  
Chunlei Chu ◽  
Brian K. Macy ◽  
Phil D. Anno
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Elastic Wave ◽  
Wave Equations ◽  
Computational Cost ◽  
P Wave ◽  
Anisotropy Axis ◽  
S Wave ◽  
Time Migration ◽  
Tti Media

Pseudoacoustic anisotropic wave equations are simplified elastic wave equations obtained by setting the S-wave velocity to zero along the anisotropy axis of symmetry. These pseudoacoustic wave equations greatly reduce the computational cost of modeling and imaging compared to the full elastic wave equation while preserving P-wave kinematics very well. For this reason, they are widely used in reverse time migration (RTM) to account for anisotropic effects. One fundamental shortcoming of this pseudoacoustic approximation is that it only prevents S-wave propagation along the symmetry axis and not in other directions. This problem leads to the presence of unwanted S-waves in P-wave simulation results and brings artifacts into P-wave RTM images. More significantly, the pseudoacoustic wave equations become unstable for anisotropy parameters [Formula: see text] and for heterogeneous models with highly varying dip and azimuth angles in tilted transversely isotropic (TTI) media. Pure acoustic anisotropic wave equations completely decouple the P-wave response from the elastic wavefield and naturally solve all the above-mentioned problems of the pseudoacoustic wave equations without significantly increasing the computational cost. In this work, we propose new pure acoustic TTI wave equations and compare them with the conventional coupled pseudoacoustic wave equations. Our equations can be directly solved using either the finite-difference method or the pseudospectral method. We give two approaches to derive these equations. One employs Taylor series expansion to approximate the pseudodifferential operator in the decoupled P-wave equation, and the other uses isotropic and elliptically anisotropic dispersion relations to reduce the temporal frequency order of the P-SV dispersion equation. We use several numerical examples to demonstrate that the newly derived pure acoustic wave equations produce highly accurate P-wave results, very close to results produced by coupled pseudoacoustic wave equations, but completely free from S-wave artifacts and instabilities.

Orbital vibrator seismic source for simultaneous P‐ and S‐wave crosswell acquisition

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1471-1480 ◽  
Author(s):  
Thomas M. Daley ◽  
Dale Cox
Keyword(s):  
Seismic Energy ◽  
Seismic Source ◽  
P Wave ◽  
S Wave ◽  
Circularly Polarized ◽  
S Waves ◽  
Polarized Waves ◽  
Coordinate Rotation ◽  
Processing Algorithms ◽  
Borehole Seismic

A recently developed borehole seismic source, the orbital vibrator, was successfully deployed in a crosswell survey in a fractured basalt aquifer. This seismic source uses a rotating eccentric mass to generate seismic energy. Source sweeps with clockwise and counter‐clockwise rotations are recorded at each source location. Because this source generates circularly polarized waves, unique processing algorithms are used to decompose the recordings into two equivalent linearly oscillating, orthogonally oriented seismic sources. The orbital vibrator therefore generates P‐ and S‐waves simultaneously for all azimuths. A coordinate rotation based on P‐wave particle motion is used to align the source components from various depths. In a field experiment, both P‐ and S‐wave arrivals were recorded using fluid‐coupled hydrophone sensors. The processed field data show clear separation of P‐ and S‐wave arrivals for in‐line and crossline source components, respectively. A tensor convolutional description of the decomposition process allows for extension to multicomponent sensors.

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