scholarly journals Sensitivities of surface wave velocities to the medium parameters in a radially anisotropic spherical Earth and inversion strategies

2015 ◽  
Vol 58 (5) ◽  
Author(s):  
Sankar N. Bhattacharya
Keyword(s):  
Surface Wave ◽  
Phase Velocity ◽  
Group Velocity ◽  
Wave Velocity ◽  
Love Waves ◽  
P Wave ◽  
Model Parameters ◽  
Nonlinear Inversion ◽  
Wave Velocities ◽  
Spherical Earth

<p>Sensitivity kernels or partial derivatives of phase velocity (<em>c</em>) and group velocity (<em>U</em>) with respect to medium parameters are useful to interpret a given set of observed surface wave velocity data. In addition to phase velocities, group velocities are also being observed to find the radial anisotropy of the crust and mantle. However, sensitivities of group velocity for a radially anisotropic Earth have rarely been studied. Here we show sensitivities of group velocity along with those of phase velocity to the medium parameters <em>V<sub>SV</sub>, V<sub>SH </sub>, V<sub>PV</sub>, V<sub>PH , </sub></em><em>h</em><em> </em>and density in a radially anisotropic spherical Earth. The peak sensitivities for <em>U</em> are generally twice of those for <em>c</em>; thus <em>U</em> is more efficient than <em>c</em> to explore anisotropic nature of the medium. Love waves mainly depends on <em>V<sub>SH</sub></em> while Rayleigh waves is nearly independent of <em>V<sub>SH</sub></em> . The sensitivities show that there are trade-offs among these parameters during inversion and there is a need to reduce the number of parameters to be evaluated independently. It is suggested to use a nonlinear inversion jointly for Rayleigh and Love waves; in such a nonlinear inversion best solutions are obtained among the model parameters within prescribed limits for each parameter. We first choose <em>V<sub>SH</sub></em>, <em>V<sub>SV </sub></em>and <em>V<sub>PH</sub></em> within their corresponding limits; <em>V<sub>PV</sub></em> and <em>h</em> can be evaluated from empirical relations among the parameters. The density has small effect on surface wave velocities and it can be considered from other studies or from empirical relation of density to average P-wave velocity.</p>

Compressional‐wave velocities in attenuating media: A laboratory physical model study

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1162-1167 ◽  
Author(s):  
Joseph B. Molyneux ◽  
Douglas R. Schmitt
Keyword(s):  
Phase Velocity ◽  
Group Velocity ◽  
Wave Velocity ◽  
Propagation Distance ◽  
Compressional Wave ◽  
Arrival Times ◽  
Wave Velocities ◽  
Amplitude Maximum ◽  
Phase And Group Velocities ◽  
Group Velocities

Elastic‐wave velocities are often determined by picking the time of a certain feature of a propagating pulse, such as the first amplitude maximum. However, attenuation and dispersion conspire to change the shape of a propagating wave, making determination of a physically meaningful velocity problematic. As a consequence, the velocities so determined are not necessarily representative of the material’s intrinsic wave phase and group velocities. These phase and group velocities are found experimentally in a highly attenuating medium consisting of glycerol‐saturated, unconsolidated, random packs of glass beads and quartz sand. Our results show that the quality factor Q varies between 2 and 6 over the useful frequency band in these experiments from ∼200 to 600 kHz. The fundamental velocities are compared to more common and simple velocity estimates. In general, the simpler methods estimate the group velocity at the predominant frequency with a 3% discrepancy but are in poor agreement with the corresponding phase velocity. Wave velocities determined from the time at which the pulse is first detected (signal velocity) differ from the predominant group velocity by up to 12%. At best, the onset wave velocity arguably provides a lower bound for the high‐frequency limit of the phase velocity in a material where wave velocity increases with frequency. Each method of time picking, however, is self‐consistent, as indicated by the high quality of linear regressions of observed arrival times versus propagation distance.

scholarly journals Joint Body‐ and Surface‐Wave Tomography of Yucca Flat, Nevada, Using a Novel Seismic Source

2019 ◽  
Vol 109 (5) ◽  
pp. 1922-1934 ◽  
Author(s):  
Liam D. Toney ◽  
Robert E. Abbott ◽  
Leiph A. Preston ◽  
David G. Tang ◽  
Tori Finlay ◽  
...  
Keyword(s):  
Surface Wave ◽  
Phase Velocity ◽  
Wave Velocity ◽  
Velocity Structure ◽  
Joint Inversion ◽  
P Wave ◽  
S Wave ◽  
Surface Wave Dispersion ◽  
Velocity Models ◽  
Phase Velocity Dispersion

Abstract In preparation for the next phase of the Source Physics Experiments, we acquired an active‐source seismic dataset along two transects totaling more than 30 km in length at Yucca Flat, Nevada, on the Nevada National Security Site. Yucca Flat is a sedimentary basin which has hosted more than 650 underground nuclear tests (UGTs). The survey source was a novel 13,000 kg modified industrial pile driver. This weight drop source proved to be broadband and repeatable, richer in low frequencies (1–3 Hz) than traditional vibrator sources and capable of producing peak particle velocities similar to those produced by a 50 kg explosive charge. In this study, we performed a joint inversion of P‐wave refraction travel times and Rayleigh‐wave phase‐velocity dispersion curves for the P‐ and S‐wave velocity structure of Yucca Flat. Phase‐velocity surface‐wave dispersion measurements were obtained via the refraction microtremor method on 1 km arrays, with 80% overlap. Our P‐wave velocity models verify and expand the current understanding of Yucca Flat’s subsurface geometry and bulk properties such as depth to Paleozoic basement and shallow alluvium velocity. Areas of disagreement between this study and the current geologic model of Yucca Flat (derived from borehole studies) generally correlate with areas of widely spaced borehole control points. This provides an opportunity to update the existing model, which is used for modeling groundwater flow and radionuclide transport. Scattering caused by UGT‐related high‐contrast velocity anomalies substantially reduced the number and frequency bandwidth of usable dispersion picks. The S‐wave velocity models presented in this study agree with existing basin‐wide studies of Yucca Flat, but are compromised by diminished surface‐wave coherence as a product of this scattering. As nuclear nonproliferation monitoring moves from teleseismic to regional or even local distances, such high‐frequency (>5  Hz) scattering could prove challenging when attempting to discriminate events in areas of previous testing.

A hierarchical elastic full-waveform inversion scheme based on wavefield separation and the multistep-length approach

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. R99-R123 ◽  
Author(s):  
Zhiming Ren ◽  
Yang Liu
Keyword(s):  
Wave Velocity ◽  
Waveform Inversion ◽  
P Wave ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
S Wave ◽  
Wave Velocities ◽  
Full Waveform ◽  
Wavefield Separation ◽  
P Wave Velocity

Elastic full-waveform inversion (FWI) updates model parameters by minimizing the residuals of the P- and S-wavefields, resulting in more local minima and serious nonlinearity. In addition, the coupling of different parameters degrades the inversion results. To address these problems, we have developed a hierarchical elastic FWI scheme based on wavefield separation and a multistep-length gradient approach. First, we have derived the gradients expressed by different wave modes; analyzed the crosstalk between various parameters; and evaluated the sensitivity of separated P-wave, separated S-wave, and P- and S-wave misfit functions. Then, a practical four-stage inversion workflow was developed. In the first stage, conventional FWI is used to achieve rough estimates of the P- and S-wave velocities. In the second stage, we only invert the P-wave velocity applying the separated P-wavefields when strong S-wave energy is involved, or we merely update the S-wave velocity by matching the separated S-wavefields for the weak S-wave case. The PP and PS gradient formulas are used in these two cases, respectively. Therefore, the nonlinearity of inversion and the crosstalk between parameters are greatly reduced. In the third stage, the multistep-length gradient scheme is adopted. The density structure can be improved owing to the use of individual step lengths for different parameters. In the fourth stage, we make minor adjustments to the recovered P- and S-wave velocities and density by implementing conventional FWI again. Synthetic examples have determined that our hierarchical FWI scheme with the aforementioned steps obtains more plausible models than the conventional method. Inversion results of each stage and any three stages reveal that wavefield decomposition and the multistep-length approach are helpful to improve the accuracy of velocities and density, respectively, and all the stages of our hierarchical FWI method are necessary to give a good recovery of P- and S-wave velocities and density.

scholarly journals Upscaling of elastic properties in carbonates: A modeling approach based on a multiscale geophysical data set

2020 ◽  
Author(s):  
Jerome Fortin ◽  
Cedric Bailly ◽  
Mathilde Adelinet ◽  
Youri Hamon
Keyword(s):  
Elastic Properties ◽  
Wave Velocity ◽  
Representative Elementary Volume ◽  
P Wave ◽  
Elementary Volume ◽  
Data Set ◽  
Wave Velocities ◽  
P Wave Velocity ◽  
Ultrasonic Measurements ◽  
Seismic Scale

&lt;p&gt;Linking ultrasonic measurements made on samples, with sonic logs and seismic subsurface data, is a key challenge for the understanding of carbonate reservoirs. To deal with this problem, we investigate the elastic properties of dry lacustrine carbonates. At one study site, we perform a seismic refraction survey (100 Hz), as well as sonic (54 kHz) and ultrasonic (250 kHz) measurements directly on outcrop and ultrasonic measurements on samples (500 kHz). By comparing the median of each data set, we show that the P wave velocity decreases from laboratory to seismic scale. Nevertheless, the median of the sonic measurements acquired on outcrop surfaces seems to fit with the seismic data, meaning that sonic acquisition may be representative of seismic scale. To explain the variations due to upscaling, we relate the concept of representative elementary volume with the wavelength of each scale of study. Indeed, with upscaling, the wavelength varies from millimetric to pluri-metric. This change of scale allows us to conclude that the behavior of P wave velocity is due to different geological features (matrix porosity, cracks, and fractures) related to the different wavelengths used. Based on effective medium theory, we quantify the pore aspect ratio at sample scale and the crack/fracture density at outcrop and seismic scales using a multiscale representative elementary volume concept. Results show that the matrix porosity that controls the ultrasonic P wave velocities is progressively lost with upscaling, implying that crack and fracture porosity impacts sonic and seismic P wave velocities, a result of paramount importance for seismic interpretation based on deterministic approaches.&lt;/p&gt;&lt;p&gt;Bailly, C., Fortin, J., Adelinet, M., &amp; Hamon, Y. (2019). Upscaling of elastic properties in carbonates: A modeling approach based on a multiscale geophysical data set. Journal of Geophysical Research: Solid Earth, 124. https://doi.org/10.1029/2019JB018391&lt;/p&gt;

Ground roll: A potential tool for constraining shallow shear‐wave structure

Geophysics ◽  
1993 ◽  
Vol 58 (5) ◽  
pp. 713-719 ◽  
Author(s):  
Ghassan I. Al‐Eqabi ◽  
Robert B. Herrmann
Keyword(s):  
Surface Wave ◽  
Phase Velocity ◽  
Wave Velocity ◽  
Wave Structure ◽  
S Wave ◽  
Data Set ◽  
Velocity Inversion ◽  
Ground Roll ◽  
Lateral Variations ◽  
Wave Arrival

The objective of this study is to demonstrate that a laterally varying shallow S‐wave structure, derived from the dispersion of the ground roll, can explain observed lateral variations in the direct S‐wave arrival. The data set consists of multichannel seismic refraction data from a USGS-GSC survey in the state of Maine and the province of Quebec. These data exhibit significant lateral changes in the moveout of the ground‐roll as well as the S‐wave first arrivals. A sequence of surface‐wave processing steps are used to obtain a final laterally varying S‐wave velocity model. These steps include visual examination of the data, stacking, waveform inversion of selected traces, phase velocity adjustment by crosscorrelation, and phase velocity inversion. These models are used to predict the S‐wave first arrivals by using two‐dimensional (2D) ray tracing techniques. Observed and calculated S‐wave arrivals match well over 30 km long data paths, where lateral variations in the S‐wave velocity in the upper 1–2 km are as much as ±8 percent. The modeled correlation between the lateral variations in the ground‐roll and S‐wave arrival demonstrates that a laterally varying structure can be constrained by using surface‐wave data. The application of this technique to data from shorter spreads and shallower depths is discussed.

Sonic logging of compressional‐wave velocities in a very slow formation

Geophysics ◽  
1995 ◽  
Vol 60 (6) ◽  
pp. 1627-1633 ◽  
Author(s):  
Bart W. Tichelaar ◽  
Klaas W. van Luik
Keyword(s):  
Shear Wave ◽  
Wave Velocity ◽  
Compressional Wave ◽  
P Wave ◽  
Dipole Source ◽  
Frequency Spectra ◽  
Unconsolidated Sands ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Sonic Logging

Borehole sonic waveforms are commonly acquired to produce logs of subsurface compressional and shear wave velocities. To this purpose, modern borehole sonic tools are usually equipped with various types of acoustic sources, i.e., monopole and dipole sources. While the dipole source has been specifically developed for measuring shear wave velocities, we found that the dipole source has an advantage over the monopole source when determining compressional wave velocities in a very slow formation consisting of unconsolidated sands with a porosity of about 35% and a shear wave velocity of about 465 m/s. In this formation, the recorded compressional refracted waves suffer from interference with another wavefield component identified as a leaky P‐wave, which hampers the determination of compressional wave velocities in the sands. For the dipole source, separation of the compressional refracted wave from the recorded waveforms is accomplished through bandpass filtering since the wavefield components appear as two distinctly separate contributions to the frequency spectrum: a compressional refracted wave centered at a frequency of 6.5 kHz and a leaky P‐wave centered at 1.3 kHz. For the monopole source, the frequency spectra of the various waveform components have considerable overlap. It is therefore not obvious what passband to choose to separate the compressional refracted wave from the monopole waveforms. The compressional wave velocity obtained for the sands from the dipole compressional refracted wave is about 2150 m/s. Phase velocities obtained for the dispersive leaky P‐wave excited by the dipole source range from 1800 m/s at 1.0 kHz to 1630 m/s at 1.6 kHz. It appears that the dipole source has an advantage over the monopole source for the data recorded in this very slow formation when separating the compressional refracted wave from the recorded waveforms to determine formation compressional wave velocities.

P‐wave velocity and permeability distribution of sandstones from a fractured tight gas reservoir

Geophysics ◽  
2002 ◽  
Vol 67 (1) ◽  
pp. 241-253 ◽  
Author(s):  
Helmut Dürrast ◽  
P. N. J. Rasolofosaon ◽  
Siegfried Siegesmund
Keyword(s):  
Velocity Distribution ◽  
Wave Velocity ◽  
Confining Pressure ◽  
P Wave ◽  
Tight Gas ◽  
Rock Fabric ◽  
The Core ◽  
Wave Velocities ◽  
P Wave Velocity ◽  
Tight Gas Reservoir

Fractures are an important fabric element in many tight gas reservoirs because they provide the necessary channels for fluid flow in rocks which usually have low matrix permeabilities. Several sandstone samples of such a reservoir type were chosen for a combined study of rock fabric elements and petrophysical properties. Geological investigations of the distribution and orientation of the fractures and sedimentary layering were performed. In addition, laboratory measurements were carried out to determine the directional dependence of the permeability and P‐wave velocities. Higher permeability values are generally in the plane of the nearly horizontal sedimentary layering with regard to the core axis. With the occurrence of subvertical fractures, however, the highest permeabilities were determined to be parallel to the core axis. Compressional wave velocities were measured on spherical samples in more than 100 directions to get the VP symmetry without prior assumptions. Below 50 MPa confining pressure, all samples show a monoclinic symmetry of the P wave velocity distribution, caused by sedimentary layering, fractures, and crossbedding. At higher confining pressure, sedimentary layering is approximately the only effective fabric element, resulting in a more transverse isotropic VP symmetry. Using the geological‐petrophysical model introduced here, the complex symmetry of the VP distributions can only be explained by the rock fabric elements. Furthermore, water saturation increases the velocities and decreases the anisotropy but does not change VP symmetry. This indicates that at this state, all fabric elements, including the fractures, have an influence on P‐wave velocity distribution.

Wavefield simulation and data-acquisition-scheme analysis for LWD acoustic tools in very slow formations

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. E59-E68 ◽  
Author(s):  
Hua Wang ◽  
Guo Tao
Keyword(s):  
Wave Velocity ◽  
Cutoff Frequency ◽  
P Wave ◽  
Flexural Wave ◽  
S Wave ◽  
Low Frequencies ◽  
Wave Velocities ◽  
Dipole System ◽  
P Wave Velocity ◽  
Wavefield Simulation

Propagating wavefields from monopole, dipole, and quadrupole acoustic logging-while-drilling (LWD) tools in very slow formations have been studied using the discrete wavenumber integration method. These studies examine the responses of monopole and dipole systems at different source frequencies in a very slow surrounding formation, and the responses of a quadrupole system operating at a low source frequency in a slow formation with different S-wave velocities. Analyses are conducted of coherence-velocity/slowness relationships (semblance spectra) in the time domain and of the dispersion characteristics of these waveform signals from acoustic LWD array receivers. These analyses demonstrate that, if the acoustic LWD tool is centralized properly and is operating at low frequencies (below 3 kHz), a monopole system can measure P-wave velocity by means of a “leaky” P-wave for very slow formations. Also, for very slow formations a dipole system can measure the P-wave velocity via a leaky P-wave and can measure the S-wave velocity from a formation flexural wave. With a quadrupole system, however, the lower frequency limit (cutoff frequency) of the drill-collar interference wave would decrease to 5 kHz and might no longer be neglected if the surrounding formation becomes a very slow formation, with S-wave velocities at approximately 500 m/s.

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