A curve-fitting technique for determining dispersion characteristics of guided elastic waves

Geophysics ◽  
2010 ◽  
Vol 75 (3) ◽  
pp. E153-E160 ◽  
Author(s):  
Xiao-Ming Tang ◽  
Chen Li ◽  
Douglas J. Patterson
Keyword(s):  
Dispersion Curve ◽  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Curve Fitting ◽  
Elastic Waves ◽  
P Wave ◽  
Seismic Exploration ◽  
Dispersion Characteristics ◽  
Acoustic Logging

We have developed a novel curve-fitting method to estimate dispersion characteristics of guided elastic waves and investigate its application to field wireline and logging while drilling (LWD) acoustic data processing. In an elastic waveguide such as a fluid-filled borehole with a logging tool, the frequency dispersion of a guided-wave mode is characterized by a monotonically varying dispersion curve bounded by its low- and high-frequency limits. The detailed behavior of the curves relates to various elastic/acoustic parameters of the complicated waveguide structure. The novelty of the proposed technique is that it simulates the multiparameter dispersion curve using a simple analytical function that has only four parameters. By adjusting the four parameters to fit the actual wave dispersion data, the wave’s dispersion characteristics can be satisfactorily determined. The result of this simple approach leads to several important applications in acoustic logging. The first is to correct the dispersion effect in the shear-wave velocity from wireline dipole acoustic logging. The second application obtains P-wave velocity from the dispersive leaky compressional-wave data from wireline or LWD measurements. Third, the technique is applied to obtain shear-wave velocity from LWD quadrupole shear-wave logging. Finally, the technique is applicable to layered waveguide structures encountered in surface seismic exploration.

Experimental Estimation of Shear Wave Velocity Profile Using MASW Method and Inversion Technique

2013 ◽  
Vol 300-301 ◽  
pp. 955-958
Author(s):  
Pei Hsun Tsai ◽  
Chih Chun Lou
Keyword(s):  
Genetic Algorithm ◽  
Velocity Profile ◽  
Dispersion Curve ◽  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Dispersion Curves ◽  
Real Parameter ◽  
Shear Wave Velocity Profile ◽  
Experimental Dispersion

In the paper the shear wave velocity profile is studied using the MASW test. The experimental dispersion curves were obtained from the signal process proposed by Ryden. Theoretical dispersion curve can be constructed by thin layer stiffness matrix method. A real-parameter genetic algorithm is required to minimize the error between the theoretical and experimental dispersion curves. To reduce the error of experimental and theoretical dispersion curve using real-parameter genetic algorithm is feasible. The results show that the soil layers of the study area can be modeled as a sandy fill overlaid on an underlying half space. Test results also show that the asymptotes at high frequencies of the fundamental mode approach the phase velocities for the fill of 190 m/s. The depths of weathered bedrock estimating from dispersion curves match well with that of borehole data.

Estimations of formation velocity, permeability, and shear‐wave anisotropy using acoustic logs

Geophysics ◽  
1996 ◽  
Vol 61 (2) ◽  
pp. 437-443 ◽  
Author(s):  
Ningya Cheng ◽  
Chuen Hon Cheng
Keyword(s):  
Phase Velocity ◽  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Stoneley Wave ◽  
S Wave ◽  
Acoustic Logging ◽  
Wave Phase ◽  
Wave Phase Velocity ◽  
Logging Tool

Field data sets collected by an array monopole acoustic logging tool and a shear wave logging tool are processed and interpreted. The P‐ and S‐wave velocities of the formation are determined by threshold detection with cross‐correlation correction from the full waveform and the shear‐wave log, respectively. The array monopole acoustic logging data are also processed using the extended Prony’s method to estimate the borehole Stoneley wave phase velocity and attenuation as a function of frequency. The well formation between depths of 2950 and 3150 ft (899 and 960 m) can be described as an isotropic elastic medium. The inverted [Formula: see text] from the Stoneley wave phase velocity is in excellent agreement with the shear‐wave log results in this section. The well formation between the depths of 3715 and 3780 ft (1132 and 1152 m) can be described as a porous medium with shear‐wave velocity anisotropy about 10% to 20% and with the symmetry axis perpendicular to the borehole axis. The disagreement between the shear‐wave velocity from the Stoneley wave inversion and the direct shear‐wave log velocity in this section is beyond the errors in the measurements. Estimated permeabilities from low‐frequency Stoneley wave velocity and attenuation data are in good agreement with the core measurements. Also it is proven that the formation permeability is not the cause of the discrepancy. From the estimated “shear/pseudo‐Rayleigh” phase velocities in the array monopole log and the 3-D finite‐difference synthetics in the anisotropic formation, the discrepancy can best be explained as shear‐wave anisotropy.

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

Changes in dynamic shear moduli of carbonate rocks with fluid substitution

Geophysics ◽  
2009 ◽  
Vol 74 (3) ◽  
pp. E135-E147 ◽  
Author(s):  
Gregor T. Baechle ◽  
Gregor P. Eberli ◽  
Ralf J. Weger ◽  
Jose Luis Massaferro
Keyword(s):  
Shear Modulus ◽  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Water Saturation ◽  
Acoustic Properties ◽  
P Wave ◽  
Shear Moduli ◽  
Water Saturated ◽  
Fluid Interaction

To assess saturation effects on acoustic properties in carbonates, we measure ultrasonic velocity on 38 limestone samples whose porosity ranges from 5% to 30% under dry and water-saturated conditions. Complete saturation of the pore space with water causes an increase and decrease in compressional- and shear-wave velocity as well as significant changes in the shear moduli. Compressional velocities of most water-saturated samples are up to [Formula: see text] higher than the velocities of the dry samples. Some show no change, and a few even show a decrease in velocity. Shear-wave velocity [Formula: see text] generally decreases, but nine samples show an increase of up to [Formula: see text]. Water saturation decreases the shear modulus by up to [Formula: see text] in some samples and increases it by up to [Formula: see text] in others. The average increase in the shear modulus with water saturation is [Formula: see text]; the average decrease is [Formula: see text]. The [Formula: see text] ratio shows an overall increase with water saturation. In particular, rocks displaying shear weakening have distinctly higher [Formula: see text] ratios. Grainstone samples with high amounts of microporosity and interparticle macro-pores preferentially show shear weakening, whereas recrystallized limestones are prone to increase shear strengths with water saturation. The observed shear weakening indicates that a rock-fluid interaction occurs with water saturation, which violates one of the assumptions in Gassmann’s theory. We find a positive correlation between changes in shear modulus and the inability of Gassmann’s theory to predict velocities of water-saturated samples at high frequencies. Velocities of water-saturated samples predicted by Gassmann’s equation often exceed measured values by as much as [Formula: see text] for samples exhibiting shear weakening. In samples showing shear strengthening, Gassmann-predicted velocity values are as much as [Formula: see text] lower than measured values. In 66% of samples, Gassmann-predicted velocities show a misfit to measured water-saturated P-wave velocities. This discrepancy between measured and Gassmann-predicted velocity is not caused solely by velocity dispersion but also by rock-fluid interaction related to the pore structure of carbonates. Thus, a pore analysis should be conducted to assess shear-moduli changes and the resultant uncertainty for amplitude variation with offset analyses and velocity prediction using Gassmann’s theory.

Seismic Surface Wave Tomography on dense 3D active data

2020 ◽  
Author(s):  
Ilaria Barone ◽  
Emanuel Kästle ◽  
Claudio Strobbia ◽  
Giorgio Cassiani
Keyword(s):  
Surface Wave ◽  
Phase Velocity ◽  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Seismic Exploration ◽  
Surface Wave Tomography ◽  
Travel Times ◽  
Velocity Models ◽  
Wave Tomography

<p>Surface Wave Tomography (SWT) is a well-established technique in global seismology: signals from strong earthquakes or seismic ambient noise are used to retrieve 3D shear-wave velocity models, both at regional and global scale. This study aims at applying the same methodology to controlled source data, with specific focus on 3D acquisition geometries for seismic exploration. For a specific frequency, travel times between all source-receiver couples are derived from phase differences. However, higher modes and heterogeneous spatial sampling make phase extraction challenging. The processing workflow includes different steps as (1) filtering in f-k domain to isolate the fundamental mode from higher order modes, (2) phase unwrapping in two spatial dimensions, (3) zero-offset phase estimation and (4) travel times computation. Surface wave tomography is then applied to retrieve a 2D phase velocity map. This procedure is repeated for different frequencies. Finally, individual dispersion curves obtained by the superposition of phase velocity maps at different frequencies are depth inverted to retrieve a 3D shear wave velocity model.</p>

Multichannel analysis of surface waves

Geophysics ◽  
1999 ◽  
Vol 64 (3) ◽  
pp. 800-808 ◽  
Author(s):  
Choon B. Park ◽  
Richard D. Miller ◽  
Jianghai Xia
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Dispersion Curve ◽  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Frequency Component ◽  
Multichannel Recording ◽  
Phase Velocities ◽  
Ground Roll

The frequency‐dependent properties of Rayleigh‐type surface waves can be utilized for imaging and characterizing the shallow subsurface. Most surface‐wave analysis relies on the accurate calculation of phase velocities for the horizontally traveling fundamental‐mode Rayleigh wave acquired by stepping out a pair of receivers at intervals based on calculated ground roll wavelengths. Interference by coherent source‐generated noise inhibits the reliability of shear‐wave velocities determined through inversion of the whole wave field. Among these nonplanar, nonfundamental‐mode Rayleigh waves (noise) are body waves, scattered and nonsource‐generated surface waves, and higher‐mode surface waves. The degree to which each of these types of noise contaminates the dispersion curve and, ultimately, the inverted shear‐wave velocity profile is dependent on frequency as well as distance from the source. Multichannel recording permits effective identification and isolation of noise according to distinctive trace‐to‐trace coherency in arrival time and amplitude. An added advantage is the speed and redundancy of the measurement process. Decomposition of a multichannel record into a time variable‐frequency format, similar to an uncorrelated Vibroseis record, permits analysis and display of each frequency component in a unique and continuous format. Coherent noise contamination can then be examined and its effects appraised in both frequency and offset space. Separation of frequency components permits real‐time maximization of the S/N ratio during acquisition and subsequent processing steps. Linear separation of each ground roll frequency component allows calculation of phase velocities by simply measuring the linear slope of each frequency component. Breaks in coherent surface‐wave arrivals, observable on the decomposed record, can be compensated for during acquisition and processing. Multichannel recording permits single‐measurement surveying of a broad depth range, high levels of redundancy with a single field configuration, and the ability to adjust the offset, effectively reducing random or nonlinear noise introduced during recording. A multichannel shot gather decomposed into a swept‐frequency record allows the fast generation of an accurate dispersion curve. The accuracy of dispersion curves determined using this method is proven through field comparisons of the inverted shear‐wave velocity ([Formula: see text]) profile with a downhole [Formula: see text] profile.

Shallow Shear-Wave Velocity Structure in Oklahoma Based on the Joint Inversion of Ambient Noise Dispersion and Teleseismic P-Wave Receiver Functions

2020 ◽  
Author(s):  
Jiayan Tan ◽  
Charles A. Langston ◽  
Sidao Ni
Keyword(s):  
Surface Wave ◽  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Ambient Noise ◽  
Sedimentary Basins ◽  
Velocity Model ◽  
Receiver Functions ◽  
P Wave ◽  
Velocity Models

ABSTRACT Ambient noise cross-correlations, used to obtain fundamental-mode Rayleigh-wave group velocity estimates, and teleseismic P-wave receiver functions are jointly modeled to obtain a 3D shear-wave velocity model for the crust and upper mantle of Oklahoma. Broadband data from 82 stations of EarthScope Transportable Array, the U.S. National Seismic Network, and the Oklahoma Geological Survey are used. The period range for surface-wave ambient noise Green’s functions is from 4.5 to 30.5 s constraining shear-wave velocity to a depth of 50 km. We also compute high-frequency receiver functions at these stations from 214 teleseismic earthquakes to constrain individual 1D velocity models inferred from the surface-wave tomography. Receiver functions reveal Ps conversions from the Moho, intracrustal interfaces, and shallow sedimentary basins. Shallow low-velocity zones in the model correlate with the large sedimentary basins of Oklahoma. The velocity model significantly improves the agreement of synthetic and observed seismograms from the 6 November 2011 Mw 5.7 Prague, Oklahoma earthquake suggesting that it can be used to improve earthquake location and moment tensor inversion of local and regional earthquakes.

Mapping formation radial shear-wave velocity variation by a constrained inversion of borehole flexural-wave dispersion data

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. E183-E190 ◽  
Author(s):  
Xiao-Ming Tang ◽  
Douglas J. Patterson
Keyword(s):  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
High Frequency ◽  
Wave Dispersion ◽  
Velocity Variation ◽  
Flexural Wave ◽  
Inversion Method ◽  
Dispersion Characteristics ◽  
Dispersion Data

We have developed a novel constrained inversion method for estimating a radial shear-wave velocity profile away from the wellbore using dipole acoustic logging data and have analyzed the effect of the radial velocity changes on dipole-flexural-wave dispersion characteristics. The inversion of the dispersion data to estimate the radial changes is inherently a nonunique problem because changing the degree of variation or the radial size of the variation zone can produce similar wave-dispersion characteristics. Nonuniqueness can be solved by developing a constrained inversion method. This is done by constraining the high-frequency portion of the model dispersion curve with another curve calculated using the near-borehole velocity. The constraint condition is based on the physical principle that a high-frequency dipole wave has a shallow penetration depth and is therefore sensitive to the near-borehole shear-wave velocity. We have validated the result of the constrained inversion with synthetic data testing. Combining the new inversion method with four-component crossed-dipole anisotropy processing obtains shear radial profiles in fast and slow shear polarization directions. In a sandstone formation, the fast and slow shear-wave profiles show substantial differences caused by the near-borehole stress field, demonstrating the ability of the technique to obtain radial and azimuthal geomechanical property changes near the wellbore.

scholarly journals Seismic Waves Response Characteristics of Niger Delta Soils

2021 ◽  
Vol 5 (1) ◽  
pp. 191-196
Author(s):  
J.O. Okovido ◽  
C. Kennedy
Keyword(s):  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
Niger Delta ◽  
Void Ratio ◽  
Young Modulus ◽  
P Wave ◽  
Delta Region ◽  
Heavy Load ◽  
Niger Delta Region

The study investigated the dynamic soil properties of States in Niger Delta region of Nigeria as a function of seismic activities. The down-hole seismic test was used to determine the response of the soils. The results of soil samples collected up to 30m depth, showed that the average young modulus increases with increase in depth, which ranged from 115.77±1.74 to 3231.17±1.01 kPa across the States. Also, shear wave velocity generally increases with increase in depth. The average shear wave velocity across the States ranged from 126.00±1.86 to 288.00±2.63m/s. Also, the average P-wave velocity increases with depth, with values across the States ranging from 310.60±3.51 to 656.00±3.69m/s. On the other hand, the void ratio was observed to be constant at certain range of depth, and in most with values across the States ranging from 0.651±.093 to 0.860±.067. Unlike void ratio, Poisson’s ratio fluctuates with depth, with values across the States ranging from 0.23±2.27 to 0.36±1.18. Based on the results, the Niger Delta region may be resistant to earthquake, but as an oil hub of Nigeria, it is also susceptible to earthquake that could be triggered by stress due to heavy load and seismic activities.

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