Separation of Split Shear Waves in Two Non-orthogonal Sets of Vertical Fractures

Geophysics ◽  
2021 ◽  
pp. 1-62
Author(s):  
Mengqi Li ◽  
Jun Lu ◽  
Yun Wang ◽  
Xueying Zhang ◽  
Zongjie Li
Keyword(s):  
Two Dimensions ◽  
Rotation Matrix ◽  
S Wave ◽  
S Waves ◽  
Rotation Method ◽  
Wave Splitting ◽  
Vsp Data ◽  
Christoffel Equation ◽  
Shallow Crust ◽  
Vertical Fractures

The phenomenon of S-wave splitting indicates the development of fractures in the shallow crust. Therefore, methods based on S-wave splitting have been established to predict the development of one set of parallel fractures. However, for rocks containing two non-orthogonal sets of vertical fractures, the mechanism of S-wave splitting is more complex, and the available methods cannot be applied. To resolve this inadequacy, we propose a two-way rotation method to separate split S-waves with the aim of restoring the split S-wave polarizations and predicting the fracture azimuths. First, we calculate the stiffness matrix of fractured media based on the linear slip theory and derive the phase velocities and polarizations of split S-waves induced by fractures using the Christoffel equation. Second, we clarify the S-wave splitting mechanism in this media by employing velocity analysis and deconstruct the S-wave polarizations on the horizontal components. Third, we deduce a two-way rotation matrix obtained by the S-wave splitting modes to separate the split S-waves. To solve for the angle parameters related to the fracture azimuths in the two-way rotation matrix, we superpose the subspace polarizations in two dimensions to determine the polarization azimuths of the split S-waves. Numerical model tests demonstrate that the proposed method is stable under noisy conditions. Finally, we apply the proposed method to real near-offset and walkaround VSP data, and the predicted fracture results are verified by imaging logs and prior knowledge.

Application of seismic interferometry to extract P- and S-wave propagation and observation of shear-wave splitting from noise data at Cold Lake, Alberta, Canada

Geophysics ◽  
2008 ◽  
Vol 73 (4) ◽  
pp. D35-D40 ◽  
Author(s):  
Masatoshi Miyazawa ◽  
Roel Snieder ◽  
Anupama Venkataraman
Keyword(s):  
Wave Propagation ◽  
Shear Wave ◽  
Structural Parameters ◽  
Shear Wave Splitting ◽  
Seismic Interferometry ◽  
Stress Axis ◽  
S Wave ◽  
S Waves ◽  
Wave Splitting ◽  
Cold Lake

We extract downward-propagating P- and S-waves from industrial noise generated by human and/or machine activity at the surface propagating down a borehole at Cold Lake, Alberta, Canada, and measure shear-wave splitting from these data. The continuous seismic data are recorded at eight sensors along a downhole well during steam injection into a 420–470-m-deep oil reservoir. We crosscorrelate the waveforms observed at the top sensor and other sensors to extract estimates of the direct P- and S-wave components of the Green’s function that account for wave propagation between sensors. Fast high-frequency and slow low-frequency signals propagating vertically from the surface to the bottom are found for the vertical and horizontal components of the wave motion, which are identified with P- and S-waves, respectively. The fastest S-wave polarized in the east-northeast–west-southwest direction is about 1.9% faster than the slowest S-wave polarized in the northwest-southeast direction. The direction of polarization of the fast S-wave is rotated clockwise by [Formula: see text] from the maximum principal stress axis as estimated from the regional stress field. This study demonstrates the useful application of seismic interferometry to field data to determine structural parameters, which are P- and S-wave velocities and a shear-wave-splitting coefficient, with high accuracy.

Synthesis of multicomponent quasi-P and converted quasi-P-S seismograms for intersecting fracture systems

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1261-1271 ◽  
Author(s):  
Andrey A. Ortega ◽  
George A. McMechan
Keyword(s):  
Shear Wave ◽  
Transverse Isotropy ◽  
Normal Incidence ◽  
Shear Wave Splitting ◽  
P Wave ◽  
Orthorhombic Symmetry ◽  
S Wave ◽  
Stiffness Constant ◽  
Wave Splitting ◽  
Vertical Fractures

Dynamic ray shooting with interpolation is an economical way of computing approximate Green’s functions in 3-D heterogeneous anisotropic media. The amplitudes, traveltimes, and polarizations of the reflected rays arriving at the surface are interpolated to synthesize three‐component seismograms at the desired recording points. The algorithm is applied to investigate kinematic quasi-P-wave propagation and converted quasi-P-S-wave splitting variations produced in reflections from the bottom of a layer containing two sets of intersecting dry vertical fractures as a function of the angle between the fracture sets and of the intensity of fracturing. An analytical expression is derived for the stiffness constant C16 that extends Hudson’s second‐order scattering theory to include tetragonal-2 symmetry systems. At any offset, the amount of splitting in nonorthogonal (orthorhombic symmetry) intersecting fracture sets is larger than in orthogonal (tetragonal-1 symmetry) systems, and it increases nonlinearly as a function of the intensity of fracturing as offset increases. Such effects should be visible in field data, provided that the dominant frequency is sufficiently high and the offset is sufficiently large. The amount of shear‐wave splitting at vertical incidence increases nonlinearly as a function of the intensity of fracturing and increases nonlinearly from zero in the transition from tetragonal-1 anisotropy through orthorhombic to horizontal transverse isotropy; the latter corresponds to the two crack systems degenerating to one. The zero shear‐wave splitting corresponds to a singularity, at which the vertical velocities of the two quasi‐shear waves converge to a single value that is both predicted theoretically and illustrated numerically. For the particular case of vertical fractures, there is no P-to-S conversion of vertically propagating (zero‐offset) waves. If the fractures are not vertical, the normal incidence P-to-S reflection coefficient is not zero and thus is a potential diagnostic of fracture orientation.

Shear‐wave studies in glacial till

Geophysics ◽  
1998 ◽  
Vol 63 (4) ◽  
pp. 1273-1284 ◽  
Author(s):  
Bradley J. Carr ◽  
Zoltan Hajnal ◽  
Arnfinn Prugger
Keyword(s):  
Shear Wave ◽  
P Wave ◽  
Vertical Resolution ◽  
S Wave ◽  
Glacial Deposits ◽  
Seismic Line ◽  
S Waves ◽  
Additional Information ◽  
Vsp Data ◽  
Clay Percentage

Within a high‐resolution shallow reflection survey program in Saskatchewan, Canada, S-waves were produced using a single seismo‐electric blasting cap and were found to be distinguishable from surface wave phases. The local glacial deposits have average velocities of 450 m/s. [Formula: see text] ratios average 3.6 in these sequences, but they vary laterally, according to the velocity analyses done in two boreholes drilled along the seismic line. Vertical resolution for S-wave reflections are 0.75 m [in the vertical seismic profiling (VSP) data] and 1.5 m (in the CDP data). Yet, the S-wave CDP results are still better than corresponding P-wave data, which had a vertical resolution of 2.6 m. S-wave anisotropy is inferred in the glacial deposits on the basis of particle motion analysis and interpretations of S-wave splitting. However, the amount of observed splitting is small (∼2–6 ms over 5–10 m) and could go undetected for seismic surveys with larger sampling intervals. VSPs indicate that S-wave reflectivity is caused by both distinct and subtle lithologic changes (e.g., clay/sand contacts or changes in clay percentage within a particular till unit) and changes in bulk porosity. Migrated S-wave sections from line 1 and line 2 image reflections from sand layers within the tills as well as the first “bedrock” sequence (known as the Judith River Formation). Shear wave images are not only feasible in unconsolidated materials, but provide additional information about structural relationships within these till units.

Elastic-wavefield interferometry using P-wave source VSPs at the Wamsutter field, Wyoming

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. Q27-Q36 ◽  
Author(s):  
James Gaiser ◽  
Ivan Vasconcelos ◽  
Rosemarie Geetan ◽  
John Faragher
Keyword(s):  
Stationary Phase ◽  
Wave Velocity ◽  
P Wave ◽  
Phase Point ◽  
S Wave ◽  
Wave Source ◽  
S Waves ◽  
Wave Splitting ◽  
Zero Offset ◽  
Tube Wave

In this study, elastic-wavefield interferometry was used to recover P- and S-waves from the 3D P-wave vibrator VSP data at Wamsutter field in Wyoming. S-wave velocity and birefringence is of particular interest for the geophysical objectives of lithology discrimination and fracture characterization in naturally fractured tight gas sand reservoirs. Because we rely on deconvolution interferometry for retrieving interreceiver P- and S-waves in the subsurface, the output fields are suitable for high-resolution, local reservoir characterization. In 1D media where the borehole is nearly vertical, data at the stationary-phase point is not conducive to conventional interferometry. Strong tube-wave noise generated by physical sources near the borehole interfere with S-wave splitting analyses. Also, converted P- to S-wave (PS-wave) polarity reversals occur at zero offset and cancel their recovery. We developed methods to eliminate tube-wave noise by removing physical sources at the stationary-phase point and perturbing the integration path in the integrand based on P-wave NMO velocity of the direct-arrival. This results in using nonphysical energy outside a Fresnel radius that could not have propagated between receivers. To limit the response near the stationary-phase point, we also applied a weighting condition to suppress energy from large offsets. For PS-waves, a derivative-like operator was applied to the physical sources at zero offset in the form of a polarity reversal. These methods resulted in effectively recovering P-wave dipole and PS-wave quadrupole pseudosource VSPs. The retrieved wavefields kinematically correspond to a vertical incidence representation of reflectivity/transmissivity and can be used for conventional P- and S-wave velocity analyses. Four-component PS-wave VSPs retrieve S-wave splitting in transmitted converted waves that provide calibration for PS-wave and P-wave azimuthal anisotropy measurements from surface-seismic data.

Seismic vertical transversely isotropic parameter inversion from P- and S-wave cross-borehole measurements in an aquifer environment

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. D101-D116
Author(s):  
Julius K. von Ketelhodt ◽  
Musa S. D. Manzi ◽  
Raymond J. Durrheim ◽  
Thomas Fechner
Keyword(s):  
Transversely Isotropic ◽  
P Wave ◽  
Perturbation Equation ◽  
S Wave ◽  
P Waves ◽  
Data Set ◽  
Near Surface ◽  
S Waves ◽  
Wave Measurements ◽  
Wave Splitting

Joint P- and S-wave measurements for tomographic cross-borehole analysis can offer more reliable interpretational insight concerning lithologic and geotechnical parameter variations compared with P-wave measurements on their own. However, anisotropy can have a large influence on S-wave measurements, with the S-wave splitting into two modes. We have developed an inversion for parameters of transversely isotropic with a vertical symmetry axis (VTI) media. Our inversion is based on the traveltime perturbation equation, using cross-gradient constraints to ensure structural similarity for the resulting VTI parameters. We first determine the inversion on a synthetic data set consisting of P-waves and vertically and horizontally polarized S-waves. Subsequently, we evaluate inversion results for a data set comprising jointly measured P-waves and vertically and horizontally polarized S-waves that were acquired in a near-surface ([Formula: see text]) aquifer environment (the Safira research site, Germany). The inverted models indicate that the anisotropy parameters [Formula: see text] and [Formula: see text] are close to zero, with no P-wave anisotropy present. A high [Formula: see text] ratio of up to nine causes considerable SV-wave anisotropy despite the low magnitudes for [Formula: see text] and [Formula: see text]. The SH-wave anisotropy parameter [Formula: see text] is estimated to be between 0.05 and 0.15 in the clay and lignite seams. The S-wave splitting is confirmed by polarization analysis prior to the inversion. The results suggest that S-wave anisotropy may be more severe than P-wave anisotropy in near-surface environments and should be taken into account when interpreting cross-borehole S-wave data.

Separation and enhancement of split S‐waves on multicomponent shot records from the BIRPS WISPA experiment

Geophysics ◽  
1994 ◽  
Vol 59 (1) ◽  
pp. 131-139 ◽  
Author(s):  
M. Boulfoul ◽  
D. R. Watts
Keyword(s):  
Synthetic Data ◽  
P Wave ◽  
Moving Window ◽  
Wave Analysis ◽  
S Wave ◽  
Near Surface ◽  
S Waves ◽  
Wave Velocities ◽  
Wave Splitting ◽  
Explosive Source

Instantaneous rotations are combined with f-k filtering to extract coherent S‐wave events from multicomponent shot records recorded by British Institutions Reflection Profiling Syndicate (BIRPS) Weardale Integrated S‐wave and P‐wave analysis (WISPA) experiment. This experiment was an attempt to measure the Poisson’s ratio of the lower crest by measuring P‐wave and S‐wave velocities. The multihole explosive source technique did generate S‐waves although not of opposite polarization. Attempts to produce stacks of the S‐wave data are unsuccessful because S‐wave splitting in the near surface produced random polarizations from receiver group to receiver group. The delay between the split wavelets varies but is commonly between 20 to 40 ms for 10 Hz wavelets. Dix hyperbola are produced on shot records after instantaneous rotations are followed by f-k filtering. To extract the instantaneous polarization, the traces are shifted back by the length of a moving window over which the calculation is performed. The instantaneous polarization direction is computed from the shifted data using the maximum eigenvector of the covariance matrix over the computation window. Split S‐waves are separated by the instantaneous rotation of the unshifted traces to the directions of the maximum eigenvectors determined for each position of the moving window. F-K filtering is required because of the presence of mode converted S‐waves and S‐waves produced by the explosive source near the time of detonation. Examples from synthetic data show that the method of instantaneous rotations will completely separate split S‐waves if the length of the moving window over which the calculation is performed is the length of the combined split wavelets. Separation may be achieved on synthetic data for wavelet delays as small as two sample intervals.

scholarly journals Responses of dipole-source reflected shear waves in acoustically slow formations

2019 ◽  
Author(s):  
Hao Wang ◽  
Ning Li ◽  
Caizhi Wang ◽  
Hongliang Wu ◽  
Peng Liu ◽  
...  
Keyword(s):  
Finite Difference Time Domain ◽  
Dipole Source ◽  
Sh Wave ◽  
S Wave ◽  
High Fracture ◽  
S Waves ◽  
Angle Fracture ◽  
Dip Angle ◽  
Difference Time

Abstract In the process of dipole-source acoustic far-detection logging, the azimuth of the fracture outside the borehole can be determined with the assumption that the SH–SH wave is stronger than the SV–SV wave. However, in slow formations, the considerable borehole modulation highly complicates the dipole-source radiation of SH and SV waves. A 3D finite-difference time-domain method is used to investigate the responses of the dipole-source reflected shear wave (S–S) in slow formations and explain the relationships between the azimuth characteristics of the S–S wave and the source–receiver offset and the dip angle of the fracture outside the borehole. Results indicate that the SH–SH and SV–SV waves cannot be effectively distinguished by amplitude at some offset ranges under low- and high-fracture dip angle conditions, and the offset ranges are related to formation properties and fracture dip angle. In these cases, the fracture azimuth determined by the amplitude of the S–S wave not only has a $180^\circ $ uncertainty but may also have a $90^\circ $ difference from the actual value. Under these situations, the P–P, S–P and S–S waves can be combined to solve the problem of the $90^\circ $ difference in the azimuth determination of fractures outside the borehole, especially for a low-dip-angle fracture.

Pure S-waves in land P-wave source VSP data

2007 ◽  
Vol 4 (3) ◽  
pp. 173-182 ◽  
Author(s):  
Liu Yang ◽  
Zhang Qinghong ◽  
Bao Leiying ◽  
Wei Xiucheng
Keyword(s):  
P Wave ◽  
Wave Source ◽  
S Waves ◽  
Vsp Data

Estimates of Q in central Asia as a function of frequency and depth using the coda of locally recorded earthquakes

1982 ◽  
Vol 72 (1) ◽  
pp. 129-149
Author(s):  
S. W. Roecker ◽  
B. Tucker ◽  
J. King ◽  
D. Hatzfeld
Keyword(s):  
Frequency Dependence ◽  
Central Asia ◽  
Wide Frequency Range ◽  
S Wave ◽  
Uppermost Mantle ◽  
Regional Heterogeneity ◽  
S Waves ◽  
Tectonic Processes ◽  
Hindu Kush ◽  
Attenuation Mechanism

abstract Digital recordings of microearthquake codas from shallow and intermediate depth earthquakes in the Hindu Kush region of Afghanistan were used to determine the attenuation factors of the S-wave coda (Qc) and primary S waves (Qβ). An anomalously rapid decay of the coda shortly after the S-wave arrival, observed also in a study of coda in central Asia by Rautian and Khalturin (1978), seems to be due primarily to depth-dependent variations in Qc. In particular, we deduce the average Qc in the crust and uppermost mantle (<100-km depth) is approximately four times lower than the deeper mantle (<400-km depth) over a wide frequency range (0.4 to 24 Hz). Further, while Qc generally increases with frequency at any depth, the degree of frequency dependence of Qc depends on depth. Except at the highest frequency studied here (∼48 Hz), the magnitude of Qc at a particular frequency increases with depth while its frequency dependence decreases. For similar depths, determinations of Qβ and Qc agree, suggesting a common wave composition and attenuation mechanism for S waves and codas. Comparison of these determinations of Qc in Afghanistan with those in other parts of the world shows that the degree of frequency dependence of Qc correlates with the expected regional heterogeneity. Such a correlation supports the prejudice that Qc is primarily influenced by scattering and suggests that tectonic processes such as folding and faulting are instrumental in creating scattering environments.

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