3-D seismic modeling for cracked media: Shear‐wave splitting at zero‐offset

Geophysics ◽  
2000 ◽  
Vol 65 (1) ◽  
pp. 211-221 ◽  
Author(s):  
Jaime Ramos‐Martínez ◽  
Andrey A. Ortega ◽  
George A. McMechan
Keyword(s):  
Shear Wave ◽  
Effective Properties ◽  
Transverse Isotropy ◽  
Shear Waves ◽  
Crack Density ◽  
Shear Wave Splitting ◽  
Carbonate Reservoir ◽  
Vertical Crack ◽  
Wave Splitting ◽  
Zero Offset

Splitting of zero‐offset reflected shear‐waves is measured directly from three‐component finite‐difference synthetic seismograms for media with intersecting vertical crack systems. Splitting is simulated numerically (by finite differencing) as a function of crack density, aspect ratio, fluid content, bulk density, and the angle between the crack systems. The type of anisotropy symmetry in media containing two intersecting vertical crack systems depends on the angular relation between the cracks and their relative crack densities, and it may be horizontal transverse isotropy (HTI), tetragonal, orthorhombic, or monoclinic. The transition from one symmetry to another is visible in the splitting behavior. The polarities of the reflected quasi‐shear waves polarized perpendicular and parallel to the source particle motion distinguish between HTI and orthorhombic media. The dependence of the measured amount of splitting on crack density for HTI symmetry is consistent with that predicted theoretically by the shear‐wave splitting factor. In orthorhombic media (with two orthogonal crack systems), a linear increase is observed in splitting when the difference between crack densities of the two orthogonal crack systems increases. Splitting decreases nonlinearly with the intersection angle between the two crack systems from 0° to 90°. Surface and VSP seismograms are simulated for a model with several flat homogeneous layers, each containing vertical cracks with the same and with different orientations. When the crack orientation varies with depth, previously split shear waves are split again at each interface, leading to complicated records, even for simple models. Isotropic and anisotropic three‐component S-wave zero‐offset sections are synthesized for a zero‐offset survey line over a 2.5-D model of a carbonate reservoir with a complicated geometry and two intersecting, dipping crack sets. The polarization direction of the fast shear wave, propagating obliquely through the cracked reservoir, is predicted by theoretical approximations for effective properties of anisotropic media with two nonorthogonal intersecting crack sets.

Linear‐transform techniques for processing shear‐wave anisotropy in four‐component seismic data

Geophysics ◽  
1993 ◽  
Vol 58 (2) ◽  
pp. 240-256 ◽  
Author(s):  
Xiang‐Yang Li ◽  
Stuart Crampin
Keyword(s):  
Time Series ◽  
Shear Wave ◽  
Seismic Data ◽  
Shear Waves ◽  
Shear Wave Splitting ◽  
Data Set ◽  
Reflection Data ◽  
Wave Splitting ◽  
Linear Transform ◽  
Zero Offset

Most published techniques for analyzing shear‐wave splitting tend to be computing intensive, and make assumptions, such as the orthogonality of the two split shear waves, which are not necessarily correct. We present a fast linear‐transform technique for analyzing shear‐wave splitting in four‐component (two sources/ two receivers) seismic data, which is flexible and widely applicable. We transform the four‐component data by simple linear transforms so that the complicated shear‐wave motion is linearized in a wide variety of circumstances. This allows various attributes to be measured, including the polarizations of faster split shear waves and the time delays between faster and slower split shear waves, as well as allowing the time series of the faster and slower split shear waves to be separated deterministically. In addition, with minimal assumptions, the geophone orientations can be estimated for zero‐offset verticle seismic profiles (VSPs), and the polarizations of the slower split shear waves can be measured for offset VSPs. The time series of the split shear‐waves can be separated before stack for reflection surveys. The technique has been successfully applied to a number of field VSPs and reflection data sets. Applications to a zero‐offset VSP, an offset VSP, and a reflection data set will be presented to illustrate the technique.

Reflection moveout and parameter estimation for horizontal transverse isotropy

Geophysics ◽  
1997 ◽  
Vol 62 (2) ◽  
pp. 614-629 ◽  
Author(s):  
Ilya Tsvankin
Keyword(s):  
Shear Wave ◽  
Symmetry Axis ◽  
Transverse Isotropy ◽  
Shear Waves ◽  
Shear Wave Splitting ◽  
P Wave ◽  
Symmetry Direction ◽  
Wave Splitting ◽  
Hti Media ◽  
Splitting Parameter

Transverse isotropy with a horizontal axis of symmetry (HTI) is the simplest azimuthally anisotropic model used to describe fractured reservoirs that contain parallel vertical cracks. Here, I present an exact equation for normal‐moveout (NMO) velocities from horizontal reflectors valid for pure modes in HTI media with any strength of anisotropy. The azimuthally dependent P‐wave NMO velocity, which can be obtained from 3-D surveys, is controlled by the principal direction of the anisotropy (crack orientation), the P‐wave vertical velocity, and an effective anisotropic parameter equivalent to Thomsen's coefficient δ. An important parameter of fracture systems that can be constrained by seismic data is the crack density, which is usually estimated through the shear‐wave splitting coefficient γ. The formalism developed here makes it possible to obtain the shear‐wave splitting parameter using the NMO velocities of P and shear waves from horizontal reflectors. Furthermore, γ can be estimated just from the P‐wave NMO velocity in the special case of the vanishing parameter ε, corresponding to thin cracks and negligible equant porosity. Also, P‐wave moveout alone is sufficient to constrain γ if either dipping events are available or the velocity in the symmetry direction is known. Determination of the splitting parameter from P‐wave data requires, however, an estimate of the ratio of the P‐to‐S vertical velocities (either of the split shear waves can be used). Velocities and polarizations in the vertical symmetry plane of HTI media, that contains the symmetry axis, are described by the known equations for vertical transverse isotropy (VTI). Time‐related 2-D P‐wave processing (NMO, DMO, time migration) in this plane is governed by the same two parameters (the NMO velocity from a horizontal reflector and coefficient ε) as in media with a vertical symmetry axis. The analogy between vertical and horizontal transverse isotropy makes it possible to introduce Thomsen parameters of the “equivalent” VTI model, which not only control the azimuthally dependent NMO velocity, but also can be used to reconstruct phase velocity and carry out seismic processing in off‐symmetry planes.

Shear‐wave splitting in cross‐hole surveys: Modeling

Geophysics ◽  
1989 ◽  
Vol 54 (1) ◽  
pp. 57-65 ◽  
Author(s):  
Enru Liu ◽  
Stuart Crampin ◽  
David C. Booth
Keyword(s):  
Shear Wave ◽  
Seismic Anisotropy ◽  
Pore Space ◽  
Shear Waves ◽  
Shear Wave Splitting ◽  
Surface Layers ◽  
Near Surface ◽  
Crustal Rocks ◽  
Wave Splitting ◽  
Almost All

Shear‐wave splitting, diagnostic of some form of effective seismic anisotropy, is observed along almost all near‐vertical raypaths through the crust. The splitting is caused by propagation through distributions of stress‐aligned vertical parallel fluid‐filled cracks, microcracks, and preferentially oriented pore space that exist in most crustal rocks. Shear waves have severe interactions with the free surface and may be seriously disturbed by the surface and by near‐surface layers. In principle, cross‐hole surveys (CHSs) should be free of much of the near‐surface interference and could be used for investigating shear waves at higher frequencies and greater resolution along shorter raypaths than is possible with reflection surveys and VSPs. Synthetic seismograms are examined to estimate the effects of vertical cracks on the behavior of shear waves in CHS experiments. The azimuth of the CHS section relative to the strike of the cracks is crucial to the amount of information about seismic anisotropy that can be extracted from such surveys. Interpretation of data from only a few boreholes located at azimuths chosen from other considerations is likely to be difficult and inconclusive. Application to interpreting acoustic events generated by hydraulic pumping is likely to be more successful.

scholarly journals Shear-wave splitting in the crust: Regional compressive stress from polarizations of fast shear-waves

2012 ◽  
Vol 25 (1) ◽  
pp. 35-45 ◽  
Author(s):  
Yuan Gao ◽  
Yutao Shi ◽  
Jing Wu ◽  
Lingxue Tai
Keyword(s):  
Compressive Stress ◽  
Shear Wave ◽  
Shear Waves ◽  
Shear Wave Splitting ◽  
Wave Splitting

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.

scholarly journals Methods and Computational Techniques for Investigating and Monitoring Seismic Velocities in the Earth's Crust

2021 ◽  
Author(s):  
◽  
Adrian Shelley
Keyword(s):  
Shear Wave ◽  
Cross Correlation ◽  
Seismic Velocity ◽  
Crack Density ◽  
Shear Wave Splitting ◽  
Noise Interferometry ◽  
Stress Changes ◽  
Wave Splitting ◽  
Velocity Variations ◽  
Velocity Changes

<p>This thesis is concerned with scrutinising the source, distribution and detectability of seismic velocity phenomena that may be used as proxies to study conditions in the crust. Specifically, we develop modelling techniques in order to analyse the directional variation of seismic wave speed in the crust and test them at Mt. Asama in Japan and Canterbury, New Zealand. We also implement both active source and noise interferometry to identify velocity variations at Mt. Ruapehu, New Zealand.  Observations of temporal variation of anisotropic seismic velocity parameters at Asama volcano in Japan indicate that there is some process (or processes) affecting anisotropy, attributed to closure of microcracks in the rock as it is subjected to volcanic stress in the crust. To test this assertion, a 3D numerical model is created incorporating volcanic stress, ray tracing and estimation of the anisotropy to produce synthetic shear wave splitting results using a dyke stress model. Anisotropy is calculated in two ways; by considering a basic scenario where crack density is uniform and a case where the strength of anisotropy is related to dry crack closure from deviatoric stress. We find that the approach is sensitive to crack density, crack compliance, and the regional stress field. In the case of dry crack closure, modelled stress conditions produce a much smaller degree of anisotropy than indicated by measurements. We propose that the source of anisotropy changes at Asama is tied to more complex processes that may precipitate from stress changes or other volcanic processes, such as the movement of pore fluid.  We develop a generalised anisotropy inversion model based on the linearised, iterative least-squares inversion technique of Abt and Fischer [2008]. The model is streamlined for use with results from the MFAST automatic shear wave splitting software [Savage et al., 2010]. The method iteratively solves for the best fitting magnitude and orientation of anisotropy in each element of the model space using numerically calculated partial derivatives. The inversion is applied to the Canterbury plains in the region surrounding the Greendale fault, using shear-wave splitting data from the 2010 Darfield earthquake sequence. Crustal anisotropy is resolved down to a depth of 20 km at a spatial resolution of 5 km, with good resolution near the Greendale fault. We identify a lateral variation in anisotropy strength across the Greendale fault, possibly associated with post-seismic stress changes.  We perform active source and noise interferometry at Ruapehu in order to investigate potential seismic velocity changes and assess their use as a possible eruption forecasting method. Six co-located 100 kg ammonium nitrate fuel oil explosives were set off serially at Lake Moawhango, situated approximately 20 km south-east of Mount Ruapehu. Two methods of interferometry, using moving window cross correlation in the time and frequency domains, respectively, were applied to the recorded signal from each explosion pair in order to determine velocity changes from the signal coda waves. We identify possible diurnal velocity variations of ~ 0:7% associated with strain caused by the solid Earth tide. Synthetic testing of velocity variation recoverability was also performed using both methods. Interferometry of noise cross-correlations during the period was also performed using moving window cross correlation in the frequency domain. Analysis of velocity variations in the ZZ, RR and TT component pairs show little coherency. This, combined with results from synthetic testing that show that the frequency domain interferometry technique employed is unstable above velocity variations of 0.1%, indicate that the method may not be suitable for determining velocity variations at Ruapehu.</p>

Crustal anisotropy from shear-wave splitting of local earthquakes in the Garhwal Lesser Himalaya

2019 ◽  
Vol 219 (3) ◽  
pp. 2013-2033
Author(s):  
Jyotima Kanaujia ◽  
Supriyo Mitra ◽  
S C Gupta ◽  
M L Sharma
Keyword(s):  
Shear Wave ◽  
Crack Density ◽  
Shear Wave Splitting ◽  
Homogeneous Distribution ◽  
Lesser Himalaya ◽  
Crustal Anisotropy ◽  
Axis Orientation ◽  
Composite Effect ◽  
Wave Splitting ◽  
The Mean

SUMMARY Crustal anisotropy of the Garhwal Lesser Himalaya has been studied using local earthquake data from the Tehri seismic network. Earthquakes with magnitude (mL) up to 3, which occurred between January 2008 to December 2010, have been used for the shear wave splitting (SWS) analysis. SWS measurements have been done for steeply incident ray paths (ic ≤ 45°) to estimate the anisotropy fast axis orientation (ϕ) and the delay time (∂t). A total of 241 waveforms have been analysed, which yielded 209 splitting measurements, and 32 null results. The analysis reveals spatial and depth variation of ϕ and ∂t, suggesting complex anisotropic structure beneath the Garhwal Lesser Himalaya. The mean ∂t is estimated to be 0.07 ± 0.065 s with a mean depth normalized ∂t of 0.005 s km–1. We present the ϕ and Vs per cent anisotropy results by segregating these as a function of depth, for earthquakes originating above and below the Main Himalayan Thrust (MHT); and spatially, for stations located in the Outer Lesser Himalaya (OLH) and the Inner Lesser Himalaya (ILH). Earthquakes above the MHT sample only the Himalayan wedge, while those below the MHT sample both the underthrust Indian crust and the Himalayan wedge. Within the Himalayan wedge, for both OLH and ILH, the mean ϕ is oriented NE–SW, in the direction of maximum horizontal compressive stress axis (SHmax). This anisotropy is possibly due to stress-aligned microcracks controlled by the local stress pattern within the Himalayan wedge. The mean of normalized ∂t for all events originating within the Himalaya is 0.006 s km–1, which yields a Vs per cent anisotropy of ∼2.28 per cent. Assuming a homogeneous distribution of stress-aligned microcracks we compute a crack density of ∼0.0228 for the Garhwal Lesser Himalaya. At stations close to the regional fault systems, the mean ϕ is subparallel to the strike of the faults, and the anisotropy, locally, appears to be structure-related. For earthquakes originating below the MHT, in OLH, the mean ϕ orientation matches those from the Himalayan wedge and the normalized ∂t decreases with depth. This suggests depth localization of the anisotropy, primarily present within the Himalayan wedge. In the ILH, we observe large variations in the mean ϕ orientation and larger values of ∂t close to the regional fault/thrust systems. This is possibly a composite effect of the structure-related shallow crustal anisotropy and the frozen anisotropy of the underthrusting Indian crust. However, these cannot be segregated in this study.

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