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

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.

2018 ◽  
Vol 12 (5) ◽  
pp. 1715-1734 ◽  
Author(s):  
Johanna Kerch ◽  
Anja Diez ◽  
Ilka Weikusat ◽  
Olaf Eisen

Abstract. One of the great challenges in glaciology is the ability to estimate the bulk ice anisotropy in ice sheets and glaciers, which is needed to improve our understanding of ice-sheet dynamics. We investigate the effect of crystal anisotropy on seismic velocities in glacier ice and revisit the framework which is based on fabric eigenvalues to derive approximate seismic velocities by exploiting the assumed symmetry. In contrast to previous studies, we calculate the seismic velocities using the exact c axis angles describing the orientations of the crystal ensemble in an ice-core sample. We apply this approach to fabric data sets from an alpine and a polar ice core. Our results provide a quantitative evaluation of the earlier approximative eigenvalue framework. For near-vertical incidence our results differ by up to 135 m s−1 for P-wave and 200 m s−1 for S-wave velocity compared to the earlier framework (estimated 1 % difference in average P-wave velocity at the bedrock for the short alpine ice core). We quantify the influence of shear-wave splitting at the bedrock as 45 m s−1 for the alpine ice core and 59 m s−1 for the polar ice core. At non-vertical incidence we obtain differences of up to 185 m s−1 for P-wave and 280 m s−1 for S-wave velocities. Additionally, our findings highlight the variation in seismic velocity at non-vertical incidence as a function of the horizontal azimuth of the seismic plane, which can be significant for non-symmetric orientation distributions and results in a strong azimuth-dependent shear-wave splitting of max. 281 m s−1 at some depths. For a given incidence angle and depth we estimated changes in phase velocity of almost 200 m s−1 for P wave and more than 200 m s−1 for S wave and shear-wave splitting under a rotating seismic plane. We assess for the first time the change in seismic anisotropy that can be expected on a short spatial (vertical) scale in a glacier due to strong variability in crystal-orientation fabric (±50 m s−1 per 10 cm). Our investigation of seismic anisotropy based on ice-core data contributes to advancing the interpretation of seismic data, with respect to extracting bulk information about crystal anisotropy, without having to drill an ice core and with special regard to future applications employing ultrasonic sounding.


Geophysics ◽  
1997 ◽  
Vol 62 (2) ◽  
pp. 614-629 ◽  
Author(s):  
Ilya Tsvankin

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.


Geophysics ◽  
2000 ◽  
Vol 65 (6) ◽  
pp. 1818-1830 ◽  
Author(s):  
Andrey Bakulin ◽  
Vladimir Grechka ◽  
Ilya Tsvankin

Geophysical and geological data acquired over naturally fractured reservoirs often reveal the presence of multiple vertical fracture sets. Here, we discuss modeling and inversion of the effective anisotropic parameters of two types of fractured media with monoclinic symmetry. The first model is formed by two different nonorthogonal sets of rotationally invariant vertical fractures in an isotropic host rock; the other contains a single set of fractures with microcorrugated faces. In monoclinic media with two fracture sets, the shear‐wave polarizations at vertical incidence and the orientation of the NMO ellipses of pure modes in a horizontal layer are controlled by the fracture azimuths as well as by their compliances. While the S-wave polarization directions depend only on the tangential compliances, the axes of the P-wave NMO ellipse are also influenced by the normal compliances and therefore have a different orientation. This yields an apparent discrepancy between the principal anisotropy directions obtained using P and S data that does not exist in orthorhombic media. By first using the weak‐anisotropy approximation for the effective anisotropic parameters and then inverting the exact equations, we devise a complete fracture characterization procedure based on the vertical velocities of the P- and two split S-waves (or converted PS-waves) and their NMO ellipses from a horizontal reflector. Our algorithm yields the azimuths and compliances of both fracture systems as well as the P- and S-wave velocities in the isotropic background medium. In the model with a single set of microcorrugated fractures, monoclinic symmetry stems from the coupling between the normal and tangential (to the fracture faces) slips, or jumps in displacement. We demonstrate that for this model the shear‐wave splitting coefficient at vertical incidence varies with the fluid content of the fractures. Although conventional fracture models that ignore microcorrugation predict no such dependence, our conclusions are supported by experimental observations showing that shear‐wave splitting for dry cracks may be substantially greater than that for fluid‐filled ones.


2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Wojciech Gajek ◽  
Dominik Gräff ◽  
Sebastian Hellmann ◽  
Alan W. Rempel ◽  
Fabian Walter

AbstractFractures contribute to bulk elastic anisotropy of many materials in the Earth. This includes glaciers and ice sheets, whose fracture state controls the routing of water to the base and thus large-scale ice flow. Here we use anisotropy-induced shear wave splitting to characterize ice structure and probe subsurface water drainage beneath a seismometer network on an Alpine glacier. Shear wave splitting observations reveal diurnal variations in S-wave anisotropy up to 3%. Our modelling shows that when elevated by surface melt, subglacial water pressures induce englacial hydrofractures whose volume amounts to 1-2 percent of the probed ice mass. While subglacial water pressures decrease, these fractures close and no fracture-induced anisotropy variations are observed in the absence of meltwater. Consequently, fracture networks, which are known to dominate englacial water drainage, are highly dynamic and change their volumes by 90-180 % over subdaily time scales.


Geophysics ◽  
2008 ◽  
Vol 73 (4) ◽  
pp. D35-D40 ◽  
Author(s):  
Masatoshi Miyazawa ◽  
Roel Snieder ◽  
Anupama Venkataraman

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.


2021 ◽  
Author(s):  
◽  
Sapthala Karalliyadda

<p>Seismic anisotropy in the transpressional plate-boundary zone in New Zealand is investigated with shear-wave splitting to gain insights into lithospheric deformation and mantle flow. Constraints on plate-boundary deformation in the lithosphere of the oblique-collision and subduction regimes in South Island have been estimated from the local and regional shear-wave splitting parameters that are made at both inland and offshore seismographs. Mantle and lithospheric anisotropy of the southernmost Hikurangi subduction zone in the southern North Island is examined from SKS, ScS and teleseismic S-phases. The splitting of these phases measured on a recent transect crossing the Wellington region is analyzed to understand the lateral anisotropic structure of the fore-arc Hikurangi subduction zone.  Local and regional splitting reveal both laterally and depth varying anisotropy in South Island. The scatter in splitting parameters at individual stations suggests the splitting of high-frequency S-phases is mainly controlled by heterogeneous anisotropic structure and S-wave propagation direction within those heterogeneities. When the average results are examined as a whole through 2-D delay time tomographic inversion and spatial averaging, consistent patterns in delay times and fast azimuths exist. Spatially averaged fast azimuths indicate a localized high strain zone in the southern central region of the South Island. Based on fast azimuths observed above 100 km depth, we suggest that the plate-boundary sub-parallel anisotropy that is produced by pervasive shear is mainly distributed within a zone extending ~130 km SE of the Alpine fault in the southern South Island and is widely distributed (at least 200 km wide) in the northern South Island. Average station delay times (δt) of ~0.1 - 0.4 s compared to 1.7 s SKS δt from previous studies in South Island further suggest a deep seated anisotropic zone or sensitivity of S-wave splitting to the layered and/or heterogeneous anisotropic structure of the plate-boundary zone in the inland South Island. The heterogeneous anisotropic structure further suggests that the lithosphere is not only characterized by the plate-boundary parallel shear related to Cenozoic deformation, but is also affected by anisotropic imprints from the other tectonic episodes and anisotropy that is governed by the contemporary stress.  A shear-wave splitting anisotropy investigation in the offshore South Island regions is an extended study of the inland experiment and aims to provide a broad-scale understanding of the plate-boundary deformation. Individual splitting of local and regional S-phases yield a range of δt that varies between very small δt (~0.02 s), which may represent a nearly isotropic medium, and large δt (~0.6 s), which corresponds to lithospheric anisotropy. The average station δt of ~0.25 s and variable delays of the individual splitting measurements imply that the observed splitting is most likely controlled by the geometry of the ray paths. Long ray paths that are detected at the stations further away from the plate-boundary appear to penetrate to deeper lithosphere and capture a significant portion of the upper-mantle anisotropy to produce fast azimuths parallel to the plate-boundary shear (NE-SW). Thus, the long and deep ray paths respond to the deeper structure, but may not be re-split by the upper-most crustal structures. However, the observed variable delays suggest that changes in ray propagation direction with respect to the orientation of symmetry axes of the anisotropic media may have an effect on the measured anisotropy. Offshore measurements that are close to the land are consistent with the inland measurements and appear to be controlled by the regional stress field. This implies that short and shallow ray paths are mostly sensitive to the crustal anisotropy. The uneven distribution of ray paths from the shallow and deep events, therefore, plays a dominant role in controlling the observed splitting depending on their depth sensitivity and/or extent of anisotropy. Consequently, when fast directions are spatially averaged along with the inland measurements consistent patterns appear to correlate with the possible depth contribution of anisotropy in the region. We are unable to provide accurate constraints on the offshore extent of plate-boundary parallel shear because of the shallow stress-controlled anisotropy that likely overlies the mantle-shear zone. However, the splitting parameters from long and deep ray paths suggest a deep-seated, plate-boundary sub-parallel shear in a broad zone at least in the northern and upper-central South Island.  Mantle anisotropy detected from teleseismic earthquakes recorded across the southern North Island displays NE-SW fast axis alignment, consistent with the strike of the Hikurangi trench and the predominant upper-plate faulting trends, with a range of δt (~0.5 - 3.0 s) and small-scale variation in NE-SW fast azimuths. When combined with the previous measurements in the western side of the array, δt from long period (>7 s) S-phases indicate an abrupt lateral variation across the fore-arc Hikurangi subduction zone. This lateral variation together with frequency dependence suggest that the shear wave splitting in the fore-arc of the Hikurangi subduction zone in the southern North Island is governed in part by the laterally varying crustal contribution of anisotropy or isotropic velocity variations within the shallow crust. Frequency dependent splitting also suggests that the anisotropic structure is governed by either multilayer or more complex anisotropy perhaps due to the combined effects of laterally varying multilayer structure. If the variations are due to lateral changes in crustal anisotropy, then mantle and crustal deformation are most likely coupled in the east of the Wairarapa fault where there is a possibility of strong crustal contribution.</p>


Geophysics ◽  
2000 ◽  
Vol 65 (1) ◽  
pp. 211-221 ◽  
Author(s):  
Jaime Ramos‐Martínez ◽  
Andrey A. Ortega ◽  
George A. McMechan

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.


Geophysics ◽  
1998 ◽  
Vol 63 (3) ◽  
pp. 935-947 ◽  
Author(s):  
Andreas Rüger

P-wave amplitudes may be sensitive even to relatively weak anisotropy of rock mass. Recent results on symmetry‐plane P-wave reflection coefficients in azimuthally anisotropic media are extended to observations at arbitrary azimuth, large incidence angles, and lower symmetry systems. The approximate P-wave reflection coefficient in transversely isotropic media with a horizontal axis of symmetry (HTI) (typical for a system of parallel vertical cracks embedded in an isotropic matrix) shows that the amplitude versus offset (AVO) gradient varies as a function of the squared cosine of the azimuthal angle. This change can be inverted for the symmetry‐plane directions and a combination of the shear‐wave splitting parameter γ and the anisotropy coefficient [Formula: see text]. The reflection coefficient study is also extended to media of orthorhombic symmetry that are believed to be more realistic models of fractured reservoirs. The study shows the orthorhombic and HTI reflection coefficients are very similar and the azimuthal variation in the orthorhombic P-wave reflection response is a function of the shear‐wave splitting parameter γ and two anisotropy parameters describing P-wave anisotropy for near‐vertical propagation in the symmetry planes. The simple relationships between the reflection amplitudes and anisotropic coefficients given here can be regarded as helpful rules of thumb in quickly evaluating the importance of anisotropy in a particular play, integrating results of NMO and shear‐wave‐splitting analyses, planning data acquisition, and guiding more advanced numerical amplitude‐inversion procedures.


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