Estimation of fracture parameters from reflection seismic data—Part III: Fractured models with monoclinic symmetry

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.

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 ◽  
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.


Geophysics ◽  
2004 ◽  
Vol 69 (3) ◽  
pp. 699-707 ◽  
Author(s):  
Andrés Pech ◽  
Ilya Tsvankin

Interpretation and inversion of azimuthally varying nonhyperbolic reflection moveout requires accounting for both velocity anisotropy and subsurface structure. Here, our previously derived exact expression for the quartic moveout coefficient A4 is applied to P‐wave reflections from a dipping interface overlaid by a medium of orthorhombic symmetry. The weak‐anisotropy approximaton for the coefficient A4 in a homogeneous orthorhombic layer is controlled by the anellipticity parameters η(1), η(2), and η(3), which are responsible for time processing of P‐wave data. If the dip plane of the reflector coincides with the vertical symmetry plane [x1, x3], A4 on the dip line is proportional to the in‐plane anellipticity parameter η(2) and always changes sign for a dip of 30○. The quartic coefficient on the strike line is a function of all three η–parameters, but for mild dips it is mostly governed by η(1)—the parameter defined in the incidence plane [x2, x3]. Whereas the magnitude of the dip line A4 typically becomes small for dips exceeding 45○, the nonhyperbolic moveout on the strike line may remain significant even for subvertical reflectors. The character of the azimuthal variation of A4 depends on reflector dip and is quite sensitive to the signs and relative magnitudes of η(1), η(2), and η(3). The analytic results and numerical modeling show that the azimuthal pattern of the quartic coefficient can contain multiple lobes, with one or two azimuths of vanishing A4 between the dip and strike directions. The strong influence of the anellipticity parameters on the azimuthally varying coefficient A4 suggests that nonhyperbolic moveout recorded in wide‐azimuth surveys can help to constrain the anisotropic velocity field. Since for typical orthorhombic models that describe naturally fractured reservoirs the parameters η(1,2,3) are closely related to the fracture density and infill, the results of azimuthal nonhyperbolic moveout analysis can also be used in reservoir characterization.


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>


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