Horizontal Axis Of Symmetry Research Articles

Significant spatial variation of upper crustal anisotropy in Southern Sichuan Basin, China: constraints from local shear wave splitting analysis

SUMMARY The recent upsurge in seismic activity within the southern Sichuan Basin has garnered considerable public attention and simultaneously offers a valuable opportunity for investigating upper crustal anisotropy. Such investigations can provide critical insights into the stress field and crustal deformation in the region. We obtained a total of 1845 high-quality local shear wave splitting measurements at 15 stations and 2027 null measurements at 19 stations. These results indicate the presence of a single layer of anisotropy with a horizontal axis of symmetry at a depth of 3 to 7 km. The fast polarization directions display discernible spatial variations that are primarily influenced by the geographical location of earthquakes rather than changes over time. In the vicinity of the Baimazhen Syncline, the fast polarization directions coincide with the strike of the stratum, forming a circular pattern around the core of the syncline, suggesting that the observed anisotropy is structure-controlled. In contrast, stations situated in the southern Weiyuan Anticline and western Baimazhen Syncline display fast directions trending N171.7 °E and N45.9 °E, respectively. These directions are consistent with the P axes of the focal mechanism of earthquakes, signifying that the anisotropy in these areas is governed by the regional stress field. The findings of this study not only deepen our understanding of the intricate geological structures in the southern Sichuan Basin, but also indicate the need for greater caution when interpreting potential temporal changes in anisotropy in future research.

Lateral and vertical variations of seismic anisotropy in the lithosphere–asthenosphere system underneath Central Europe from long-term splitting measurements

SUMMARY Backazimuthal variations in the shear wave splitting of core-refracted shear waves (SKS, SKKS and PKS phases, jointly referred to as XKS) at the Black Forest Observatory (BFO, Southwest Germany) indicate small-scale lateral and partly vertical variations of the seismic anisotropy. However, existing anisotropy studies and models for the nearby Upper Rhine Graben (URG) area in the northern Alpine foreland are mostly based on short-term recordings and by this suffer from a limited backazimuthal coverage and averaging over a wide or the whole backazimuth range. To identify and delimit laterally confined anisotropy regimes in this region, we carry out XKS splitting measurements at six neighbouring (semi-)permanent broad-band seismological recording stations (interstation distance 10–80 km). We manually analyse long-term (partly > 20 yr) recordings to achieve a sufficient backazimuthal coverage to resolve complex anisotropy. The splitting parameters (fast polarization direction $\phi $, delay time $\delta t$) are determined in a single- and multi-event analysis. We test structural anisotropy models with one layer with horizontal or tilted symmetry axis and with two layers with horizontal symmetry axes (transverse isotropy). To account for lateral variations around a single recording site, modelling is compared for the whole and for limited backazimuth ranges. Based on this, we provide a 3-D block model with spatial variation of anisotropic properties. Based on delay times > 0.3 s and missing discrepancies between SKS and SKKS phases, which do not support lower mantle anisotropy, the found anisotropy is placed in the lithosphere and asthenosphere. The spatial distribution as well as the lateral and backazimuthal variations of the splitting parameters confirm lateral and partly vertical variations in anisotropy. On the east side of the URG, we suggest two anisotropic layers in the Moldanubian Zone (south) and one anisotropic layer in the Saxothuringian Zone (north). In the Moldanubian Zone, a change of the fast polarization directions is observed between the east and the west side of the URG, indicating different textures. At the boundary between the two terranes, an inclined anisotropy is modelled which may be related with deformation during Variscan subduction. Regarding the observation of numerous null measurements and inconsistent splitting parameters, especially (southwest of BFO) in the southern URG, different hypothesis are tested: scattering of the seismic wavefield due to small-scale lateral heterogeneities, a vertical a-axis due to a vertical mantle flow related to the Kaiserstuhl Volcanic Complex, as well as a different preferred orientation of the olivine crystals (not A-type, but C-type) due to specific ambient conditions (high temperature, water content).

3D reverse-time migration for pure P-wave in orthorhombic media

Compared with the transverse isotropic (TI) medium, the orthorhombic anisotropic medium has both horizontal and vertical symmetry axes and it can be approximated as a set of vertical fissures developed in a group of horizontal strata. Although the full-elastic orthorhombic anisotropic wave equation can accurately simulate seismic wave propagation in the underground media, a huge computational cost is required in seismic modeling, migration, and inversion. The conventional coupled pseudo-acoustic wave equations based on acoustic approximation can be used to significantly reduce the cost of calculation. However, these equations usually suffer from unwanted shear wave artifacts during wave propagation, and the presence of these artifacts can significantly degrade the imaging quality. To solve these problems, we derived a new pure P-wave equation for orthorhombic media that eliminates shear wave artifacts while compromising computational efficiency and accuracy. In addition, the derived equation involves pseudo-differential operators and it must be solved by 3D FFT algorithms. In order to reduce the number of 3D FFT, we utilized the finite difference and pseudo-spectral methods to conduct 3D forward modeling. Furthermore, we simplified the equation by using elliptic approximation and implemented 3D reverse-time migration (RTM). Forward modeling tests on several homogeneous and heterogeneous models confirm that the accuracy of the new equation is better than that of conventional methods. 3D RTM imaging tests on three-layer and SEG/EAGE 3D salt models confirm that the ORT media have better imaging quality.

Second-Order Approximate Reflection Coefficient of Thin Interbeds with Vertical Fractures

The horizontal fractures in the strata will close in the compaction effect of overlying strata, while the vertical cracks are widely developed, which can be equivalent to HTI (transverse isotropy with a horizontal axis of symmetry) medium. When an S-wave propagates into HTI media, the shear wave will divide into two types of waves: a fast S-wave and slow S-wave. When the strata of HTI are thin and overlapping, called the thin interbeds model, the wave field exhibits complex primary reflections, converted waves, and multiples. We introduce a new second-order approximation of the total reflection coefficient, with the incidence angle lower than the critical angle in thin-interbed HTI media using a recursive algorithm. We verify the effectiveness of the second-order approximation by analyzing the energy of multiples. Comparing the second-order approximate solution that degenerates the HTI medium into isotropic and Kennett’s exact solution, we find that our solution has an accuracy of over 99.9% in any azimuth, with the incidence angle lower than the critical angle under P-wave incidence. However, our solution of the SP wave field is suitable for incidence azimuth angles between 0–75° and 120–180°, with the lowest accuracy occurring at an incidence angle of 25° and a relative error of 6.4%. The approximate solution in the SS wave field has the same applicable range as the SP wave, with the maximum error of 6.3% occurring at the incident angle of 1°. This new second-order approximate formula for the total reflection coefficient of thin interbeds composed of HTI helps us to understand the reflection characteristics of complex thin interbeds. It also lays a theoretical foundation for the development of AVO (Amplitude Versus Offset) analysis and inversion techniques for lithological and stratigraphic oil and gas reservoirs.

The Supersymmetry Genetic Code Table and Quadruplet Symmetries of DNA Molecules Are Unchangeable and Synchronized with Codon-Free Energy Mapping during Evolution.

The Supersymmetry Genetic code (SSyGC) table is based on five physicochemical symmetries: (1) double mirror symmetry on the principle of the horizontal and vertical mirror symmetry axis between all bases (purines [A, G) and pyrimidines (U, C)] and (2) of bases in the form of codons; (3) direct-complement like codon/anticodon symmetry in the sixteen alternating boxes of the genetic code columns; (4) A + T-rich and C + G-rich alternate codons in the same row between both columns of the genetic code; (5) the same position between divided and undivided codon boxes in relation to horizontal mirror symmetry axis. The SSyGC table has a unique physicochemical purine-pyrimidine symmetry net which is as the core symmetry common for all, with more than thirty different nuclear and mitochondrial genetic codes. This net is present in the SSyGC table of all RNA and DNA living species. None of these symmetries are present in the Standard Genetic Code (SGC) table which is constructed on the alphabetic horizontal and vertical U-C-A-G order of bases. Here, we show that the free energy value of each codon incorporated as fundamentally mapping the "energy code" in the SSyGC table is compatible with mirror symmetry. On the other hand, in the SGC table, the same free energy values of codons are dispersed and a mirror symmetry between them is not recognizable. At the same time, the mirror symmetry of the SSyGC table and the DNA quadruplets together with our classification of codons/trinucleotides are perfectly imbedded in the mirror symmetry energy mapping of codons/trinucleotides and point out in favor of maintaining the integrity of the genetic code and DNA genome. We also argue that physicochemical symmetries of the SSyGC table in the manner of the purine-pyrimidine symmetry net, the quadruplet symmetry of DNA molecule, and the free energy of codons have remined unchanged during all of evolution. The unchangeable and universal symmetry properties of the genetic code, DNA molecules, and the energy code are decreasing disorder between codons/trinucleotides and shed a new light on evolution. Diversity in all living species on Earth is broad, but the symmetries of the Supersymmetry Genetic Code as the code of life and the DNA quadruplets related to the "energy code" are unique, unchangeable, and have the power of natural laws.

Investigation on the cavitation bubble collapse and the movement characteristics near spherical particles based on Weiss theorem.

In this paper, the cavitation bubble dynamics near two spherical particles of the same size are investigated theoretically and experimentally. According to the Weiss theorem, the flow characteristics and the Kelvin impulse are obtained and supported by the sufficient experimental data. In terms of the initial bubble position, the bubble size and the distance between the two particles, the collapse morphology and the movement characteristics of the bubble are revealed in detail. The main findings include: (1) Based on a large number of experimental results, it is found that the Kelvin impulse theoretical model established in this paper can effectively predict the movement characteristics of the cavitation bubble near two particles of the same size. (2) When the initial bubble position is gradually away from the particles along the horizontal symmetry axis near two particles of the same size, the movement distance of the bubble centroid in the first period increases first and then decreases. (3) When the initial position of the bubble centroid is at the asymmetric position near the two particles, the movement direction of the bubble centroid is biased towards the particle closer to the bubble, but not towards the center of this particle.

Seismic upper mantle anisotropy beneath the Polish Sudetes from SKS splitting — Effect of present-day asthenospheric mantle flow deflected by cratonic keel?

To better characterize the structure and evolution of the upper mantle beneath the Polish Sudetes (NE margin of the Variscan internides), we performed shear-wave splitting analysis using teleseismic data from 23 temporary and 8 permanent broadband seismic stations from a period of about two years. SKS and SKKS phases were analysed using the minimum energy and the rotation-correlation method to determine average splitting parameters (φ, δt), characterizing orientation and strength of mantle anisotropy. The observations were interpreted in terms of one-layer anisotropy with a horizontal symmetry axis. The average fast polarization azimuth for this region is equal to ∼113°, and the delay time to ∼1.1 s. The results document a large-scale trend of the upper mantle fabric with NW-SE to WNW-ESE orientation, coinciding with fast velocity axes obtained from the shallower lithospheric studies of the Pn and Pg phases. At smaller scale, anisotropy parameters seem to vary between the SW and NE regions, suggesting moderate differences in orientation of the mantle fabric. Small-scale variations are likely to reflect anisotropy changes related to differences between lithospheric blocks, while more uniform large-scale trend may be related with fabric induced by asthenospheric flow. Estimated thickness of the anisotropic layer exceeds the thickness of the mantle lithosphere, supporting plausibility of substantial asthenospheric contribution. According to previous studies, the large-scale trend of fast polarizations observed in the Sudetes extends also over broader area located to the SW of the Teisseyre-Tornquist Zone, independently of the orientation of the tectonic sutures and of lithospheric inhomogeneity, suggesting its asthenospheric origin. The trend runs obliquely to the plate motion direction, but is sub-parallel to the NW-SE-striking margin of thick East European Craton lithosphere located to the NE of the study area, supporting the concept of the mantle flow re-oriented to ∼NW-SE direction by a thick cratonic keel.

Simulation of improved pure P‐wave equation in transversely isotropic media with a horizontal symmetry axis

AbstractCharacterizing the expressions of seismic waves in elastic anisotropic media depends on multiparameters. To reduce the complexity, decomposing the P‐mode wave from elastic seismic data is an effective way to describe the considerably accurate kinematics with fewer parameters. The acoustic approximation for transversely isotropic media is widely used to obtain P‐mode wave by setting the axial S‐wave phase velocity to zero. However, the separated pure P‐wave of this approach is coupled with undesired S‐wave in anisotropic media called S‐wave artefacts. To eliminate the S‐wave artefacts in acoustic waves for anisotropic media, we set the vertical S‐wave phase velocity as a function related to propagation directions. Then, we derive a pure P‐wave equation in transversely isotropic media with a horizontal symmetry axis by introducing the expression of vertical S‐wave phase velocity. The differential form of new expression for pure P‐wave is reduced to second‐order by inserting the expression of S‐wave phase velocity as an auxiliary operator. The results of numerical simulation examples by finite difference illustrate the stability and accuracy of the derived pure P‐wave equation.

P-, SV- and SH-wave eikonal approximations for HTI media based on perturbation theory

SUMMARY The eikonal equation for transversely isotropic media is a complex quartic partial differential equation that causes instability in traveltime inversion. The phenomenon of shear wave splitting in a transversely isotropic model with a horizontal symmetry axis (HTI) provides information for inversion. However, the involvement of shear waves makes the computation of forward modelling and inversion more time-consuming than when only using Pwaves. Most studies of traveltime approximation based on the eikonal equation are based on an acoustic assumption, which does not work for shear waves. Therefore, based on perturbation theory, we derive approximate solutions of the eikonal equation in a heterogeneous elastic HTI model for P, SV and SH waves to improve the traveltime computation efficiency. The approximate solutions of linear, quadratic and Shanks forms are based on the linearization of the traveltime function in terms of fracture weaknesses in an isotropic background, which are suitable for joint P-, SV- and SH-wave traveltime inversion and tomography for fracture parameters. When applied for a homogenous model, the proposed formulation results in a simple and accurate traveltime approximation. The first- and second-order perturbation coefficients are used to analyse the sensitivity of the traveltime to fracture weakness. To improve the accuracy of our approximation, we also expand the approximation of the P-wave traveltime with respect to the anellipticity parameter η in an elliptic background, which is evaluated by performing an error test. Based on the accuracy and stability of the perturbation, we select a set of linear equations with respect to the fracture weaknesses and a set of more accurate nonlinear equations to serve different needs.

Location of singular points in orthorhombic media

The dependence of the location of singular points of orthorhombic (ORT) media on the stiffness coefficients , and phase velocity at the singularity point is studied under the assumption that are larger than and . In this case, singular points appear only at the intersection of slowness surfaces of S1- and S2-waves. To simplify the presentation of the results, the values , are fixed and changed within the limits at which the stiffness matrix remains positive definite. We define the parameters, , , , which result in 0, 1, or 2 singular points in the symmetry planes of the ORT medium. The types of these singular points and their location on the unit circle are described. It is shown that, by selecting parameters , any singular point in the symmetry plane 13 can be combined with the limiting position of the singularity point in-between the symmetry planes, or this point can be included in the singular curve of the degenerate ORT medium. We derive equations for the semi-axes of an ellipse of conical refraction, which is the image of a singular point from plane 13 in the group domain. Conditions for degeneration of the ellipse of conical refraction into a segment or a point are defined. It is shown that there exists only one ORT medium with a fixed phase velocity of S1- and S2-waves in a given singular direction n. If we present the ORT media as projections of these vectors n onto the plane 12 and mark the value of the Poincaré index of the S1- or S2-wave at the point n, we get 2 regions with indices 1/2 and –1/2 separated by projection of the singular curve in the form of an ellipse or hyperbola. We compute equations for of a degenerate ORT medium in terms of the values, , and velocity of S1-, S2-waves on a singular curve. The singular curve is defined by the intersection of a unit sphere with an elliptic cone. It is proved that a degenerate ORT medium for or is, respectively, a transversally isotropic medium with a vertical or horizontal axis of symmetry. The results are illustrated in several examples.

D″ anisotropy inverted from shear wave splitting intensity

The D″ layer, located at the bottom of the mantle, is an active thermochemical boundary layer. The upwelling of mantle plumes, as well as possible plate subduction in the D″ layer, could lead to large-scale material transformation and mineral deformation, which could result in significant seismic anisotropy. However, owing to limited observations and immense computational cost, the anisotropic structures and geodynamic mechanisms in the D″ layer remain poorly understood. In this study, we proposed a new inversion method for the seismic anisotropy in the D″ layer quantitatively with shear wave splitting intensities. We first proved the linearity of the splitting intensities under the ray-theory assumption. The synthetic tests showed that, with horizontal axes of symmetry and ray incidences lower than 30º in the D″ layer (typical SKS phase), the anisotropy is well resolved. We applied the method to the measured dataset in Africa and Western Europe, and obtained strong D″ anisotropy in the margins of the large low shear-wave velocity provinces and subducting slabs. The new method makes it possible to obtain D″ anisotropy, which provides essential constraints on the geodynamical processes at the base of the mantle.

Exact and beam solutions for a narrow clamped rectangle

The paper presents formulas describing an exact solution to the boundary value problem of the theory of elasticity in a rectangle in which the horizontal sides are rigidly clamped, and normal and tangential stresses are given on the vertical ones. Only an odd-symmetric deformation of the rectangle with respect to the horizontal axis of symmetry and an even-symmetric deformation of the rectangle with respect to the vertical axis of symmetry are considered. The paper is based on the previously obtained solutions for a free half-strip and a free rectangle.

Generalized Effective Biot Theory and Seismic Wave Propagation in Anisotropic, Poroviscoelastic Media

AbstractThe interior of the Earth is quite complex due to the actual geometrical structure and the presence of complex rheological materials, including viscoelastic rocks, porous sediments and the presence of anisotropy. Seismic wavefield forward modeling in such media forms the basis of most wave equation‐based methods for investigating the structure of the Earth and processing and imaging of seismic data, e.g., seismic full waveform inversion. Numerical modeling using Biot's equations that describe the physics of poroelasticity provides a useful framework to investigate wave attenuation and dispersion. Poroelasticity describes the interaction between the deformation of an elastic porous solid and the fluid flow in the porous structure. We present a time‐domain finite‐difference method for seismic wavefield modeling, taking into account both attenuation and anisotropy of poroviscoelastic Earth structure. The mathematical formulations and modeling methods are based on (a) the linear Biot's poroelastic theory and double porosity models in anisotropic media and (b) a relaxation function that uses the generalized standard linear solid model with anisotropic τ parameter for magnitude of attenuation and nearly constant Q model. Using a modified relaxation function that is suggested to describe the anisotropy attenuation, we develop a generalized anisotropic Biot model in the anisotropic, viscoelastic media. In addition to the anisotropic poroelasticity based on Biot theory, we implement the generalized anisotropic Biot model with complex moduli for an effective Biot's model in which the attenuative anisotropic viscoelastic model with the generalized standard linear solid model is used to approximate the attenuation factor function. The method generalizes the linear poroviscoelastic model based on effective Biot theory for seismic wave modeling to the attenuative, anisotropic case. In the anisotropic, poroviscoelastic model, we represent the bulk modulus and shear modulus of the solid frame by the modified relaxation function. We present time‐domain finite‐difference modeling for seismic wavefields in anisotropic, viscoelastic porous media including transversely isotropic media with a vertical, tilted or horizontal symmetry axis (VTI, TTI, and HTI). We also consider the extension of the two new models to nearly constant Q viscoelastic anisotropy.

Exact solutions of the theory of elasticity for a clamped rectangle

We present the formulas that describe the exact solutions of the boundary value problems in the theory of elasticity for a half-strip and a rectangle in which the horizontal sides are firmly clamped, while normal and tangential stresses are specified on the vertical ones. We consider only an even-symmetric deformation of the half-strip and the rectangle relative to the horizontal axis of symmetry as well as even-symmetric and odd-symmetric deformations relative to the vertical axis of symmetry for the rectangle. This paper is based on the previously obtained solutions for a free half-strip and a free rectangle.

Joint PP, PS1, and PS2 AVA Inversion of HTI Media

Sedimentary strata formed by orientational vertical fractures are approximately equivalent to transversely isotropic media with a horizontal symmetry axis (HTI). Parameter inversion for the isotropic background and fracture parameters can provide valuable information for predicting fractured reservoirs. Following Bakulin’s modeling theory, we parameterized the HTI medium with the first- and second-order Lamé parameters of the isotropic background, host rock density, fracture density, and fracture azimuth. We calculated the fracture azimuth and separated split shear waves using the Alford rotation. Based on the exact reflection coefficients, we develop a joint P-to-P reflected wave (PP), PS1, and PS2 amplitude variation with angle (AVA) inversion method in the depth domain by using the second-order Levenberg–Marquardt (LM) algorithm to invert the remaining four parameters. Numerical model tests revealed that our method was more accurate compared to the traditional LM method and works for both weak/strong contrasts and anisotropy magnitudes. We used real data from the walkaway vertical seismic profiling (VSP) as an example to propose a set of strategies, thereby improving the practicality of our inversion method. To protect the fracture information contained in the wavefields, we adopted vector-feature-preserving data processing procedures to preprocess the field VSP data and separate PP, PS1, and PS2 reflections. We utilized P-wave first breaks to successfully discriminate and match these three wave modes from the same fractured formation in the depth domain; these were subsequently transformed to AVA gathers with ray tracing. We synthetically incorporated the time delays and layer velocities to build the initial models and to constrain the inversion process.

Inversion of Fracture Weaknesses Based on Linearly Approximated Traveltime

Seismic traveltime is crucial for the inversion of anisotropy parameters. In the inversion for fractured rock, a typical transversely isotropic medium with a horizontal symmetry axis (HTI), the joint utilization of traveltime of P- and split shear waves can provide more anisotropy information than the utilization of only P-wave traveltime. The computational effort of nonlinear parameter inversion also increases with the involvement of split shear waves. Therefore, based on the series expansion of vertical slowness projection, we derive the linear approximations for the first-break traveltimes of P-, S1-, and S2-waves with respect to fracture weaknesses, which are used to accelerate and stabilize the inversion process. Linear coefficients are used to analyze the sensitivity of the traveltime to fracture weakness and thus the accuracy of the results. To make our proposed approximation more practical, we expand our linear equations to the traveltime difference between the HTI model and its isotropic background model and derive the joint inversion equation for fracture weaknesses in a vertical seismic profile (VSP) survey by jointly using P-, S1-, and S2-waves. Field data application shows that our method is feasible for estimating fracture weaknesses by using walkaround VSP data. The error caused by linear approximation can be reduced by the joint utilization of multiple wave modes.

Effects of Blowing Location on Aeroacoustics of the Flow over a Circular Cylinder

This study investigated the effect of blowing on vortex shedding and aerodynamic noise due to flow over a circular cylinder. The flow simulation is performed by the URANS equations using k-ω-SST turbulence model. Calculations of the aerodynamic noise are performed through F-fowcs Williams-Hawkins analogy. The cylinder’s cross-section with a diameter of D=16mm, and the blowing jet is applied through slot windows that are located on the cylinder back surface. In this study, three positions for slot windows are considered. Verification of the numerical results is confirmed by comparing numerical results with the reported experimental ones (Uncontrolled case). The results showed that the optimal blowing position could reduce noise, lift coefficient, and drag coefficient; this result occurs for a slot window located near the cylinder horizontal axis of symmetry. On the other hand, if the blowing slot is located at the cylinder symmetric vertical axis, the aerodynamic noise increases by approximately 4 dB. In this case, the average lift and drag fluctuations are increased by more than 200%. The present study gives a new idea to the reduction of noise of the single body systems.

Approaches for investigation of oriented cracks of reservoirs using multicomponent VSP

The paper analyses the VSP data inversion in order to determine elastic constants of a transversely isotropic medium with a horizontal axis of symmetry of an infinite order (HTI), simulating an oriented fractured reservoir. Acquisition system of VSP is characterized by the absence of sub-horizontal directions of propagation of seismic waves. In this regard, it was necessary to determine the accuracy with which the elastic constants of the anisotropic layer are restored. The seismograms of the full wave field were selected as the initial data, calculated synthetically for the model of the medium containing azimuthally anisotropic layers. A complex of compressional and shear waves propagating from a source and recorded in the well. In such layers, the shear wave incident on the roof of the HTI layer splits into two waves that propagate at different velocities and have a mutually orthogonal displacement vectors. The processing task was to select waves S 1 and S 2 and build their arrival time curves. These arrival time curves were used in the inversion. The inversion was solved in the form of minimizing the functional of the mean square residual. Elastic constants, determined by inversion, almost exactly coincided with the model ones. The results obtained show the validity of the chosen approach for solving the inverse problem.

A systematic investigation of piercing-point-dependent seismic azimuthal anisotropy

SUMMARYThe vast majority of teleseismic XKS (including SKS, SKKS and PKS) shear wave splitting studies interpret the observed splitting parameters (fast orientation and splitting time) based on the assumption of a spatially invariant anisotropy structure in the vicinity of a recording station. For such anisotropy structures the observed splitting parameters are either independent of the arriving azimuth of the seismic ray paths if the medium traversed by the ray paths can be represented by a single layer of anisotropy with a horizontal axis of symmetry (i.e. simple anisotropy), or demonstrate a periodic variation with respect to the arriving azimuth for a more complicated structure of anisotropy (e.g. multiple layers with a horizontal axis of symmetry, or a single layer with a dipping axis). When a recording station is located near the boundary of two or more regions with different anisotropy characteristics, the observed splitting parameters are dependent on the location of the ray piercing points. Such a piercing-point dependence is clearly observed using a total of 360 pairs of XKS splitting parameters at three stations situated near the northeastern edge of the Sichuan Basin in central China. For a given station, the fast orientations differ as much as 90°, and the azimuthal variation of the fast orientations lacks a 90° or 180° periodicity which is expected for double-layered or dipping axis anisotropy. The observed splitting parameters from the three stations are spatially most consistent when they are projected at a depth of ∼250 km, and can be explained by shear strain associated with the absolute plate motion and mantle flow deflected by the cone-shaped lithospheric root of the Sichuan Basin.

PS energy imaging condition for microseismic data — Part 2: Sensitivity analysis in 3D anisotropic media

In microseismic monitoring, obtaining reliable information about event properties, such as the location, origin time, and moment-tensor components, is critical for evaluating the success of fluid-injection programs. Elastic wavefield-based migration approaches can robustly image microseismic sources by extrapolating data through an earth model and evaluating an imaging condition. The success of these imaging methods, though, primarily depends on the elastic model’s accuracy. The previously developed extended PS energy imaging condition can provide valuable information about the accuracy of the elastic model parameters including vertical P- and S-wave velocities as well as anisotropy coefficients. Using the SEG advanced modeling Barrett Unconventional model, we have assessed the influence of errors in the anisotropy parameters by conducting a sensitivity analysis in three types of 3D models: transversely isotropic with a vertical symmetry axis, transversely isotropic with a horizontal symmetry axis, and orthorhombic media. Our analysis on zero-lag and extended PS energy images computed with perturbed anisotropy models shows that event images exhibit different moveout patterns of misfocused energy with respect to the distorted Thomsen parameters [Formula: see text] and [Formula: see text]; however, for this model, the [Formula: see text] parameters have almost no influence on images regardless of the applied perturbations, which are reflected in the minimal traveltime differences in the data. The dependence of microseismic source images on these parameters provides essential insights into anisotropic model accuracy, and it suggests that misfocused energy on extended image gathers may be used as a criterion for updating earth models through anisotropic elastic image-domain inversion.