S-wave Polarization Research Articles

A time-lapse multicomponent (9C 4D) seismic study at Vacuum Field, New Mexico, USA

In November and December 1995, the Reservoir Characterization Project (RCP) at the Colorado School of Mines acquired time-lapse multicomponent 3D surveys over the Central Vacuum Unit of Vacuum Field in Lea County, New Mexico. Two surveys were acquired — one before and one after the injection of 50 MMscf CO2 through a single wellbore into the San Andres Reservoir. The project determined that repeated multicomponent seismic surveys at the earth's surface can detect changes in bulk rock properties due to variations in reservoir pressures and fluid properties. Interpretation of the dynamic seismic response due to reservoir production processes over time provides an image of the relative permeability structure of the reservoir. Time-lapse multicomponent data were acquired using three-component geophones and vertically and horizontally actuated vibrator sources at the surface. A data processing flow was developed for time-lapse multicomponent 3D surveys. It uses surface-consistent processing algorithms and the source and receiver redundancy between initial and repeat surveys to derive surface-consistent corrections. Differences in S-wave polarization are measured between the initial and repeat surveys. S-wave data show sensitivity (through birefringence) to anisotropy caused by the orientation of fractures and low-aspect-ratio pore structure in a nonuniform stress field. The direction of fast S-wave polarization can be related to the direction of maximum horizontal stress and preferential permeability. Pore-pressure variations alter the effective stress. This varies the direction and intensity of open fractures and low-aspect-ratio pore structure within the current permeability structure of the reservoir, causing detectable changes in S-wave anisotropy. Anomalies in S-wave anisotropy, interpreted from time-lapse multicomponent 3D data, in conjunction with reservoir production data, are consistent with the fluid composition and pore-pressure changes associated with the CO2 injection program and reservoir processes in the survey area. Applications include monitoring hydrocarbon enhanced oil recovery; carbon capture, utilization, and storage; hydraulic stimulation; induced seismicity; and geothermal investigations.

Body-wave speeds and polarizations in the presence of an initial deviatoric stress

SUMMARY Body-wave speeds and polarization directions in a homogeneous and isotropic medium can be influenced by the presence of an initial deviatoric stress, which is conventionally ignored in seismic-wave propagation theories. To the first order, the P-wave speed is sensitive to the initial deviatoric stress, and the P-wave polarization has a perturbation perpendicular to the propagation direction. In addition, the S waves travel at two distinct speeds, and the S-wave polarizations are in two orthogonal directions, which are constrained by the initial deviatoric stress and involve a perturbation parallel to the propagation direction. Using a subduction zone setting with an initial deviatoric stress on the order of tens of MPa, the P-wave speed perturbation, S-wave splitting time and polarization perturbation are estimated to be on the order of 0.01 per cent, 0.01 s and 0.01 per cent, respectively. While these effects are too small to be reliably resolved using seismic observations, the theory presented in this paper could be useful for ultrasonic stress measurements in engineering applications.

Imaging faults and fractures with the difference of fast and slow shear-wave splitting reflectivity, Δγ(S): 3D/9C survey in Midland Basin, West Texas, and 3D/3C survey in Washakie Basin, Wyoming

One of the most important applications of shear-wave (S-wave) seismic exploration has been in reservoir fracture characterization. While many advancements have been made over the past 30 years to compute and correct for the long-wavelength kinematics of S-wave splitting (SWS) (fast S-wave polarization directions and slow S-wave time delays), practically no progress has been made in imaging the short-wavelength reflectivity of fractures directly with Δγ(S). This property is the contrast in the SWS anisotropy parameter, γ(S), and represents the reflection amplitude at vertical incidence for changes in fracture density and orientation across an interface. In this article, we examine the Lupin nine-component survey in Midland Basin, Texas, for the technical reliability of imaging fractures in depth with converted P to S waves (PS waves) guided by pure-mode horizontal shear waves and vertical shear waves. Final Δγ(S) amplitude maps for each mode show sensitivity to fractures, faults, and the maximum horizontal stress direction. These maps are computed from the difference between fast and slow S-wave stacks (after SWS analysis and correction) and P-wave amplitude variation with offset gradient stacks. The S-wave difference maps identify an east–west lineament, possibly a strike-slip fault or fracture corridor, that is not observed by P-wave depth slices. Pure-mode S waves and PS waves are orders of magnitude more sensitive to Δγ(S) than P waves. We also review the development of Δγ(S) and find that it has been relatively unexploited by the exploration industry. In addition, we demonstrate that Δγ(S) can be obtained directly from the objective function of the transverse energy to correct for SWS, and show a four-component Alford rotation example from a previous PS-wave survey in the Washakie Basin, Wyoming.

A fast anisotropic decoupled operator of elastic wave propagation in the space domain for P-/S-wave-mode decomposition and angle calculation, with its application to elastic reverse time migration in a TI medium

The conventional anisotropic P-/S-wave-mode decomposition and angle calculation usually are performed in the wavenumber domain and require multiple Fourier transforms and rely on strong model assumptions. Therefore, it is difficult to use in production due to the prohibitively high computational cost. To tackle this problem, we develop a fast anisotropic P-/S-wave-mode decomposition approach in the space domain and further apply this decomposition to the vertical transversely isotropic (VTI)/tilted transversely isotropic (TTI) elastic reverse time migration (ERTM) and the associated angle-domain common-image gathers (ADCIGs). To start with, we solve the Christoffel equation of the VTI media and obtain an anisotropic-Helmholtz (AH) operator that represents the P- and S-wave polarizations in the wavenumber domain. The decoupled operators for the P-/S-wave decomposition are then derived in terms of the AH operator. To improve the efficiency and model adaptability, we convert the decoupled operators from the wavenumber domain to the space domain as a function of the model parameters and phase angle. By further eliminating the phase-angle term, such space-domain decoupled operators lead to the approximate P- and S-wave components which are proven to achieve the same effect as the accurate P and S wavefields applied in the angle calculation and ERTM images. A fast space-domain AH decomposition approach is thus obtained and can be used for P-/S-wave-mode decomposition, ADCIGs, and ERTM. In addition, we extend our approach to the TTI media by using the coordinate transform. Three examples are used to demonstrate the effectiveness and feasibility of our method.

A novel and efficient engine for P-/S-wave-mode vector decomposition for vertical transverse isotropic elastic reverse time migration

Wave-mode decomposition plays a very important role in elastic reverse time migration (ERTM). Improved imaging quality can be achieved due to reduced wave-mode crosstalk artifacts. The current state-of-the-art methods for anisotropic wavefield separation are based on either splitting model strategy, low-rank approximation, or lower-upper (LU) factorization. Most of these involve expensive matrix computation and Fourier transforms with strong model assumptions. Based on the anisotropic-Helmholtz (ani-Helmholtz) decomposition operator and decoupled formulations, we develop a novel and efficient P-/S-wave-mode vector decomposition method in vertical transverse isotropic (VTI) media with application in ERTM. We first review the basics of classical Helmholtz decomposition and isotropic decoupled formulations. In addition, the ani-Helmholtz decomposition operator is built from the P- and S-wave polarizations of the Christoffel equation in VTI media. We then derive novel decoupled formulations of anisotropic P-/S-waves based on the obtained ani-Helmholtz operator. Moreover, we use the first-order Taylor expansion to approximate the normalization term from the derived decoupled formulations and obtain an efficient ani-Helmholtz decomposition approach, which produces vector P- and S-wavefields with correct units, phases, and amplitudes. Compared with the previous studies, our approach mitigates model assumptions, avoids intricate calculations, such as LU factorization or low-rank approximation, and only needs three fast Fourier transforms at each time step. In addition, the graphic processing unit technique is used to dramatically accelerate various functions of ERTM, such as wavefields extrapolation, decomposition, and imaging. Three synthetic examples demonstrate the effectiveness and feasibility of our proposed approach.

Separation of split S-waves in two nonorthogonal sets of vertical fractures

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

Seismic properties across an amphibolite- to greenschist-facies strain gradient (Neves area, eastern Alps, Italy): New considerations for shear zone imaging

Detecting the presence and geometry of crustal shear zones by geophysical methods relies on our understanding of the intrinsic parameters controlling the seismic properties of these deformed rocks, over the range of pressure-temperature conditions expected in the Earth's crust. To this end, we aimed to track changes in P-wave propagation velocity (VP), anisotropy (AVP) and S-wave splitting (AVS) across a natural shear zone using experimental and electron backscatter diffraction methods. Five samples were collected across a meter-scale shear zone developed under amphibolite- to greenschist-facies in the Neves metagranodiorite (Tauern Window, Eastern Alps). With increasing strain, seismic properties show a non-linear evolution resulting from interactions among structural, textural and mineralogical changes. Geometry and magnitude of seismic anisotropy are controlled by the interference of strongly anisotropic phyllosilicates with less anisotropic but more abundant quartz and plagioclase. The amphibolite-facies shear zone margin (> 500 °C) is free of major mineral transformations, and rather characterized by the development of S-C structure, inducing an orthorhombic symmetry to the VP distribution and up to 12 % AVP, with the fast axis parallel to lineation. AVS is maximized (6 %) in the two directions parallel to the C-planes. Further deformation under greenschist-facies (450–500 °C) induces significant crystallization of muscovite, chlorite, and albite. A dominant hexagonal symmetry develops, with a fast VP plane and a fast S-wave polarization plane along the C-planes. AVP and AVS exceed 10 %. The computed elastic tensor of the whole shear zone emphasizes the importance of the strain gradient on the seismic signature of the overall structure. In our model, the bulk seismic properties are dominated by the orthorhombic symmetry of the protomylonitic zone rather than by the ultramylonite core with hexagonal symmetry (C-plane), which may explain why seismic studies of shear zones commonly involve a fast velocity plane oblique to the layer boundaries.

Reflection and transmission coefficient approximations for P, S1 and S2 waves in triclinic media

SUMMARY The conventional assumptions, in most published approximations of the reflection and transmission (R/T) coefficients of plane waves at a plane interface between two anisotropic half-spaces, confine their applications to weakly anisotropic and/or weak contrast models. We consider the horizontal interface enclosed by two triclinic half-spaces to approximate the R/T coefficients normalized by the vertical energy flux. The homogeneous background medium can be anisotropic with arbitrary symmetry to better simulate the strongly anisotropic media. The second-order approximations are proposed to accommodate the strong contrast interface. We also consider an isotropic background medium under the weak anisotropy assumption. The obtained approximations can be applied to P, S1 and S2 waves, except for the transmission coefficients between the S1 and S2 waves. The S-wave transmission coefficients are insensitive to the model parameter contrasts and predominately rely on the S-wave polarization directions in the half-spaces above and below the interface. The proposed approximations are tested numerically.

Azimuthal shear-wave anisotropy measurement in a borehole: Physical modeling and dipole acoustic verification.

An anisotropic physical model is constructed to evaluate the anisotropy measurement. The model consists of a series of equally spaced thin limestone slab sheets cemented with concrete, resulting in a transversely isotropic medium. For the anisotropy measurement evaluation, the borehole model is tested by a standard multipole acoustic tool. The measurement finds an S-wave anisotropy magnitude about 20% and determines the fast S-wave polarization along the alignment direction of the slab sheets. The results of the work not only validate the borehole measurement technology, but also provide a testing facility for calibrating the measurement acoustic tool.

Experimentally deformed lawsonite at high pressure and high temperature: Implication for low velocity layers in subduction zones

Lawsonite is considered to be one of the most likely hydrous minerals to explain the persistence of seismic low-velocity layers (LVLs) atop subducted slabs to depths of 100–250 km due mainly to the fact that it can persist to these depths, in contrast to other hydrous minerals such as antigorite. However, as it is highly anisotropic and subjected to intense deformation during subduction, further constrains on the development of lawsonite crystal preferred orientation (CPO) at high pressure and temperature are required in order to evaluate its role in slowing seismic waves. We have deformed lawsonite aggregates at 5 GPa and 500–800 °C corresponding to 150 km depth and covering temperatures for both cold and hot subduction zones. In this study, we report a new lawsonite CPO pattern resulting from dislocation creep deformation that has not been previously observed. The [100] axes concentrate into the shear direction and the [010] axes are normal to the shear plane, respectively (we refer to this as “type-1” CPO). Such CPO is consistent with our transmission electron microscope (TEM) observations identifying (010)[100] as a dominant dislocation slip-system. The seismic properties resulting from this CPO show the fast P-wave direction to be parallel to the shear direction, and the slow P-wave direction and maximum S-wave anisotropy normal to the shear plane. We performed calculation of omphacite-lawsonite aggregates using our experimental data and varied both the lawsonite contents and the slab dipping angle. Our results show that a reasonable amount of lawsonite can explain Vs reduction in the LVLs, but cannot explain the Vp reduction. However, the presence of lawsonite would induce a rotation of the fast S-wave polarization toward the trench direction as the S-wave anisotropy increases or decreases according to the lawsonite proportion, its CPO strength and the slab dipping angle. We believe that our calculation can now be used for investigation of lawsonite effect in various subductions zones.

Effects of site\u2013city interaction and polarization of the incident S-wave on the transfer function and fundamental frequency of structures

The variation of 2D fundamental frequency of stand-alone structure on rock ({F}_{{02{text{D}}}}^{text{S}} ) and in a basin ({F}_{{02{text{D}}}}^{text{BS}} ) with the polarization of the incident S-wave is presented. This paper also presents the role of city density and polarization of the exciting S-wave in the site–city interaction effects on the response of structures in a city as well as free-field motion. The seismic responses of the various considered basin and site–city models are computed using SH-wave and P-SV-wave finite-difference programs. A considerable decrease in the value of {F}_{{02{text{D}}}}^{text{S}} of stand-alone structure on rock is obtained with the increase in shape ratio for the SV-wave but not for the SH-wave, as compared to the 1D fundamental frequency of structure ( {F}_{{01{text{D}}}}^{text{S}} ). However, a considerable decrease in the value of {F}_{{02{text{D}}}}^{text{BS}} of a stand-alone structure in basin under double resonance condition is obtained for the SH-wave and not for the SV-wave. The spectral amplification factor at the top of a structure at {F}_{{02{text{D}}}}^{text{BS}} of structure is larger for the SV-wave as compared to the SH-wave. A splitting of the bandwidth of the fundamental mode of vibration of structure and very large reduction in spectral amplification factor at {F}_{{02{text{D}}}}^{text{BS}} of structure is obtained due to the site–city interaction effects under double resonance condition for both the S-wave polarizations. Further, an increase in these inferred effects with an increase in city density and number of structures in a city with a constant city density is obtained. This finding raises the question concerning the validity of ground-motion prediction using soil–structure interaction for the design of structures in an urban environment. Further, the decrease in spectral amplification factor at {F}_{{02{text{D}}}}^{text{BS}} of structure due to the site–city interaction effects is larger in the case of SV-wave as compared to SH-wave. Furthermore, a considerable site–city interaction effects on free-field motion is obtained.

PROPOSITION OF A SPECTRAL AMPLIFICATION MODEL FOR NEAR FAULT DIRECTIVITY EFFECT WITH UTILIZING PROBABILISTIC EARTHQUAKE SCENARIOS

Near fault ground motions with directivity effect show larger spectral demands due to their specific waveform features. Directivity effect occur due to S-wave polarization when the fault rupture propagation and waveform travel direction coincide on each other. In this situation, a pulse arises in the beginning of ground motion displacement and velocity waveforms which is mostly seen in the fault normal direction. The pulse period (Tp) is directly proportional to the earthquake magnitude (moment magnitude, Mw) and its amplitude is inversely proportional to the rupture distance (Rrup) from the site. The other characteristic of the near fault ground motions due to S-wave polarization is known as “Fling Step” in which a residual displacement is seen in the fault parallel displacement waveform. This study summarizes the observations from the effect of near fault ground motions on design spectrum. The results of these observations are used to develop simplified equations for incorporation of near fault effect in design spectrum. Probabilistic seismic hazard scenarios are utilized in this study in order to investigate the effect of fault seismicity, fault length (characteristic magnitude of the fault), pulse period and source-to-site geometry on the level of spectral amplification due to directivity effect. The near fault effect is modelled with assembling two narrow-band directivity models (Shahi and Baker 2011; Chiou and Spudich 2013) on the probabilistic seismic hazard scenarios respectively. In the last part of this study the significance of seismological and geometrical parameters on the level of spectral amplification due to directivity will be shown and discussed. The results are used to propose relationships for the incorporation of near fault directivity effect for different geometrical distributions of the sites around the fault.

Modern Geodynamics and Focal Mechanisms of Earthquakes near the Bushehr Nuclear Power Plant

A method for determining the focal mechanisms of earthquakes using the S-wave polarization direction for weak close seismic events is developed based on the detailed seismological studies carried out by the seismological expedition of the Institute of Physics of the Earth of the Russian Academy of Sciences in 1999–2001 near the Bushehr nuclear power plant (NPP) in Southern Iran. The results of the reconstruction of such determinations are compared with the focal mechanisms of strong earthquakes determined in ISC catalogs using the standard method and with modern concepts of tectonic deformation of the earth’s crust in a wide vicinity of the region under consideration. It has been established that this reconstruction is in good agreement with both the typification of movements in the foci of strong earthquakes and modern concepts about the nature of the deformation of the earth’s crust within the observation network. This allows us to recommend this method for reconstructing focal mechanisms in other regions.

Stress studies in the Central Alborz by inversion of earthquake focal mechanism data

The Alborz is one of the most important seismotectonic provinces in Iran. Furthermore, emplacement of Tehran as a mega city in southern part of the Alborz intensifies the seismic vulnerability in this area. In this study, the focal mechanism data from teleseismic and local seismic networks are used for stress tensor inversion. The earthquake focal mechanisms in the Central Alborz are divided into several groups with respect to their location. Two different stress tensor inversions, linear and nonlinear, are used for obtaining the principal stress orientations. The results show spatial variations in tectonic stress field, consistent with fault orientations and faulting mechanisms. The maximum compressional stress directions obtained in this study are confirmed by fast S-wave polarization axes reported by a previous shear wave splitting study. The maximum horizontal stress directions are also compared with GPS strain rates. The results indicate a partitioning of deformation in the area due to regional stresses along preexisting faults.

Seismic anisotropies of the Songshugou peridotites (Qinling orogen, central China) and their seismic implications

Though extensively studied, the roles of olivine crystal preferred orientations (CPOs or fabrics) in affecting the seismic anisotropies in the Earth's upper mantle are rather complicated and still not fully known. In this study, we attempted to address this issue by analyzing the seismic anisotropies [e.g., P-wave anisotropy (AVp), S-wave polarization anisotropy (AVs), radial anisotropy (ξ), and Rayleigh wave anisotropy (G)] of the Songshugou peridotites (dunite dominated) in the Qinling orogen in central China, based on our previously reported olivine CPOs. The seismic anisotropy patterns of olivine aggregates in our studied samples are well consistent with the prediction for their olivine CPO types; and the magnitude of seismic anisotropies shows a striking positive correlation with equilibrium pressure and temperature (P–T) conditions. Significant reductions of seismic anisotropies (AVp, max. AVs, and G) are observed in porphyroclastic dunite compared to coarse- and fine-grained dunites, as the results of olivine CPO transition (from A-/D-type in coarse-grained dunite, through AG-type-like in porphyroclastic dunite, to B-type-like in fine-grained dunite) and strength variation (weakening: A-/D-type → AG-type-like; strengthening: AG-type-like → B-type-like) during dynamic recrystallization. The transition of olivine CPOs from A-/D-type to B-/AG-type-like in the forearc mantle may weaken the seismic anisotropies and deviate the fast velocity direction and the fast S-wave polarization direction from trench-perpendicular to trench-oblique direction with the cooling and aging of forearc mantle. Depending on the size and distribution of the peridotite body such as the Songshugou peridotites, B- and AG-type-like olivine CPOs can be an additional (despite minor) local contributor to the orogen-parallel fast velocity direction and fast shear-wave polarization direction in the orogenic crust such as in the Songshugou area in Qinling orogen.

B-type olivine fabric induced by low temperature dissolution creep during serpentinization and deformation in mantle wedge

The B-type olivine fabric (i.e., the [010] axes subnormal to foliation and the [001] axes subparallel to the lineation) has been regarded as an important olivine fabric for interpreting global trench-parallel S-wave polarization in fore-arc regions. However, strong serpentinization and cold temperature environment in the mantle wedge should inhibit development of the B-type olivine fabric that requires high temperature to activate solid-state plastic deformation. Here we report fabrics of olivine and antigorite generated at low temperatures (300–370°C) during serpentinization in a fossil mantle wedge of the Val Malenco area, Central Alps. Olivine in the serpentine matrix develops a pronounced B-type fabric, while antigorite in the same matrix displays a strong crystallographic preferred orientation (CPO) with the (001) planes and the [010] axes subparallel to foliation and lineation, respectively. The following evidence leads to the conclusion that the B-type olivine fabric results from dissolution creep assisted by grain boundary sliding (GBS) and grain rotation, rather than solid-state plastic deformation: (1) serpentinization took place at low temperatures and a fluid-enriched environment, ideal for dissolution-precipitation creep; (2) the voids and zigzag boundaries along the interface between antigorite and olivine suggest a fluid dissolution reaction; (3) the primary coarse olivine develops a nearly random fabric, indicating the B-type fabrics in the fine-grained olivine may not be inherited fabrics. These results document for the first time the B-type olivine CPO formed by dissolution creep at low temperatures during serpentinization and provide a mechanism to reconcile petrofabric observations with geophysical observations of trench parallel fast S-wave seismic anisotropy in fore-arc mantle wedge regions.

Wavefield simulation of 3D borehole dipole radiation

Reflections in acoustic borehole-logging data can be used to image near-borehole geologic structures, using either monopole or dipole measurements, the latter of which resolve azimuthal ambiguities. Dipole methods in particular can characterize small and subtle fractures in reservoir environments. Accurate tools for wavefield simulation are required to account for wave modes in and out of the borehole, and for the receiver responses to these modes. We have evaluated a 3D elastic staggered-grid finite-difference method for isotropic and anisotropic media in the context of the borehole acoustic imaging problem. Based on the convolutional perfectly matched layer and the multiaxial perfectly matched layer schemes, a hybrid perfectly matched layer method was developed and implemented to reduce artificial boundary reflections. The superiority of this hybrid perfectly matched layer beyond the convolutional perfectly matched layer and the multiaxial perfectly matched layer was proven based on numerical benchmarks in isotropic and anisotropic media. Numerical simulation of radiation, reflection, and multipole reception of elastic waves, excited by a dipole source, was carried out. To optimize azimuthal detection, the relationships between S-wave polarization as well as source-receiver offset and source-reflector angle was analyzed. Results indicated that the S-S reflection is most sensitive to the angle between the incident ray and the normal to the reflector. Its maximum amplitude occurs as the incident angle reaches its critical value, a fact that can be used to calculate the total propagation distance of the S-S wave. The critical angle as well as the SH-wave velocities of geologic structures outside the borehole can thus be determined.

Joint inversion for effective anisotropic velocity model and event locations using S-wave splitting measurements from downhole microseismic data

An accurate velocity model is essential in microseismic imaging. Layered sediments and subvertical cracks from tectonic stress and hydraulic fracturing make velocity models more complicated than isotropy or simple anisotropy, such as vertical transverse isotropy. Downhole microseismic acquisition usually cannot achieve sufficient ray coverage that is required to develop a low-symmetry anisotropic model from traveltimes alone. To solve this problem, we have developed a new type of data, S-wave splitting parameters (the delay time of the slow S-wave and fast S-wave polarization direction), to determine anisotropic models. A genetic algorithm inversion is adopted to solve for the locations of events and the stiffness tensor of an anisotropic medium simultaneously. We applied this method to synthetic waveforms from numerical modeling and successfully recovered the input event locations and the velocity model. The effectiveness of this method is further demonstrated by using real microseismic data acquired in the Bakken shale reservoir. Compared with the inversion with an isotropic velocity model, event locations from an anisotropic model become well-aligned with natural fractures in the Bakken Formation. Our experiments have evidenced that adding full S-wave splitting parameters makes a significant improvement in constraining a low-symmetry anisotropic model from downhole microseismic data.

Characterization of naturally fractured Arbuckle Group in the Wellington Field, Kansas, using S-wave amplitude variation with offset

S-wave amplitude variation with offset (AVO) analysis is sensitive to the presence of fractures and can provide a high-resolution seismic-based fracture characterization as compared with traditionally used traveltime-based methods. To determine viable attributes for estimation of properties such as spatial density and fluid fill of fractures, S-wave AVO modeling and analysis is carried out in the Wellington Field, Kansas, where 9C-2D seismic data have been acquired. Analysis is performed on the Ordovician fractured-carbonate interval called the Arbuckle Group, which is being considered for [Formula: see text] sequestration. AVO modeling of the Arbuckle interval indicates that differences in AVO intercepts of different S-wave polarizations can estimate S-wave anisotropy parameter [Formula: see text], which gives an estimate of fracture density. In addition, modeling suggests that AVO gradients of [Formula: see text] and [Formula: see text] waves can be used to derive a seismic attribute to discriminate fluid fill in fractures, provided good-quality S-wave gathers are available. The intercept anisotropy (IA) attribute obtained from AVO intercepts of S-waves provides fracture density estimates within the Arbuckle Group. These estimates are consistent with the field-wide, low-frequency observations from seismic velocities and spatially limited, high-frequency estimates obtained from drill cores and sonic and borehole-image logs. The IA attribute highlights possible high-permeability zones in the Upper and Lower Arbuckle suitable for [Formula: see text] injection. The Middle Arbuckle indicates low fracture density, potentially acting as a baffle to vertical flow and providing a seal for the Lower Arbuckle. The gradient anisotropy attribute obtained from the AVO gradient of S-waves suggests that most fractures in the Arbuckle are brine saturated. This attribute has a potential application in monitoring the movement of a [Formula: see text] plume in the Arbuckle Group when time-lapse data become available. These results demonstrate that S-wave AVO attributes can supplement the P-wave derived subsurface properties and significantly reduce uncertainties in subsurface fracture characterization.

A Bayesian method for microseismic source inversion

Earthquake source inversion is highly dependent on location determination and velocity models. Uncertainties in both the model parameters and the observations need to be rigorously incorporated into an inversion approach. Here, we show a probabilistic Bayesian method that allows formal inclusion of the uncertainties in the moment tensor inversion. This method allows the combination of different sets of far-field observations, such as P-wave and S-wave polarities and amplitude ratios, into one inversion. Additional observations can be included by deriving a suitable likelihood function from the uncertainties. This inversion produces samples from the source posterior probability distribution, including a best-fitting solution for the source mechanism and associated probability. The inversion can be constrained to the double-couple space or allowed to explore the gamut of moment tensor solutions, allowing volumetric and other non-double-couple components. The posterior probability of the double-couple and full moment tensor source models can be evaluated from the Bayesian evidence, using samples from the likelihood distributions for the two source models, producing an estimate of whether or not a source is double-couple. Such an approach is ideally suited to microseismic studies where there are many sources of uncertainty and it is often difficult to produce reliability estimates of the source mechanism, although this can be true of many other cases. Using full-waveform synthetic seismograms, we also show the effects of noise, location, network distribution and velocity model uncertainty on the source probability density function. The noise has the largest effect on the results, especially as it can affect other parts of the event processing. This uncertainty can lead to erroneous non-double-couple source probability distributions, even when no other uncertainties exist. Although including amplitude ratios can improve the constraint on the source probability distribution, the measurements are often systematically affected by noise, leading to deviation from their noise-free true values and consequently adversely affecting the source probability distribution, especially for the full moment tensor model. As an example of the application of this method, four events from the Krafla volcano in Iceland are inverted, which show clear differentiation between non-double-couple and double-couple sources, reflected in the posterior probability distributions for the source models.