Amplitude Variation With Azimuth Research Articles

Feasibility of characterizing an aligned fracture set from azimuthal amplitude variations of PP and converted waves

The amplitude variation with azimuth (AVAz) is commonly used to predict subsurface fracture properties. Published analyses demonstrate the ambiguous characterization from PP-wave AVAz for a vertical set of rotationally variant fractures. Thus, it is worth analyzing the extra information hidden in the converted wave AVAz. We have considered the linear-slip theory to model a vertical or tilted set of rotationally variant fractures in either of two welded half-spaces with polar anisotropy. We investigate the AVAz of PP and converted waves to determine their ability to create unambiguous fracture characterizations. Reflectivity approximations are derived for PP and converted waves to extract their AVAz attributes exclusively depending on fracture properties. We consider pseudo-PSV and pseudo-PSH waves with linear reflectivity approximations transformed from the nonlinear ones for typical converted waves in fractured media. The pseudoconverted waves degenerate into the typical PSV and PSH waves when the incident medium is azimuthally isotropic. For a vertical fracture set, the AVAz of PSV and PSH waves conveys no more deterministic fracture information than that of PP waves. It is demonstrated that the unambiguous characterization is feasible for a fluid-filled vertical fracture set, whereas it might be not for a gas-filled one. For a tilted fracture set, the fracture normal azimuth can be obtained uniquely from the AVAz of PSV or PSH waves but ambiguously from the PP-wave counterpart. Using multiwave AVAz attributes only gives rather vague estimates of the fracture tilt angle. For vertical and titled fracture sets, numerical model tests demonstrate overall better inversions from jointly using PP and PSV waves than solely using either of them.

Analysis of AVAZ Seismic Forward Modeling of Fracture-Cavity Reservoirs of the Dengying Formation, Central Sichuan Basin

For the purpose of clarifying the seismic response characteristics of fractured-cavity reservoirs of Dengying Formation in the central Sichuan Basin, the paper first intends to establish three geological models of fracture cave reservoirs based on drilling, logging, and core data of the Dengying Formation in the central Sichuan Basin. Then, the formation reflection is calculated with reference to anisotropic Horizontal Transverse Isotropy (HTI) medium. Finally, further research on Amplitude Variation with Azimuth (AVAZ) seismic forward modeling has been conducted to clarify the seismic response characteristics of different reservoir types in the study area. The results suggest that: Seismic response characteristics of fractured-cavity reservoirs are controlled by incident angle and azimuth angle of seismic waves in different types of reservoirs. The incident angle of the seismic wave controls the difference in amplitude caused by different micro-fracture densities, and the azimuth angle controls the identification ability of the micro-fracture direction. The increase in incident angle brings about a gradual decline in amplitude. The magnitude reaches the highest when the azimuth is parallel to the normal direction of the fracture surface; however, it’ll come down to the lowest as the azimuth is perpendicular to the normal direction of the fracture surface. The fracture density fails to affect the amplitude as long as the azimuth angle is parallel to the direction of the fracture. However, the decreased amplitude reflects the increasing fracture density as the azimuth angle is identical to the normal direction of the fracture surface. The comparison between the theoretical model of three different types of fractured-cavity reservoirs and the actual uphole trace shows that the model has high accuracy. The prospect of seismic identification of fractured-cavern reservoirs, based on the results, can provide us with feasible and applicable evidence for future research on seismic identification of reservoirs and prediction of fracture distribution in the Dengying Formation of central Sichuan.

Estimating SHmax azimuth with P sources and vertical geophones: Use P-P reflection amplitudes or use SV-P reflection times?

We compared two methods for extracting the azimuth of maximum horizontal stress (SHmax) from 3D land-based seismic data generated by a P source and recorded with vertical geophones. In the first method, we used the direct-SV mode that is produced by all land-based P sources. P sources generate SV illumination that radiates in all azimuth directions from a source station and creates SV-P reflections that are recorded by vertical geophones. Unless stratigraphy has steep dip, SV-P raypaths recorded by vertical geophones are the reverse of P-SV raypaths recorded by horizontal geophones. Thus, SV-P data provide the same S-wave sensitivity to stress fields as popular P-SV data do. In the second method, we retrieved P-P reflections and then performed an amplitude-variation-with-azimuth (AVA) analysis of the amplitude-gradient behavior of P-P reflection wavelets. We did this analysis in narrow azimuth corridors to determine the gradient of reflection-wavelet amplitudes as a function of azimuth. This P-P AVA amplitude-gradient method has been of great interest in the reflection seismology community since it was introduced in the late 1990s. Each of these methods, AVA analysis of the gradient of P-P reflection amplitudes and azimuth-dependent arrival times of SV-P reflections, can be used to determine the azimuth of SHmax stress. We compare the results of the two methods with ground truth measurements of SHmax azimuth at a CO2 sequestration site in the Michigan Basin. SHmax azimuths were determined from P-P and SV-P data at three major boundaries at depths of approximately 3500 ft (1067 m), 5500 ft (1676 m), and 7500 ft (2286 m). Two estimates of SHmax azimuth (one using SV-P data and one using P-P data) were made at each stacking bin inside a 24 mi2 (62 km2) image space. The result was approximately 98,000 estimates of SHmax azimuth across each of these three boundaries for each of these two prediction strategies. Histogram displays of PP AVA gradient estimates had peaks at correct azimuths of SHmax at all three depths, but the spread of the distributions widened with depth and split into two peaks at the deepest boundary. In contrast, each histogram of SHmax azimuth predicted by azimuth-dependent SV-P traveltimes had a single, definitive peak that was positioned at the correct SHmax azimuth at all three boundary depths.

Anisotropic Poroelasticity and AVAZ Inversion for in Situ Stress Estimate in Fractured Shale-Gas Reservoirs

Knowledge of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> stress is of great significance for hydraulic fracture stimulating of unconventional reservoirs. Quantitative estimation of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> stress, especially in the far field, is a major challenge. This research mainly focuses on developing a novel Bayesian AVAZ inversion approach to estimate <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> stress of fractured shale-gas reservoirs with horizontal transversely isotropic (HTI) symmetry. Using the generalized Hooke’s law and Schoenberg’s linear slip model, we first deduce the anisotropic horizontal stress equation in an HTI medium formed by a single set of vertically aligned fractures embedded in an isotropic background rock. Based on the critical porosity model, we then obtain the saturated stiffness matrix with vertical effective stress-sensitive parameters and dry fracture weaknesses using the relationship between vertical effective stress and porosity. Combining the scattering function and the perturbed stiffness matrix, we deduce a linearized PP-wave reflection coefficient as a function of fluid bulk modulus, vertical effective stress-sensitive parameter, dry-rock P- and S-wave moduli, density, and fracture density. Finally, we propose a novel Bayesian amplitude variation with azimuth (AVAZ) inversion constrained by the Cauchy regularization and low-frequency regularization to estimate these model parameters, which are further used to calculate <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> stress. The analysis of synthetic data demonstrates that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> stress can be reasonably estimated even with moderate noise. A field data set test reveals that the inversion results agree well with the well log interpretation, and the proposed approach can generate meaningful results that are useful for seismic identification of potential fracturing barriers during fracturing stimulation of shale-gas reservoirs.

Prior Analysis in Determination of TI Anisotropy Type through Well-Based Modelling: A Case Study on the Deep Water Environment

The existence of anisotropy phenomena in the subsurface will affect the image quality of seismic data. Hence a prior knowledge of the type of anisotropy is quite essential, especially when dealing with deep water targets. The preliminary result of the anisotropy of the well-based modelling in deep water exploration and development is discussed in this study. Anisotropy types are modelled for Vertical Transverse Isotropy (VTI) and Horizontal Transverse Isotropy (HTI) based on Thomsen Parameters of ε and γ. The parameters are obtained from DSI Logging paired with reference δ value for modelling. Three initial conditions are then analysed. The first assumption is isotropic, in which the P-Wave Velocity, S-Wave Velocity, and Density Log modelled at their in-situ condition. The second and third assumptions are anisotropy models that are VTI and HTI. In terms of HTI, the result shows that the model of CDP Gather in the offset domain has a weak distortion in Amplitude Variation with Azimuth (AVAz). However, another finding shows a relatively strong hockey effect in far offset, which indicates that the target level is a VTI dominated type. It is supported by the geomechanical analysis result in which vertical stress acts as the maximum principal axis while horizontal stress is close to isotropic one. To sum up, this prior anisotropy knowledge obtained based on this study could guide the efficiency guidance in exploring the deep water environment.

The SEAM Barrett model: Strengths and weaknesses

The SEG Advanced Modeling (SEAM) Barrett model was designed to model typical land basins found in the North American midcontinent that host unconventional reservoirs, such as fractured shale reservoirs. This model was used recently in several studies to assess whether shale bodies could be resolved using azimuthal 3D P-P reflection seismic data. In one study, it was claimed that near-surface complexity prevents the identification of the shale bodies using azimuthal analysis and concluded that velocity variation with azimuth (VVAz) and amplitude variation with azimuth (AVAz) are not worth running in the Permian Basin. However, another study by different authors applied a different seismic processing sequence to successfully resolve the reservoir geobodies and showed promising AVAz and VVAz results. We have focused on the SEAM Barrett model itself. Despite some advantages, the limitations of the Barrett model prevent general conclusions to be drawn about the usefulness of VVAz and AVAz to characterize fractured unconventional reservoirs.

Frequency-dependent AVAZ for fractured reservoirs

Frequency-dependent anisotropy can be used for detection and evaluation of fractured reservoirs. In this study, three numerical models of fractured reservoirs are designed to study the frequency dependence of amplitude variation with azimuth (AVAZ). Here, two factors, which can make the AVAZ responses frequency dependent, are taken into consideration, the fluid flow and the tuning effect. Model I is used for the analysis of frequency-dependent AVAZ induced only by the fluid flow. Model II is used to study frequency-dependent AVAZ induced only by the tuning effect. For Model III, these two factors are in the presence at the same time. In this study, the fluid flow is simulated by Chapman’s multi-scale rock physics model, and the azimuthal seismic gathers are generated by propagating matrix method. Spectral decomposition is implemented based on the smoothed pseudo Wigner-Ville distribution, so that the frequency dependence for the AVAZ gathers can be discussed. It is demonstrated that both the fluid flow and the tuning effect can cause significant frequency-dependent AVAZ, and the frequency-dependent AVAZ is helpful for fluid identification and anisotropic thin bed detection. Besides, for both factors, the incident angle can influence the frequency-dependent AVAZ responses, accordingly azimuthal seismic gathers with large incident angles are necessary for field data application.

Using seismic and well data to determine processes of folding in the Pomeranian segment of the Caledonian Foredeep Basin, Poland

Recognition of fractures and faults related to different types of folding is important for understanding how fluids flow in folds or which parts of folds represent a better productive sector of reservoirs due to, for example, changes in the intensity and distribution of fractures.In this paper, we suggest that seismic data alone may be insufficient to determine the style of buckle folding. The differences in mechanical properties of the rock masses favour the development of two main types of internal deformation within the buckle folds, that originated as a result of layer-parallel shortening: flexural slip/flow folding and neutral-surface folding. However, it is difficult to tell from seismic data alone which type of deformation had occurred.This paper presents the advantages of analyzing structures in core combined with results of amplitude variation with azimuth (AVAZ) analysis applied on the 3D seismic survey, when compared to the use of seismic data alone. To illustrate this, we use examples of seismic-scale folds, interpreted as buckle folds formed within the Pomeranian segment of the Caledonian Foredeep Basin.The analysis of structures related to the amplification of one fold known as the Opalino Anticline leads us to conclude, that this approach allowed us to recognize that folding within the mostly homogenous, isotropic Ordovician and Silurian mudstone formations is associated with bed-parallel and bed-perpendicular veins, reverse faults, thrusts, stylolites and normal faults, which formed at different depths within the fold. We consider the structures to have developed as a result of buckling of the mudstone formations and demonstrate that the process facilitated neutral-surface folding, which caused outer-arc extension in the higher parts of the Opalino Anticline and the development of an inner-arc contraction zone in the lower parts of the anticline. We show that this approach helps to predict the distribution of structures related with folding, which in turn aids in estimating the reservoir quality.

A method to compensate for migration stretch to improve the resolution of amplitude variation with offset, S-impedance (ZS), and density (ρ)

Because of their improved leverage against ground roll and multiples, as well as the ability to estimate azimuthal anisotropy, wide-azimuth 3D seismic surveys routinely now are acquired over most resource plays. For a relatively shallow target, most of these surveys can be considered to be long offset as well, containing incident angles up to 45°. Unfortunately, effective use of the far-offset data often is compromised by noise and normal moveout (NMO) (or, more accurately, prestack migration) stretch. The conventional NMO correction is well-known to decrease the frequency content and distort the seismic wavelet at far offsets, sometimes giving rise to tuning effects. Most quantitative interpreters work with prestack migrated gathers rather than unmigrated NMO-corrected gathers. However, prestack migration of flat reflectors suffers from the same limitation called migration stretch. Migration stretch leads to lower S-impedance ([Formula: see text]) and density ([Formula: see text]) resolution estimated from inversion, misclassification of amplitude variation with offset (AVO) types, and infidelity in amplitude variation with azimuth (AVAZ) inversion results. We have developed a matching pursuit algorithm commonly used in spectral decomposition to correct the migration stretch by scaling the stretched wavelets using a wavelet compensation factor. The method is based on hyperbolic moveout approximation. The corrected gathers show increased resolution and higher fidelity amplitudes at the far offsets leading to improvement in AVO classification. Correction for migration stretch rather than conventional “stretch-mute” corrections provides three advantages: (1) preservation of far angles required for accurate [Formula: see text] inversion, (2) improvement in the vertical resolution of [Formula: see text] and [Formula: see text] volumes, and (3) preservation of far angles that provide greater leverage against multiples. We apply our workflow to data acquired in the Fort Worth Basin and retain incident angles up to 42° at the Barnett Shale target. Comparing [Formula: see text], [Formula: see text], and [Formula: see text] of the original gather and migration stretch-compensated data, we find an insignificant improvement in [Formula: see text], but a moderate to significant improvement in resolution of [Formula: see text] and [Formula: see text]. The method is valid for reservoirs that exhibit a dip of no more than 2°. Consistent improvement is observed in resolving thick beds, but the method might introduce amplitude anomalies at far offsets for tuning beds.

Azimuthal anisotropy analysis applied to naturally fractured unconventional reservoirs: A Barnett Shale example

Studying the seismic responses of velocity and amplitude on wide-/full-azimuth seismic data is now common for unconventional reservoir characterization. Velocity variation with azimuth (VVAz) and amplitude variation with azimuth (AVAz) are two of the most popular tools to map not only the relative intensity and orientation of natural fractures but also the strength and orientation of the maximum horizontal stress SH. We prestack time migrated a wide-azimuth Barnett Shale survey in North Texas into eight azimuths and reduced noise on the gathers using prestack structure-oriented filtering. We then computed the envelope, spectral peak frequency, and prestack P-wave impedance attributes for each azimuthally limited seismic volume. We compensated the VVAz effects by flattening each sector along the Barnett Shale key horizons, thereby registering the gathers for subsequent AVAz analysis. The results indicate the intensity, orientation, and confidence of azimuthal anisotropy effects on seismic velocity and amplitude, which can be referred to smaller scale vertical cracks or natural fractures. Our analysis reveals four zones of high anisotropy intensity that can be tied to either the regional structures or paleo stress field. Analysis of production data indicate from the anisotropy interpretation results that vertical, sealed fractures are the dominant cause of anisotropy and those specific fractures inhibit production. This observation and results indicate that horizon-based azimuthal anisotropy analysis avoids the VVAz effect and can be applied to fractures and regional stress field prediction.

Comment on: “A skeptic's view of VVAz and AVAz” (N. Van De Coevering, K. Koster, and R. Holt, The Leading Edge, 39, no. 2, 128–134)

Van De Coevering et al. (2020) recently published a paper using the SEAM Phase II Barrett model to perform velocity variation with azimuth (VVAz) and amplitude variation with azimuth (AVAz) analysis. Based on this work, they concluded that the outcome of these methods does not show a positive correlation with the properties of the reservoir bodies. Here we explain that, due to the design of the model, the data cannot be expected to show these correlations. We base our discussion on the model parameters as shown in Figure 1b from the published paper ( Figure 1 ).

Azimuthal anisotropy analysis of wide-azimuth P-wave seismic data for fracture orientation and density characterization in a tight gas reservoir

The role of anisotropy in fracture detection has dramatically increased with the advent of wide-azimuth (WAZ) and high-density seismic acquisition. Fracture prediction using horizontal transverse isotropy (HTI) anisotropic theory is a useful tool for identifying reservoir characteristics. We have developed an approach for fracture density and orientation estimation based on the combination of a velocity variation with azimuth (VVAZ) and an amplitude variation with azimuth (AVAZ) analysis workflow. First, we sort the prestack WAZ data into offset vector tile (OVT) sectors and perform VVAZ inversion by elliptical velocity fitting of measured azimuth-differential traveltimes. In this step, we can predict the fast P-wave velocity, slow P-wave velocity, and fracture orientation. Second, we apply AVAZ inversion to extract more accurate predictions of the anisotropic gradient and fracture orientation. We implement the method with 3D prestack WAZ seismic data acquired in the Sichuan Basin, from the southwest part of China. The field data example indicates that the inversion results agree with geologic information and well-log imaging data, which confirm the effectiveness of this technology.

Seismic azimuthal anisotropy study of the Lower Paleozoic shale play in northern Poland

We have developed a case study of amplitude variation with azimuth (AVAZ) analysis applied to quantify the amount of the azimuthal anisotropy present in the Lower Paleozoic shales of the Baltic Basin (northern Poland). The challenges encountered here are related to thin (up to 25 m) deeply buried (approximately 3 km) targets, characterized by a weak average azimuthal anisotropy (1%–2% from cross-dipole sonic data). Synthetic AVAZ modeling confirms the applicability of the method. We used data after full-azimuth angle-domain prestack depth migration (PSDM) processed by a contractor and in-house sectored prestack time migration (PSTM). Application of AVAZ on full-azimuth PSDM data provided results that were further corroborated by the available calibration data. Anisotropy azimuths from AVAZ correlate with natural fracture direction from image logs (x-tended range microimager [XRMI]) interpretation, especially at the wells with only one dominant fracture system present. Fracture strikes inferred from AVAZ also correspond with fracture strikes inverted from the microseismic S-wave splitting analysis. Hudson’s crack densities calculated from the AVAZ anisotropic gradients matched crack densities from cross-dipole sonic as well as followed the same trend as the fracture intensities from XRMI data. Part of the success in this case should be attributed to the high-end processing of the input data because such obvious correlations are absent for AVAZ results on sectored PSTM data.

Azimuthal seismic responses from shale formation based on anisotropic rock physics and reflectivity method: a case study from south-west China

Due to intrinsic anisotropy related to preferred alignment of clay particles and the existence of vertical or high angle fractures, shales usually present orthorhombic anisotropy. The objective of this study was to build anisotropic rock physics models for shales at the seismic scale. Based on the well-log and Formation Micro Imager (FMI) log data from a shale formation in the Sichuan Basin in south-west China, we derive an orthorhombic model at the seismic scale by using Schoenberg and Helbig’s method and generalised Backus averaging method in the rock physics workflow. In order to understand the relationship between physical properties of the rock physics model and seismic wave propagation, we apply the simplified reflectivity method to calculate seismic responses for amplitude variation with azimuth (AVAz) analysis. The method is based on the scheme of anisotropic reflectivity method which is commonly used to simulate the full-wave field in stratified anisotropic media, in analogy with the formula of horizontal slowness components in Schoenberg and Protázio’s method. The AVAz analysis is conducted on the seismograms of PP-wave, radial and transverse components of PS-wave. The results show that overburden effects caused by wave propagation in anisotropic media can’t be ignored. Azimuthal variations in amplitudes of both PP-wave and radial component of PS-wave can be used to indicate strikes of fractures, while PS-wave appears to be more sensitive.

Modelling Orthorhombic Anisotropic Effects for Reservoir Fracture Characterization of a Naturally Fractured Tight Carbonate Reservoir, Onshore Texas, USA

In this study we present a step-by-step theoretical modelling approach, using established seismic wave propagation theories in anisotropic media, to generate unique anisotropic reflection patterns observed from three-dimensional pure-mode pressure (3D-PP), full-azimuth and full-offset seismic reflection data acquired over a naturally fractured tight carbonate field, onshore Texas, USA. Our aim is to gain an insight into the internal structures of the carbonate reservoir responsible for the observed anisotropic reflection patterns. From the generated model we were able to establish that the observed field seismic reflection patterns indicate azimuthal anisotropy in the form of crack induced shear-wave splitting and variation in P-wave velocity with offset and azimuth. Amplitude variation with azimuth (AVAZ) analysis also confirmed multi-crack sets induced anisotropy which is characteristic of orthorhombic symmetry, evident as multiple bright and dim-amplitude azimuth directions as well as complete reversal of bright-amplitude to dim-amplitude azimuth direction as the angle of incidence increases from near (≤15°) to mid (≥30°) offsets. Finally, we fitted the generated P-wave velocity into an ellipse to determine the intensity and orientation (N26E) of the open crack set as well as the direction of the minimum in situ stress axis (N116E) within the reservoir. The derived information served as an aid for the design of horizontal well paths that would intercept open fractures and ensure production optimization of the carbonate reservoir, which was on production decline despite reservoir studies that indicate un-depleted reserves.

Vector correlation of amplitude variation with azimuth and curvature in a post-hydraulic-fracture Barnett Shale survey

Knowledge of induced fractures can help to evaluate the success of reservoir stimulation. Seismic P-waves through fracturing media can exhibit azimuthal variation in traveltime, amplitude, and thin-bed tuning, so amplitude variation with azimuth (AVAz) can be used to evaluate the hydraulic-fracturing-caused anisotropy. The Barnett Shale of the Fort Worth Basin was the first large-scale commercial shale gas play. We have analyzed two adjacent Barnett Shale seismic surveys: one acquired before hydraulic fracturing and the other acquired after hydraulic fracturing by more than 400 wells. Although not a rigorous time-lapse experiment, comparison of AVAz anisotropy of these two surveys provided valuable insight into the possible effects of hydraulic fracturing. We found that in the survey acquired prior to hydraulic fracturing, AVAz anomalies were stronger and highly correlated with major structural lineaments measured by curvature. In contrast, AVAz anomalies in the survey acquired after hydraulic fracturing were weaker and compartmentalized by rather than correlated to the most-positive curvature lineaments. We found in five microseismic experiments within the survey that these ridge lineaments form fracture barriers. These findings suggested that future time-lapse experiments may be valuable in mapping the modified horizontal stress field to guide future drilling and in recognizing zones of bypassed pay.

Uncertainty and nonuniqueness in linearized AVAZ for orthorhombic media

Orthorhombic symmetry is one of the simplest models capable of representing fractured media such as naturally fractured shale reservoirs. However, low elastic symmetry translates to a large number of unknown elastic parameters, which affects the ability to obtain unique solutions. Therefore, the uncertainty associated with seismic-amplitude inversion must be considered for better understanding of the limitations and potential benefit of the inversion. An analysis of linearized amplitude variation with azimuth (AVAZ) inversion resulted in the development of workflows for practical AVAZ parameter estimation with uncertainty analysis. The inverted orthorhombic parameters are ranked by their uncertainty. Inversion attributes have clear meaning and can be used quantitatively when performing anisotropic orthorhombic subsurface characterization. The technique was applied in a field case for estimation of reservoir properties in orthorhombic media.

Interpreting azimuthal Fourier coefficients for anisotropic and fracture parameters

Amplitude variation with offset and azimuth (AVOAz) analysis can be separated into two separate parts: amplitude variation with offset (AVO) analysis and amplitude variation with azimuth (AVAz) analysis. Useful information about fractures and anisotropy can be obtained just by examining the AVAz. The AVAz can be described as a sum of sinusoids of different periodicities, each characterized by its magnitude and phase. This sum is mathematically equivalent to a Fourier series, and hence the coefficients describing the AVAz response are azimuthal Fourier coefficients (FCs). This FC parameterization is purely descriptive. The aim of this paper is to help the interpreter understand what these coefficients mean in terms of anisotropic and fracture parameters for the case of P-wave reflectivity using a linearized approximation. The FC representation is valid for general anisotropy. However, to gain insight into the significance of FCs, more restrictive assumptions about the anisotropy or facture system must be assumed. In the case of transverse isotropic media with a horizontal axis of symmetry, the P-wave reflectivity linearized approximation may be rewritten in terms of azimuthal FCs with the magnitude and phase of the different FCs corresponding to traditional AVAz attributes. Linear slip theory is used to show that the FCs can be interpreted similarly for the cases of a single set of parallel vertical fractures in isotropic media and in transverse isotropic media with a vertical axis of symmetry (VTI). The magnitude of the FCs depends on the fracture weakness parameters and the background media. For the case of vertical fractures in a VTI background, the AVOAz inverse problem is underdetermined, so extra information must be incorporated to determine how the weights are modified due to this background anisotropy. We evaluated this on a 3D data set from northwest Louisiana for which the main target was the Haynesville shale.

Anisotropic characteristics of mesoscale fractures and applications to wide azimuth 3D P-wave seismic data

Mesoscale fractures of length on the order of centimeters to meters play a crucial role in fluid flow and hydrocarbon production in fractured reservoirs, and are of great interest to reservoir engineers. Therefore, we need to find a method for obtaining information on mesoscale fractures. Most information on fractures comes from seismic data, specifically through the study of fracture-induced azimuthal anisotropic attributes, such as velocity variation with azimuth (VVAZ), amplitude variation with azimuth (AVAZ) and Q (quality factor for attenuation) variation with azimuth (QVAZ). Using these anisotropic attributes to characterize fracture orientations and densities has been performed for a long time. However, it has not been reported whether these methods can be used to detect mesoscale fractures. In this study, through analysis of the anisotropic response to different lengths of fractures based on a mesoscale fracture model, we find that azimuthal anisotropic attenuation is only sensitive to mesoscale fractures, while the anisotropic velocity represents the response for overall scale fractures. Two models, containing mesoscale fractures of length 1 m and microscale fractures of length 0.01 m, are used to calculate synthetic seismograms. Through analysis of the azimuthal anisotropic attributes (VVAZ, AVAZ and QVAZ) from the synthetic seismograms, the identification ability for microscale and mesoscale fractures is compared. It is observed that QVAZ can be used to invert mesoscale fractures while VVAZ and AVAZ cannot. Finally, the QVAZ method is applied in a wide azimuth 3D P-wave seismic dataset to detect mesoscale fractures and the results are confirmed by imaging loggings. Thus, synthetic seismograms, rock physics analysis and field seismic application demonstrates that anisotropic attenuation is the most effective method to detect mesoscale fractures in wide azimuth 3D P-wave seismic data.

Constructing the convex quadratic function for the evaluation of crack density of HTI media using P- and converted waves

In future years, cracked reservoirs will be an important target for oil and gas exploration. Cracks play an essential role in the evaluation and prediction of cracked reservoirs. The amplitude variation with azimuth (AVA) method of studying crack properties is becoming an important means of evaluating cracks and now the P-wave AVA method can be used in the inversion of crack density. In order to improve the precision of inversion, we constructed a convex objective function on the basis of the combination of P- and converted-wave data. We then used conjugate gradient methods for the inversion of crack density. Numerical calculations in both fluid-filled and dry crack models and stability analysis of this method proved its viability and stability.