Fluid‐dependent shear‐wave splitting in fractured media

Azimuthal anisotropy in rocks can result from the presence of one or more sets of partially aligned fractures with orientations determined by the stress history of the rock. A shear wave propagating in an azimuthally anisotropic medium splits into two components with different polarizations if the source polarization is not aligned with the principal axes of the medium. For vertical propagation of shear waves in a horizontally layered medium containing vertical fractures, the shear‐wave splitting depends on the shear compliance of the fractures, but is independent of their normal compliance. If the fractures are not perfectly vertical, the shear‐wave splitting also depends on the normal compliance of the fractures. The normal compliance of a fluid‐filled fracture decreases with increasing fluid bulk modulus. For dipping fractures, this results in a decrease in shear‐wave splitting and an increase in shear‐wave velocity with increasing fluid bulk modulus. The sensitivity of the shear‐wave splitting to fluid bulk modulus depends on the interconnectivity of the fracture network, the permeability of the background medium and on whether the fracture is fully or partially saturated.     

Finite-difference modelling of S-wave splitting in anisotropic media

We have implemented a 3D finite‐difference scheme to simulate wave propagation in arbitrary anisotropic media. The anisotropic media up to orthorhombic symmetry were modelled using a standard staggered grid scheme and beyond (monoclinic and triclinic) using a rotated staggered grid scheme. The rationale of not using rotated staggered grid for all types of anisotropic media is that the rotated staggered grid schemes are more expensive than standard staggered grid schemes. For a 1D azimuthally anistropic medium, we show a comparison between the seismic data generated by our finite‐difference code and by the reflectivity algorithm; they are in excellent agreement. We conducted a study on zero‐offset shear‐wave splitting using the finite‐difference modelling algorithm using the rotated staggered grid scheme. Our S‐wave splitting study is mainly focused on fractured media. On the scale of seismic wavelenghts, small aligned fractures behave as an equivalent anisotropic medium. We computed the equivalent elastic properties of the fractures and the background in which the fractures were embedded, using low‐frequency equivalent media theories. Wave propagation was simulated for both rotationally invariant and corrugated fractures embedded in an isotropic background for one, or more than one, set of fluid‐filled and dry fractures. S‐wave splitting was studied for dipping fractures, two vertical non‐orthogonal fractures and corrugated fractures. Our modelling results confirm that S‐wave splitting can reveal the fracture infill in the case of dipping fractures. S‐wave splitting has the potential to reveal the angle between the two vertical fractures. We also notice that in the case of vertical corrugated fractures, S‐wave splitting is sensitive to the fracture infill.     

Effect of fracture fill on frequency‐dependent anisotropy of fractured porous rocks

In fractured reservoirs, seismic wave velocity and amplitude depend on frequency and incidence angle. Frequency dependence is believed to be principally caused by the wave‐induced flow of pore fluid at the mesoscopic scale. In recent years, two particular phenomena, i.e., patchy saturation and flow between fractures and pores, have been identified as significant mechanisms of wave‐induced flow. However, these two phenomena are studied separately. Recently, a unified model has been proposed for a porous rock with a set of aligned fractures, with pores and fractures filled with two different fluids. Existing models treat waves propagating perpendicular to the fractures. In this paper, we extend the model to all propagation angles by assuming that the flow direction is perpendicular to the layering plane and is independent of the loading direction. We first consider the limiting cases through poroelastic Backus averaging, and then we obtain the five complex and frequency‐dependent stiffness values of the equivalent transversely isotropic medium as a function of the frequency. The numerical results show that, when the bulk modulus of the fracture‐filling fluid is relatively large, the dispersion and attenuation of P‐waves are mainly caused by fractures, and the values decrease as angles increase, almost vanishing when the incidence angle is 90° (propagation parallel to the fracture plane). While the bulk modulus of fluid in fractures is much smaller than that of matrix pores, the attenuation due to the “partial saturation” mechanism makes the fluid flow from pores into fractures, which is almost independent of the incidence angle.     

The effect of orthorhombic anisotropy and its implication for oil recovery and reservoir exploitation

Results of an experimental study of shear‐ and compressional‐wave propagation in an orthorhombically anisotropic medium are presented. The experiments were performed on a physical model consisting of two sets of fractures. The first set consisted of orientated rubber inclusions simulating weak material‐filled cracks. The second set consisted of a system of closely spaced parallel fractures simulated by thin plates of epoxy resin, superimposed orthogonally on the first set. Three cases of fracture orientations within the model were identified and studied. Case 1 is analogous to a jointed fracture reservoir with one vertical set of fluid‐filled cracks or fractures and one non‐filled horizontal set. This case is referred to as JFV. Case 2 is analogous to a double fracture reservoir with one horizontal set of fluid‐filled fractures or cracks and one non‐filled vertical set. This is referred to as DFH. Case 3 is analogous to a double fracture reservoir with two vertical sets of fractures or cracks, with only one fluid‐filled. Case 3 is referred to as DFV. A pulse transmission method was performed on all three modelled cases along the three principal axes. A directional variation in the compressional‐ and shear‐wave velocities, as well as distinct shear‐wave splitting, was observed. The elastic constants for each case were determined and differences between them were noted and compared with the controlled results of both layered (transverse isotropy, TI) and vertically fractured (azimuthally anisotropic models, VF) media. The differences in elastic moduli and velocities indicate the potential of recognizing the different fracture orientations and suggest an approach to designing a method of drilling to further enhance oil recovery and reservoir exploitation.     

Observations of fluid‐dependent shear‐wave splitting in synthetic porous rocks with aligned penny‐shaped fractures‡

P‐ and S‐wave velocity and attenuation coefficients (accurate to ±0.3% and ±0.2 dB/cm, respectively) were measured in synthetic porous rocks with aligned, penny‐shaped fractures using the laboratory ultrasonic pulse‐echo method. Shear‐wave splitting was observed by rotating the S‐wave transducer and noting the maximum and minimum velocities relative to the fracture direction. A block of synthetic porous rock of fracture density 0.0201 ± 0.0068 and fracture size 3.6 ± 0.38 mm (measured from image analysis of X‐ray CT scans) was sub‐sampled into three 20–30 mm long, 50 mm diameter core plugs oriented at 0°, 45° and 90° to the fracture normal (transversely isotropic symmetry axis). Full waveform data were collected over the frequency range 500–1000 kHz for both water and glycerin saturated cores to observe the effect of pore fluid viscosity at 1 cP and 100 cP, respectively. The shear‐wave splitting observed in the 90° core was 2.15 ± 0.02% for water saturated and 2.39 ± 0.02% for glycerin saturated, in agreement with the theory that suggests that the percentage splitting should be 100 times the fracture density and independent of the saturating fluid. In the 45° core, by contrast, splitting was 0.00 ± 0.02% for water saturation and ?0.77 ± 0.02% for glycerin saturation. This dependence on fracture orientation and pore fluid viscosity is consistent with the poro‐visco‐elastic theory for aligned, meso‐scale fractures in porous rocks. The results suggest the possible use of shear‐ or converted‐wave data to discriminate between fluids on the basis of viscosity variations.     

Pore fluid viscosity effects on P‐ and S‐wave anisotropy in synthetic silica‐cemented sandstone with aligned fractures

Ultrasonic (500 kHz) P‐ and S‐wave velocity and attenuation anisotropy were measured in the laboratory on synthetic, octagonal‐shaped, silica‐cemented sandstone samples with aligned penny‐shaped voids as a function of pore fluid viscosity. One control (blank) sample was manufactured without fractures, another sample with a known fracture density (measured from X‐ray CT images). Velocity and attenuation were measured in four directions relative to the bedding fabric (introduced during packing of successive layers of sand grains during sample construction) and the coincident penny‐shaped voids (fractures). Both samples were measured when saturated with air, water (viscosity 1 cP) and glycerin (100 cP) to reveal poro‐visco‐elastic effects on velocity and attenuation, and their anisotropy. The blank sample was used to estimate the background anisotropy of the host rock in the fractured sample; the bedding fabric was found to show transverse isotropy with shear wave splitting (SWS) of 1.45 ± 1.18% (i.e. for S‐wave propagation along the bedding planes). In the fractured rock, maximum velocity and minimum attenuation of P‐waves was seen at 90° to the fracture normal. After correction for the background anisotropy, the fractured sample velocity anisotropy was expressed in terms of Thomsen's weak anisotropy parameters ε, γ & δ. A theory of frequency‐dependent seismic anisotropy in porous, fractured, media was able to predict the observed effect of viscosity and bulk modulus on ε and δ in water‐ and glycerin‐saturated samples, and the higher ε and δ values in air‐saturated samples. Theoretical predictions of fluid independent γ are also in agreement with the laboratory observations. We also observed the predicted polarisation cross‐over in shear‐wave splitting for wave propagation at 45° to the fracture normal as fluid viscosity and bulk modulus increases.     

利用含可控裂缝人工岩样研究裂缝密度对各向异性的影响

利用新方法制作出含可控裂缝的双孔隙人工砂岩物理模型,具有与天然岩石更为接近的矿物成分、孔隙结构和胶结方式,其中裂缝密度、裂缝尺寸和裂缝张开度等裂缝参数可以控制以得到实验所需要的裂缝参数,岩样具有真实的孔隙和裂缝空间并可以在不同饱和流体状态下研究流体性质对于裂缝介质性质的影响.本次实验制作出一组具有不同裂缝密度的含裂缝人工岩样,对岩样利用SEM扫描电镜分析可以看到真实的孔隙结构和符合我们要求的裂缝参数,岩样被加工成八面棱柱以测量不同方向上弹性波传播的速度,用0.5 MHz的换能器使用透射法测量在饱和空气和饱和水条件下各个样品不同方向上的纵横波速度,并得出纵横波速度、横波分裂系数和纵横波各向异性强度受裂缝密度和饱和流体的影响.研究发现流体对于纵波速度和纵波各向异性强度的影响较强,而横波速度、横波分裂系数和横波各向异性强度受饱和流体的影响不大,但是对裂缝密度的变化更敏感.     

Seismic dispersion and attenuation in layered porous rocks with fractures of varying orientations

Wave‐induced fluid flow plays an important role in affecting the seismic dispersion and attenuation of fractured porous rocks. While numerous theoretical models have been proposed for the seismic dispersion and attenuation in fractured porous rocks, most of them neglect the wave‐induced fluid flow resulting from the background anisotropy (e.g. the interlayer fluid flow between different layers) that can be normal in real reservoirs. Here, according to the theories of poroelasticity, we present an approach to study the frequency‐dependent seismic properties of more realistic and complicated rocks, i.e. horizontally and periodically layered porous rock with horizontal and randomly orienting fractures, respectively, distributed in one of the two periodical layers. The approach accounts for the dual effects of the wave‐induced fluid flow between the fractures and the background pores and between different layers (the interlayer fluid flow). Because C₃₃ (i.e., the modulus of the normally incident P‐wave) is directly related to the P‐wave velocity widely measured in the seismic exploration, and its comprehensive dispersion and attenuation are found to be most significant, we study mainly the effects of fracture properties and the stiffness contrast between the different layers on the seismic dispersion and attenuation of C₃₃. The results show that the increasing stiffness contrast enhances the interlayer fluid flow of the layered porous rocks with both horizontal and randomly orienting fractures and weakens the wave‐induced fluid flow between the fractures and the background pores, especially for the layered porous rock with horizontal fractures. The modelling results also demonstrate that for the considered rock construction, the increasing fracture density reduces the interlayer fluid flow while improves the dispersion and attenuation in the fracture‐relevant frequency band. Increasing fracture aspect ratio is found to reduce the dispersion and attenuation in the fracture‐relevant frequency band only, especially for the layered porous rock with horizontal fractures.     

Characterization of dipping fractures in a transverselyisotropic background

Although it is believed that natural fracture sets predominantly have near‐vertical orientation, oblique stresses and some other mechanisms may tilt fractures away from the vertical. Here, we examine an effective medium produced by a single system of obliquely dipping rotationally invariant fractures embedded in a transversely isotropic with a vertical symmetry axis (VTI) background rock. This model is monoclinic with a vertical symmetry plane that coincides with the dip plane of the fractures. Multicomponent seismic data acquired over such a medium possess several distinct features that make it possible to estimate the fracture orientation. For example, the vertically propagating fast shear wave (and the fast converted PS‐wave) is typically polarized in the direction of the fracture strike. The normal‐moveout (NMO) ellipses of horizontal reflection events are co‐orientated with the dip and strike directions of the fractures, which provides an independent estimate of the fracture azimuth. However, the polarization vector of the slow shear wave at vertical incidence does not lie in the horizontal plane – an unusual phenomenon that can be used to evaluate fracture dip. Also, for oblique fractures the shear‐wave splitting coefficient at vertical incidence becomes dependent on fracture infill (saturation). A complete medium‐characterization procedure includes estimating the fracture compliances and orientation (dip and azimuth), as well as the Thomsen parameters of the VTI background. We demonstrate that both the fracture and background parameters can be obtained from multicomponent wide‐azimuth data using the vertical velocities and NMO ellipses of PP‐waves and two split SS‐waves (or the traveltimes of PS‐waves) reflected from horizontal interfaces. Numerical tests corroborate the accuracy and stability of the inversion algorithm based on the exact expressions for the vertical and NMO velocities.     

涪陵地区井下页岩岩芯裂缝体密度与声学性质关系实验研究

本研究对涪陵地区井下产气的龙马溪组页岩岩芯,采用三轴压机压裂制造裂缝,用工业CT扫描压裂前后岩芯,应用图像识别技术统计出裂缝体密度,又用超声脉冲透射法测定样品破裂前后裂缝方向上的纵波、单偏振方向与裂缝不同夹角的横波,来研究裂缝对页岩岩芯声学性质的影响.实验结果表明:压裂后样品的纵波速度略微降低,只有含较多内部裂隙的150#样品纵波速度减小幅度明显.压裂前后样品的纵波波形差别不大,纵波主频随裂缝体密度呈下降趋势,即压裂后纵波频谱主频向低频端移动.压裂前横波速度随自身与裂隙方位角变化而变化,与0°和180°相比,在45°和135°时略微减小,在90°时速度降低幅度最为明显并且发生相位反转.典型样品的横波主频随偏振方向与裂缝夹角的增大而逐渐向低频移动;压裂后,横波频谱杂乱,出现多处局部峰值,速度和主频较压裂前更低,平均横波波速随裂缝体密度呈明显减小趋势.平均纵横波速比随裂缝密度呈近线性增加,表明其与裂缝体密度有较强相关性.     

Seismic attenuation and velocity dispersion in fractured rocks: The role played by fracture contact areas

The presence of fractures in fluid‐saturated porous rocks is usually associated with strong seismic P‐wave attenuation and velocity dispersion. This energy dissipation can be caused by oscillatory wave‐induced fluid pressure diffusion between the fractures and the host rock, an intrinsic attenuation mechanism generally referred to as wave‐induced fluid flow. Geological observations suggest that fracture surfaces are highly irregular at the millimetre and sub‐millimetre scale, which finds its expression in geometrical and mechanical complexities of the contact area between the fracture faces. It is well known that contact areas strongly affect the overall mechanical fracture properties. However, existing models for seismic attenuation and velocity dispersion in fractured rocks neglect this complexity. In this work, we explore the effects of fracture contact areas on seismic P‐wave attenuation and velocity dispersion using oscillatory relaxation simulations based on quasi‐static poroelastic equations. We verify that the geometrical and mechanical details of fracture contact areas have a strong impact on seismic signatures. In addition, our numerical approach allows us to quantify the vertical solid displacement jump across fractures, the key quantity in the linear slip theory. We find that the displacement jump is strongly affected by the geometrical details of the fracture contact area and, due to the oscillatory fluid pressure diffusion process, is complex‐valued and frequency‐dependent. By using laboratory measurements of stress‐induced changes in the fracture contact area, we relate seismic attenuation and dispersion to the effective stress. The corresponding results do indeed indicate that seismic attenuation and phase velocity may constitute useful attributes to constrain the effective stress. Alternatively, knowledge of the effective stress may help to identify the regions in which wave induced fluid flow is expected to be the dominant attenuation mechanism.     

Experimental verification of the fracture density and shear‐wave splitting relationship using synthetic silica cemented sandstones with a controlled fracture geometry

We present laboratory ultrasonic measurements of shear‐wave splitting from two synthetic silica cemented sandstones. The manufacturing process, which enabled silica cementation of quartz sand grains, was found to produce realistic sandstones of average porosity 29.7 ± 0.5% and average permeability 29.4 ± 11.3 mD. One sample was made with a regular distribution of aligned, penny‐shaped voids to simulate meso‐scale fractures in reservoir rocks, while the other was left blank. Ultrasonic shear waves were measured with a propagation direction of 90° to the coincident bedding plane and fracture normal. In the water saturated blank sample, shear‐wave splitting, the percentage velocity difference between the fast and slow shear waves, of <0.5% was measured due to the bedding planes (or layering) introduced during sample preparation. In the fractured sample, shear‐wave splitting (corrected for layering anisotropy) of 2.72 ± 0.58% for water, 2.80 ± 0.58% for air and 3.21 ± 0.58% for glycerin saturation at a net pressure of 40 MPa was measured. Analysis of X‐ray CT scan images was used to determine a fracture density of 0.0298 ± 0.077 in the fractured sample. This supports theoretical predictions that shear‐wave splitting (SWS) can be used as a good estimate for fracture density in porous rocks (i.e., SWS = 100ε_f, where ε_f is fracture density) regardless of pore fluid type, for wave propagation at 90° to the fracture normal.     

Azimuthal anisotropy analysis of walkaround vertical seismic profiling vertical seismic profiling: a case study from Saudi Arabia

Understanding fracture orientations is important for optimal field development of fractured reservoirs because fractures can act as conduits for fluid flow. This is especially true for unconventional reservoirs (e.g., tight gas sands and shale gas). Using walkaround Vertical Seismic Profiling (VSP) technology presents a unique opportunity to identify seismic azimuthal anisotropy for use in mapping potential fracture zones and their orientation around a borehole. Saudi Aramco recently completed the acquisition, processing and analysis of a walkaround VSP survey through an unconventional tight gas sand reservoir to help characterize fractures. In this paper, we present the results of the seismic azimuthal anisotropy analysis using seismic traveltime, shear‐wave splitting and amplitude attenuation. The azimuthal anisotropy results are compared to the fracture orientations derived from dipole sonic and image logs. The image log interpretation suggests that an orthorhombic fracture system is present. VSP data show that the P‐wave traveltime anisotropy direction is NE to SW. This is consistent with the cemented fractures from the image log interpretation. The seismic amplitude attenuation anisotropy direction is NW to SE. This is consistent with one of the two orientations obtained using transverse to radial amplitude ratio analysis, with the dipole sonic and with open fracture directions interpreted from image log data.     

On shear-wave splitting in the Los Angeles basin

Three-component seismograms at the three USC stations, PVP, GFP and DHB, have been examined. Most earthquakes, with magnitudes ranging from 1.4 to 5.0, within a period from 1985 to 1988, show evidence of shear-wave splitting. The preferred polarization of the first split-shear wave arrivals at PVP is nearly in N-S which is consistent with both regional maximum horizontal compressive stress direction and local subsurface fault strike, showing that shear-wave splitting is caused by liquid-filled cracks or fractures associated with the N-S faulting. The polarizations of first shear wave arrivals at GFP are roughly divided into two almost perpendicular directions, ENE-WSW and NNW-SSE, which are parallel or perpendicular to the strike of the geology or topography near the station. Because GFP is near the foothills of Santa Monica Mountains, the shear-wave arrivals may be disturbed by topographic irregularities and by subsurface dipping interfaces. Two examples at DHB clearly display shear-wave splitting. Their polarizations of shear wave are in the direction of N-S, which agree with the fragmentary surface and fracturing direction there. From some relatively reliable delay times, the crack densities at three stations are given, that is, 0.025 at PVP, 0.020 at GFP and 0.045 at DGB. No systematic change of shear-wave polarization is discovered in this study.     

地震资料中的多尺度断裂与流体响应特征：数值模拟分析

流体在断裂和岩石骨架间的交换被认为是影响岩石弹性参数各向异性的主要原因,理论研究表明断裂尺度同样对弹性参数的各向异性也有影响.为了说明两者对各向异性影响以实现多尺度断裂裂隙的识别,本文在等效介质模型的基础上,应用数值分析的方法研究速度和衰减(1/Q)随多尺度断裂、频率和流体因子变化规律.结果表明介质弹性参数是频率依赖的,并且参数中存在衰减项,而这种频率依赖性与介质物性参数中的断裂尺度及流体性质存在一定的联系;当断裂定向分布时,参数结果显示为各向异性;不同断裂尺度具有不同的波速频散特性,剪切波分裂程度依赖于频率,断裂尺度起着控制作用,高频时对小尺度的敏感,低频段对大尺度敏感.在地震频段Thomsen参数随着频率的增大而减小,随着断裂尺寸的增大而减小.因此地震数据可能区分断裂和微裂隙引起各向异性,从而可测量断裂尺度.     

Seismic anisotropy in a hydrocarbon field estimated from microseismic data

The study of seismic anisotropy in exploration seismology is gaining interest as it provides valuable information about reservoir properties and stress directions. In this study we estimate anisotropy in a petroleum field in Oman using observations of shear‐wave splitting from microseismic data. The data set was recorded by arrays of borehole geophones deployed in five wells. We analyse nearly 3400 microearthquakes, yielding around 8500 shear‐wave splitting measurements. Stringent quality control reduces the number of reliable measurements to 325. Shear‐wave splitting modelling in a range of rock models is then used to guide the interpretation. The difference between the fast and slow shear‐wave velocities along the raypath in the field ranges between 0–10% and it is controlled both by lithology and proximity to the NE‐SW trending graben fault system that cuts the field formations. The anisotropy is interpreted in terms of aligned fractures or cracks superimposed on an intrinsic vertical transversely isotropic (VTI) rock fabric. The highest magnitudes of anisotropy are within the highly fractured uppermost unit of the Natih carbonate reservoir. Anisotropy decreases with depth, with the lowest magnitudes found in the deep part of the Natih carbonate formation. Moderate amounts of anisotropy are found in the shale cap rock. Anisotropy also varies laterally with the highest anisotropy occurring either side of the south‐eastern graben fault. The predominant fracture strikes, inferred from the fast shear‐wave polarizations, are consistent with the trends of the main faults (NE‐SW and NW‐SE). The majority of observations indicate subvertical fracture dip (>70° ). Cumulatively, these observations show how studies of shear‐wave splitting using microseismic data can be used to characterize fractures, important information for the exploitation of many reservoirs.     

不同尺度裂缝对弹性波速度和各向异性影响的实验研究

裂缝广泛分布于地球介质中并且具有多尺度的特点,裂缝尺度对于油气勘探和开发有着重要的意义.本文制作了一组含不同长度裂缝的人工岩样,其中三块含裂缝岩样中的裂缝直径分别为2 mm、3 mm和4 mm,裂缝的厚度都约为0.06 mm,裂缝密度大致相同(分别为4.8%、4.86%和4.86%).在岩样含水的条件下测试不同方向上的纵横波速度,实验结果表明,虽然三块裂缝岩样中的裂缝密度大致相同,但是含不同直径裂缝岩样的纵横波速度存在差异.在各个方向上,含数量众多的小尺度裂缝的岩样中纵横波速度都明显低于含少量的大尺度裂缝的岩样中纵横波速度.尤其是对纵波速度和SV波速度,在不同尺度裂缝岩样中的差异更明显.在含数量多的小尺度裂缝的岩样中纵波各向异性和横波各向异性最高,而含少量的大尺度的裂缝的岩样中的纵波各向异性和横波各向异性较低.实验测量结果与Hudson理论模型预测结果进行了对比分析,结果发现Hudson理论考虑到了裂缝尺度对纵波速度和纵波各向异性的影响,但是忽略了其对横波速度和横波各向异性的影响.     

裂隙弱度参数的波场特征

本文将Schoenberg线性滑移裂隙介质理论应用到HTI(LSD)介质的弹性波波场数值模拟之中.主要针对描述裂隙状态的2个裂隙参数--法向弱度EN和切向弱度ET对波场的影响进行了有限元模拟.模拟结果揭示了EN主要影响快波而ET主要影响慢波的波场特征,通过EN和ET变化对应的裂隙含水程度说明了EN对裂隙中的流体敏感而E...     

Direct inversion for a fluid factor and its application in heterogeneous reservoirs

Prestack seismic inversion plays an important role in estimating elastic parameters that are sensitive to reservoirs and fluid underground. In this paper, a simultaneous inversion method named FMR‐AVA (Fluid Factor, Mu (Shear modulus), Rho (Density)‐Amplitude Variation with Angle) is proposed based on partial angle stack seismic gathers. This method can be used for direct inversion for the fluid factor, shear modulus and density of heterogeneous reservoirs. Firstly, an FMR approximation equation of a reflection coefficient is derived based on poroelasticity with P‐ and S‐wave moduli. Secondly, a stable simultaneous AVA inversion approach is presented in a Bayesian scheme. This approach has little dependence on initial models. Furthermore, it can be applied in heterogeneous reservoirs whose initial models for inversion are not easy to establish. Finally, a model test shows the superiority of this FMR‐AVA inversion method in stability and independence of initial models. We obtain a reasonable fluid factor, shear modulus and density even with smooth initial models and moderate Gaussian noise. A real data case example shows that the inverted fluid factor, shear modulus and density fit nicely with well log interpretation results, which verifies the effectiveness of the proposed method.     

Joint PP‐ and PSV‐wave amplitudes versus offset and azimuth inversion for fracture compliances in horizontal transversely isotropic media

We propose a robust approach for the joint inversion of PP‐ and PSV‐wave angle gathers along different azimuths for the elastic properties of the homogeneous isotropic host rock and excess compliances due to the presence of fractures. Motivated by the expression of fluid content indicator in fractured reservoirs and the sensitivity of Lamé impedances to fluid type, we derive PP‐ and PSV‐wave reflection coefficients in terms of Lamé impedances, density, and fracture compliances for an interface separating two horizontal transversely isotropic media. Following a Bayesian framework, we construct an objective function that includes initial models. We employ the iteratively reweighted least‐squares algorithm to solve the inversion problem to estimate unknown parameters (i.e., Lamé impedances, density, and fracture compliances) from PP‐ and PSV‐wave angle gathers along different azimuths. Synthetic tests reveal that the unknown parameters estimated using the joint inversion approach match true values better than those estimated using a PP‐wave amplitude inversion only. A real data test indicates that reasonable results for subsurface fracture detection are obtained from the joint inversion approach.