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1.
Elastic properties of saturated porous rocks with aligned fractures   总被引：4，自引：0，他引：4  
Elastic properties of fluid saturated porous media with aligned fractures can be studied using the model of fractures as linear-slip interfaces in an isotropic porous background. Such a medium represents a particular case of a transversely isotropic (TI) porous medium, and as such can be analyzed with equations of anisotropic poroelasticity. This analysis allows the derivation of explicit analytical expressions for the low-frequency elastic constants and anisotropy parameters of the fractured porous medium saturated with a given fluid. The five elastic constants of the resultant TI medium are derived as a function of the properties of the dry (isotropic) background porous matrix, fracture properties (normal and shear excess compliances), and fluid bulk modulus. For the particular case of penny-shaped cracks, the expression for anisotropy parameter ε has the form similar to that of Thomsen [Geophys. Prospect. 43 (1995) 805]. However, contrary to the existing view, the compliance matrix of a fluid-saturated porous-fractured medium is not equivalent to the compliance matrix of any equivalent solid medium with a single set of parallel fractures. This unexpected result is caused by the wave-induced flow of fluids between pores and fractures.  相似文献   

2.
We present a method for inversion of fracture compliance matrix components from wide‐azimuth noisy synthetic PS reflection data and quantitatively show that reflection amplitude variations with offset and azimuth for converted PS‐waves are more informative than P‐waves for fracture characterization. We consider monoclinic symmetry for fractured reservoir (parameters chosen from Woodford Shale), which can be formed by two or more sets of vertical fractures embedded in a vertically transverse isotropic background. Components of effective fracture compliance matrices for a medium with monoclinic symmetry are related to the characteristics of the fractured medium. Monte Carlo simulation results show that inversion of PS reflection data is more robust than that of PP reflection data to uncertainties in our a priori knowledge (vertically transverse isotropic parameters of unfractured rock) than PP reflection data. We also show that, while inversion of PP reflections is sensitive to contrasts in elastic properties of upper and lower media, inversion of PS reflections is robust with respect to such contrasts.  相似文献   

3.
A model of parallel slip interfaces simulates the behaviour of a fracture system composed of large, closely spaced, aligned joints. The model admits any fracture system anisotropy: triclinic (the most general), monoclinic, orthorhombic or transversely isotropic, and this is specified by the form of the 3 × 3 fracture system compliance matrix. The fracture system may be embedded in an anisotropic elastic background with no restrictions on the type of anisotropy. To compute the long wavelength equivalent moduli of the fractured medium requires at most the inversion of two 3 × 3 matrices. When the fractures are assumed on average to have rotational symmetry (transversely isotropic fracture system behaviour) and the background is assumed isotropic, the resulting equivalent medium is transversely isotropic and the effect of the additional compliance of the fracture system may be specified by two parameters (in addition to the two isotropic parameters of the isotropic background). Dilute systems of flat aligned microcracks in an isotropic background yield an equivalent medium of the same form as that of the isotropic medium with large joints, i.e. there are two additional parameters due to the presence of the microcracks which play roles in the stress-strain relations of the equivalent medium identical to those played by the parameters due to the presence of large joints. Thus, knowledge of the total of four parameters describing the anisotropy of such a fractured medium tells nothing of the size or concentration of the aligned fractures but does contain information as to the overall excess compliance due to the fracture system and its orientation. As the aligned microcracks, which were assumed to be ellipsoidal, with very small aspect ratio are allowed to become non-fiat, i.e. have a growing aspect ratio, the moduli of the equivalent medium begin to diverge from the standard form of the moduli for flat cracks. The divergence is faster for higher crack densities but only becomes significant for microcracks of aspect ratios approaching 0.3.  相似文献   

4.
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.  相似文献   

5.
Any set of isotropic layers is equivalent, in the long wavelength limit, to a unique transversely isotropic (TI) layer; to find the elastic moduli of that layer is a solved problem. The converse problem is to find a set of isotropic layers equivalent to a given TI media. Here, explicit necessary and sufficient conditions on the TI stiffness moduli for the existence of an equivalent set of isotropic layers are found by construction of a minimal decomposition consisting of either two or three isotropic constituent layers. When only two constituents are required, their elastic properties are uniquely determined. When three constituents are required, two have the same Poisson's ratio and the same thickness fraction, and even then there is a one-parameter family of satisfactory minimal decompositions. The linear slip model for fractured rock (aligned fractures in an isotropic background) yields a restricted range of transverse isotropy dependent on only four independent parameters. If the ratio of the normal to tangential fracture compliance is small enough, the medium is equivalent to thin isotropic layering and in general its minimal decomposition consists of three constituents.  相似文献   

6.
Fractures in elastic media add compliance to a rock in the direction normal to the fracture strike. Therefore, elastic wave velocities in a fractured rock will vary as a function of the energy propagation direction relative to the orientation of the aligned fracture set. Anisotropic Thomson–Haskell matrix Rayleigh-wave equations for a vertically transverse isotropic media can be used to model surface-wave dispersion along the principal axes of a vertically fractured and transversely isotropic medium. Furthermore, a workflow combining first-break analysis and azimuthal anisotropic Rayleigh-wave inversion can be used to estimate P-wave and S-wave velocities, Thomsen's ε, and Thomsen's δ along the principal axes of the orthorhombic symmetry. In this work, linear slip theory is used to map our inversion results to the equivalent vertically fractured and transversely isotropic medium coefficients. We carried out this inversion on a synthetic example and a field example. The synthetic data example results show that joint estimation of S-wave velocities with Thomsen's parameters ε and δ along normal and parallel to the vertical fracture set is reliable and, when mapped to the corresponding vertically fractured and transversely isotropic medium, provides insight into the fracture compliances. When the inversion was carried out on the field data, results indicated that the fractured rock is more compliant in the azimuth normal to the visible fracture set orientation and that the in situ normal fracture compliance to tangential fracture compliance ratio is less than half, which implies some cementation may have occurred along the fractures. Such an observation has significant implications when modelling the transport properties of the rock and its strength. Both synthetic and field examples show the potential of azimuthal anisotropic Rayleigh-wave inversion as the method can be further expanded to a more general case where the vertical fracture set orientation is not known a priori.  相似文献   

7.
Wave-induced fluid flow generates a dominant attenuation mechanism in porous media. It consists of energy loss due to P-wave conversion to Biot (diffusive) modes at mesoscopic-scale inhomogeneities. Fractured poroelastic media show significant attenuation and velocity dispersion due to this mechanism. The theory has first been developed for the symmetry axis of the equivalent transversely isotropic (TI) medium corresponding to a poroelastic medium containing planar fractures. In this work, we consider the theory for all propagation angles by obtaining the five complex and frequency-dependent stiffnesses of the equivalent TI medium as a function of frequency. We assume that the flow direction is perpendicular to the layering plane and is independent of the loading direction. As a consequence, the behaviour of the medium can be described by a single relaxation function. We first consider the limiting case of an open (highly permeable) fracture of negligible thickness. We then compute the associated wave velocities and quality factors as a function of the propagation direction (phase and ray angles) and frequency. The location of the relaxation peak depends on the distance between fractures (the mesoscopic distance), viscosity, permeability and fractures compliances. The flow induced by wave propagation affects the quasi-shear (qS) wave with levels of attenuation similar to those of the quasi-compressional (qP) wave. On the other hand, a general fracture can be modeled as a sequence of poroelastic layers, where one of the layers is very thin. Modeling fractures of different thickness filled with CO2 embedded in a background medium saturated with a stiffer fluid also shows considerable attenuation and velocity dispersion. If the fracture and background frames are the same, the equivalent medium is isotropic, but strong wave anisotropy occurs in the case of a frameless and highly permeable fracture material, for instance a suspension of solid particles in the fluid.  相似文献   

8.
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.  相似文献   

9.
裂缝诱导HTI双孔隙介质中的裂缝参数分析   总被引：1，自引：0，他引：1       下载免费PDF全文
裂缝诱导HTI双孔隙介质模型是将一组垂直排列的裂缝系统嵌入到统计各向同性的孔隙岩石基质系统中而建立的.为了研究裂缝参数对地震波在该模型中传播规律的影响,本文分别对裂缝弱度、裂缝孔隙度和裂缝渗透率这三个主要的裂缝参数进行了分析研究.数值结果表明,裂缝诱导HTI双孔隙介质中,裂缝弱度越大,介质的各向异性强度越强;与基质孔隙系统相比,裂缝系统孔隙度对介质等效孔隙度的影响很小,而裂缝系统渗透率的增大则将显著提高介质在裂缝发育方向上的等效渗透率,这符合对裂缝系统"低孔"、"高渗"特性的认识.此外,裂缝系统渗透率的增大也使慢纵波的振幅显著增强.  相似文献   

10.
Fluid flow in many hydrocarbon reservoirs is controlled by aligned fractures which make the medium anisotropic on the scale of seismic wavelength. Applying the linear‐slip theory, we investigate seismic signatures of the effective medium produced by a single set of ‘general’ vertical fractures embedded in a purely isotropic host rock. The generality of our fracture model means the allowance for coupling between the normal (to the fracture plane) stress and the tangential jump in displacement (and vice versa). Despite its low (triclinic) symmetry, the medium is described by just nine independent effective parameters and possesses several distinct features which help to identify the physical model and estimate the fracture compliances and background velocities. For example, the polarization vector of the vertically propagating fast shear wave S1 and the semi‐major axis of the S1‐wave normal‐moveout (NMO) ellipse from a horizontal reflector always point in the direction of the fracture strike. Moreover, for the S1‐wave both the vertical velocity and the NMO velocity along the fractures are equal to the shear‐wave velocity in the host rock. Analysis of seismic signatures in the limit of small fracture weaknesses allows us to select the input data needed for unambiguous fracture characterization. The fracture and background parameters can be estimated using the NMO ellipses from horizontal reflectors and vertical velocities of P‐waves and two split S‐waves, combined with a portion of the P‐wave slowness surface reconstructed from multi‐azimuth walkaway vertical seismic profiling (VSP) data. The stability of the parameter‐estimation procedure is verified by performing non‐linear inversion based on the exact equations.  相似文献   

11.
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12.
A polyaxial (true‐triaxial) stress‐loading system, developed originally for determining all nine components of P‐ and S‐wave velocities and attenuation and fluid permeability for 50.8 mm‐side cubic rock specimens tested to failure, has been modified to permit the measurement of acoustic emission events associated with the failure process. Results are reported for Crosland Hill sandstone tested to failure under loading conditions leading to the formation of sets of aligned microcracks, achieved by maintaining the minor principal stress at a low value while increasing the two other principal stresses until failure of the rock. An ultrasonic survey associated with the test has been employed to map the transversely‐isotropic velocity structure created by through‐going parallel fractures resulting from the sets of aligned microcracks. This velocity structure has then been employed to locate acoustic emission events recorded during the test by four acoustic emission sensors located in each of the six specimen loading platens. A selection of acoustic emission events associated with one of the fractures has been processed for moment tensor analysis information, in order to determine the source type and orientation of microcracking as the fracture grows. The mechanisms indicate tensile behaviour during initial fracture propagation. Shear failure, however, appears to dominate as the fracture finally approaches the opposite face of the cubic specimen. The work presented here has, in part, led to the development of new rock testing systems and geophysical monitoring and processing technologies that will enable laboratory study of rock behaviour under conditions better resembling those experienced in situ.  相似文献   

13.
Tilted transversely isotropic formations cause serious imaging distortions in active tectonic areas (e.g., fold‐and‐thrust belts) and in subsalt exploration. Here, we introduce a methodology for P‐wave prestack depth imaging in tilted transversely isotropic media that properly accounts for the tilt of the symmetry axis as well as for spatial velocity variations. For purposes of migration velocity analysis, the model is divided into blocks with constant values of the anisotropy parameters ε and δ and linearly varying symmetry‐direction velocity VP0 controlled by the vertical (kz) and lateral (kx) gradients. Since determination of tilt from P‐wave data is generally unstable, the symmetry axis is kept orthogonal to the reflectors in all trial velocity models. It is also assumed that the velocity VP0 is either known at the top of each block or remains continuous in the vertical direction. The velocity analysis algorithm estimates the velocity gradients kz and kx and the anisotropy parameters ε and δ in the layer‐stripping mode using a generalized version of the method introduced by Sarkar and Tsvankin for factorized transverse isotropy with a vertical symmetry axis. Synthetic tests for several models typical in exploration (a syncline, uptilted shale layers near a salt dome and a bending shale layer) confirm that if the symmetry‐axis direction is fixed and VP0 is known, the parameters kz, kx, ε and δ can be resolved from reflection data. It should be emphasized that estimation of ε in tilted transversely isotropic media requires using nonhyperbolic moveout for long offsets reaching at least twice the reflector depth. We also demonstrate that application of processing algorithms designed for a vertical symmetry axis to data from tilted transversely isotropic media may lead to significant misfocusing of reflectors and errors in parameter estimation, even when the tilt is moderate (30°). The ability of our velocity analysis algorithm to separate the anisotropy parameters from the velocity gradients can be also used in lithology discrimination and geologic interpretation of seismic data in complex areas.  相似文献   

14.
Anisotropy is often observed due to the thin layering or aligned micro‐structures, like small fractures. At the scale of cross‐well tomography, the anisotropic effects cannot be neglected. In this paper, we propose a method of full‐wave inversion for transversely isotropic media and we test its robustness against structured noisy data. Optimization inversion techniques based on a least‐square formalism are used. In this framework, analytical expressions of the misfit function gradient, based on the adjoint technique in the time domain, allow one to solve the inverse problem with a high number of parameters and for a completely heterogeneous medium. The wave propagation equation for transversely isotropic media with vertical symmetry axis is solved using the finite difference method on the cylindrical system of coordinates. This system allows one to model the 3D propagation in a 2D medium with a revolution symmetry. In case of approximately horizontal layering, this approximation is sufficient. The full‐wave inversion method is applied to a crosswell synthetic 2‐component (radial and vertical) dataset generated using a 2D model with three different anisotropic regions. Complex noise has been added to these synthetic observed data. This noise is Gaussian and has the same amplitude f?k spectrum as the data. Part of the noise is localized as a coda of arrivals, the other part is not localized. Five parameter fields are estimated, (vertical) P‐wave velocity, (vertical) S‐wave velocity, volumetric mass and the Thomsen anisotropic parameters epsilon and delta. Horizontal exponential correlations have been used. The results show that the full‐wave inversion of cross‐well data is relatively robust for high‐level noise even for second‐order parameters such as Thomsen epsilon and delta anisotropic parameters.  相似文献   

15.
结合有限差分方法和等效介质理论,模拟了离散分布裂缝介质中地震波的传播. 基于等效介质理论,利用二维有限差分实现封闭裂缝的离散分布;裂缝可以处理成固体岩石中的高度柔性界面,并可以用线性滑动或者位移间断模型进行裂缝的物理描述. 对于含有多组裂隙的破裂固体,其有效柔度可以认为是固体骨架背景柔度和裂缝附加柔度之和. 在一阶近似条件下,固体骨架和裂缝参数可以通过有效各向异性系数联系起来,有效各向异性系数决定了各向异性（裂缝效应）对于地震波传播的影响. 通过与射线理论方法的对比检验,说明本文提出的模拟方法的有效性,并通过几个数值算例说明本方法可有效模拟不同的裂缝分布效应. 结果表明,即使在裂缝密度很小的情况下,具有相同裂缝密度的不同的空间分布可以产生不同的波场特征. 同时,也验证了不同裂缝尺度对波长的不同影响,以及裂缝尺度具有幂率分布（分形）时,尺度对波场的影响. 最后得出结论：在运用建立在等效介质理论基础上的地震各向异性概念来描述裂缝固体的特征时,要倍加小心,等效介质理论中尚未合理处理的裂缝尺度和空间分布对波的传播特征具有重要的影响.  相似文献   

16.
The detection and characterisation of domains of intersecting fractures are important goals in several disciplines of current interest, including exploration and production of unconventional reservoirs, nuclear waste storage, CO2 sequestration, and groundwater hydrology, among others. The objective of this study is to propose a theoretical framework for quantifying the effects of fracture intersections on the frequency‐dependent elastic properties of fluid‐saturated porous and fractured rocks. Three characteristic frequency regimes for fluid pressure communication are identified. In the low‐frequency limit, fractures are in full pressure communication with the embedding porous matrix and with other fractures. Conversely, in the high‐frequency limit, fractures are hydraulically isolated from the matrix and from other fractures. At intermediate frequencies, fractures are hydraulically isolated from the matrix porosity but can be in hydraulic communication with each other, depending on whether fracture sets are intersecting. For each frequency regime, the effective stiffness coefficients are derived using the linear‐slip theory and anisotropic Gassmann equations. Explicit mathematical expressions for the two characteristic frequencies that separate the three frequency regimes are also determined. Theoretical predictions are then applied to two synthetic 2D samples, each containing two orthogonal fracture sets: one with and another without intersections. The resulting stiffness coefficients, Thomsen‐style anisotropy parameters, and the transition frequencies show good agreement with corresponding numerical simulations. The theoretical results are applicable not only to 2D but also to 3D fracture systems and are amenable to being employed in inversion schemes designed to characterise fracture systems.  相似文献   

17.
Permeability is a second rank tensor relating flow rate to pressure gradient in a porous medium. If the permeability is a constant times the identity tensor the permeable medium is isotropic; otherwise it is anisotropic. A formalism is presented for the simple calculation of the permeability tensor of a heterogeneous layered system composed of interleaved thin layers of several permeable constituent porous media in the static limit. Corresponding to any cumulative thickness H of a constituent is an element consisting of scalar H and a matrix which is H times a hybrid matrix function of permeability. The calculation of the properties of a medium equivalent to the combination of permeable constituents may then be accomplished by simple addition of the corresponding scalar/matrix elements. Subtraction of an element removes a permeable constituent, providing the means to decompose a permeable medium into many possible sets of permeable constituents, all of which have the same flow properties. A set of layers of a constituent medium in the heterogeneous layered system with permeability of the order of 1/h as h→ 0, where h is that constituent's concentration, acts as a set of infinitely thin channels and is a model for a set of parallel cracks or fractures. Conversely, a set of layers of a given constituent with permeability of the order of h as h→ 0 acts as a set of parallel flow barriers and models a set of parallel, relatively impermeable, interfaces, such as shale stringers or some faults. Both sets of channels and sets of barriers are defined explicitly by scalar/matrix elements for which the scalar and three of the four sub-matrices vanish. Further, non-parallel sets of channels or barriers can be ‘added’ and 'subtracted’ from a background homogeneous anisotropic medium commutatively and associatively, but not non-parallel sets of channels and barriers reflecting the physical reality that fractures that penetrate barriers will give a different flow behaviour from barriers that block channels. This analysis of layered media, and the representations of the phenomena that can occur as the thickness of a constituent is allowed to approach zero, are applicable directly to layered heat conductors, layered electrostatic conductors and layered dielectrics.  相似文献   

18.
We analysed the complications in laboratory velocity anisotropy measurement on shales. There exist significant uncertainties in the laboratory determination of c13 and Thomsen parameter δ. These uncertainties are primarily related to the velocity measurement in the oblique direction. For reliable estimation of c13 and δ, it is important that genuine phase velocity or group velocity be measured with minimum uncertainty. The uncertainties can be greatly reduced if redundant oblique velocities are measured. For industrial applications, it is impractical to make multiple oblique velocity measurements on multiple core plugs. We demonstrated that it is applicable to make multiple genuine oblique group velocity measurements on a single horizontal core plug. The measurement results show that shales can be classified as a typical transversely isotropic medium. There is a coupling relation between c44 and c13 in determining the directional dependence of the seismic velocities. The quasi‐P‐wave or quasi‐S‐wave velocities can be approximated by three elastic parameters.  相似文献   

19.
The elastic moduli and anisotropy of organic-rich rocks are of great importance to geoengineering and geoprospecting of oil and gas reservoirs. In this paper, we probe into the static and dynamic moduli of the Ghareb–Mishash chalk through laboratory measurements and new analytical approaches. We define a new anisotropy parameter, ‘hydrostatic strain ratio’ (Ω), which describes the differential contraction of anisotropic rocks consequent to hydrostatic compression. Ω depends on the C11, C12, C13 and C33 stiffness constants of a transversely isotropic material, and therefore enables a unique insight into the anisotropic behaviour of TI rocks. Ω proves more sensitive to anisotropy within the weak anisotropy range, when compared with Thomsen's ε and γ parameters. We use Ω to derive static moduli from triaxial compression tests performed on a single specimen. This is done by novel employment of a hydrostatic-deviatoric combination for transversely isotropic elastic stiffnesses. Dynamic moduli are obtained from acoustic velocities measurements. We find that the bedding-normal velocities are described well by defining kerogen as the load-supporting matrix in a Hashin–Shtrikman model (‘Hashin–Shtrikman (HS) kerogen’). The dynamic moduli of the Ghareb–Mishash chalk in dry conditions are significantly higher than the static moduli. The dynamic/static moduli ratio decreases from ∼4 to ∼2 with increasing kerogen content. Both the static and dynamic moduli decrease significantly with increasing porosity and kerogen content. The effect of porosity on them is two times stronger than the effect of kerogen.  相似文献   

20.
Multiple vertical fracture sets, possibly combined with horizontal fine layering, produce an equivalent medium of monoclinic symmetry with a horizontal symmetry plane. Although monoclinic models may be rather common for fractured formations, they have hardly been used in seismic methods of fracture detection due to the large number of independent elements in the stiffness tensor. Here, we show that multicomponent wide-azimuth reflection data (combined with known vertical velocity or reflector depth) or multi-azimuth walkaway VSP surveys provide enough information to invert for all but one anisotropic parameters of monoclinic media. In order to facilitate the inversion procedure, we introduce a Thomsen-style parametrization for monoclinic media that includes the vertical velocities of the P-wave and one of the split S-waves and a set of dimensionless anisotropic coefficients. Our notation, defined for the coordinate frame associated with the polarization directions of the vertically propagating shear waves, captures the combinations of the stiffnesses responsible for the normal-moveout (NMO) ellipses of all three pure modes. The first group of the anisotropic parameters contains seven coefficients (ε(1,2), δ(1,2,3) and γ(1,2)) analogous to those defined by Tsvankin for the higher-symmetry orthorhombic model. The parameters ε(1,2), δ(1,2) and γ(1,2) are primarily responsible for the pure-mode NMO velocities along the coordinate axes x1 and x2 (i.e. in the shear-wave polarization directions). The remaining coefficient δ(3) is not constrained by conventional-spread reflection traveltimes in a horizontal monoclinic layer. The second parameter group consists of the newly introduced coefficients ζ(1,2,3) which control the rotation of the P-, S1- and S2-wave NMO ellipses with respect to the horizontal coordinate axes. Misalignment of the P-wave NMO ellipse and shear-wave polarization directions was recently observed on field data by Pérez et al. Our parameter-estimation algorithm, based on NMO equations valid for any strength of the anisotropy, is designed to obtain anisotropic parameters of monoclinic media by inverting the vertical velocities and NMO ellipses of the P-, S1- and S2-waves. A Dix-type representation of the NMO velocity of mode-converted waves makes it possible to replace the pure shear modes in reflection surveys with the PS1- and PS2-waves. Numerical tests show that our method yields stable estimates of all relevant parameters for both a single layer and a horizontally stratified monoclinic medium.  相似文献   

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