共查询到20条相似文献,搜索用时 664 毫秒
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Michael A. Slawinski Michael P. Lamoureux Raphael A. Slawinski R. James Brown 《Geophysical Prospecting》2003,51(2):131-140
We present a method for calculating the anisotropy parameter of a buried layer by inverting the total traveltimes of direct arrivals travelling from a surface source to a well‐bore receiver in a vertical seismic profiling (VSP) geometry. The method assumes two‐dimensional media. The medium above the layer of interest (and separated from it by a horizontal interface) can exhibit both anisotropy and inhomogeneity. Both the depth of the interface as well as the velocity field of the overburden are assumed to be known. We assume the layer of interest to be homogeneous and elliptically anisotropic, with the anisotropy described by a single parameter χ. We solve the function describing the traveltime between source and receiver explicitly for χ. The solution is expressed in terms of known quantities, such as the source and receiver locations, and in terms of quantities expressed as functions of the single argument xr, which is the horizontal coordinate of the refraction point on the interface. In view of Fermat's principle, the measured traveltime T possesses a stationary value or, considering direct arrivals, a minimum value, . This gives rise to a key result ‐‐ the condition that the actual anisotropy parameter . Owing to the explicit expression , this result allows a direct calculation of in the layer of interest. We perform an error analysis and show this inverse method to be stable. In particular, for horizontally layered media, a traveltime error of one millisecond results in a typical error of about 20% in the anisotropy parameter. This is almost one order of magnitude less than the error inherent in the slowness method, which uses a similar set of experimental data. We conclude by detailing possible extensions to non‐elliptical anisotropy and a non‐planar interface. 相似文献
3.
R.C. JOHNSTON 《Geophysical Prospecting》1980,28(5):700-715
Air guns have been used in various applications for a number of years. They were first used in coal-mining operations and were operated at up to 16000 psi charge pressures. Later, single air guns, operated at 2000 psi, found application as an oceanographic survey tool. Air gun arrays were first used in offshore seismic exploration in the mid-1960's. These early arrays were several hundred cubic inches in total volume and were operated at 2000 psi; they were either tuned arrays or several large guns of the same size with wave-shape kits. Today's arrays have total volumes greater than 5000 cu in. and are typically operated at 2000 psi. Recently, higher-pressure, lower-volume arrays operated at 4000–5000 psi have been introduced; guns used in these arrays are descendants of the coal-mining gun. On first thought one would equate increased gun pressure linearly with the amplitude of the initial pulse. This is approximately true for the signature radiated by a “free-bubble” (no confining vessel) and recorded broadband. The exact relation depends on the depth at which the gun is operated; from solution of the free-bubble oscillation equation, the relation is If Pc,1= 6014.7 psia, Pc,2= 2014.7 psia and PO, 1=PO, 2= 25.8 psia (corresponding to absolute pressure at 25 ft water depth), then Experiments were conducted offshore California in deep water to determine the performance of several models of air guns at pressures ranging from 2000 to 6000 psi and gun volumes ranging from 5 to 300 cu in. At a given gun pressure, the initial acoustic pulse Pa correlated with gun volume Vc according to the classical relation For 1 ms sampled data the ratio varied between 4.5 and 5.5 dB depending on gun model. Pulse width of the 2000 psi signatures indicated they are compatible with 2 ms sample-rate recording while pulse width of the 6000 psi signatures was greater, indicating they are less compatible with 2 ms sample-rate recording. Conclusions reached were that 2000 psi air guns are more efficient than higher pressure guns and are more compatible with 2 ms sample-rate requirements. 相似文献
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Common‐midpoint moveout of converted waves is generally asymmetric with respect to zero offset and cannot be described by the traveltime series t2(x2) conventionally used for pure modes. Here, we present concise parametric expressions for both common‐midpoint (CMP) and common‐conversion‐point (CCP) gathers of PS‐waves for arbitrary anisotropic, horizontally layered media above a plane dipping reflector. This analytic representation can be used to model 3D (multi‐azimuth) CMP gathers without time‐consuming two‐point ray tracing and to compute attributes of PS moveout such as the slope of the traveltime surface at zero offset and the coordinates of the moveout minimum. In addition to providing an efficient tool for forward modelling, our formalism helps to carry out joint inversion of P and PS data for transverse isotropy with a vertical symmetry axis (VTI media). If the medium above the reflector is laterally homogeneous, P‐wave reflection moveout cannot constrain the depth scale of the model needed for depth migration. Extending our previous results for a single VTI layer, we show that the interval vertical velocities of the P‐ and S‐waves (VP0 and VS0) and the Thomsen parameters ε and δ can be found from surface data alone by combining P‐wave moveout with the traveltimes of the converted PS(PSV)‐wave. If the data are acquired only on the dip line (i.e. in 2D), stable parameter estimation requires including the moveout of P‐ and PS‐waves from both a horizontal and a dipping interface. At the first stage of the velocity‐analysis procedure, we build an initial anisotropic model by applying a layer‐stripping algorithm to CMP moveout of P‐ and PS‐waves. To overcome the distorting influence of conversion‐point dispersal on CMP gathers, the interval VTI parameters are refined by collecting the PS data into CCP gathers and repeating the inversion. For 3D surveys with a sufficiently wide range of source–receiver azimuths, it is possible to estimate all four relevant parameters (VP0, VS0, ε and δ) using reflections from a single mildly dipping interface. In this case, the P‐wave NMO ellipse determined by 3D (azimuthal) velocity analysis is combined with azimuthally dependent traveltimes of the PS‐wave. On the whole, the joint inversion of P and PS data yields a VTI model suitable for depth migration of P‐waves, as well as processing (e.g. transformation to zero offset) of converted waves. 相似文献
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Franklyn K. Levin 《Geophysical Prospecting》1995,43(6):831-841
A simple expression ties the midpoint of a surface spread to reflection points on a dipping plane. If we use two coordinate systems, an unprimed one with a z-axis perpendicular to the surface and a primed one with a z-axis perpendicular to the reflector, we have where θ is the dip angle, φ is the profile angle, X is the source-to-receiver separation, and D is the depth of the reflector. The reflection point is (x, yp, D) and the surface midpoint is (xc, yc, 0). Using the expression, I show that if complete azimuthal coverage is required at a CMP position, the reflection points lie on an ellipse. Similarly, a fixed reflection point generates a circle of surface midpoints. A circle of CMP positions for fixed θ and φ becomes an ellipse of reflection points and a circle of reflection points becomes an ellipse of midpoints. A user can easily find the shape and location of the reflection area generated by a surface aperture. 相似文献
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The azimuthally varying non‐hyperbolic moveout of P‐waves in orthorhombic media can provide valuable information for characterization of fractured reservoirs and seismic processing. Here, we present a technique to invert long‐spread, wide‐azimuth P‐wave data for the orientation of the vertical symmetry planes and five key moveout parameters: the symmetry‐plane NMO velocities, V(1)nmo and V(2)nmo , and the anellipticity parameters, η(1), η(2) and η(3) . The inversion algorithm is based on a coherence operator that computes the semblance for the full range of offsets and azimuths using a generalized version of the Alkhalifah–Tsvankin non‐hyperbolic moveout equation. The moveout equation provides a close approximation to the reflection traveltimes in layered anisotropic media with a uniform orientation of the vertical symmetry planes. Numerical tests on noise‐contaminated data for a single orthorhombic layer show that the best‐constrained parameters are the azimuth ? of one of the symmetry planes and the velocities V(1)nmo and V(2)nmo , while the resolution in η(1) and η(2) is somewhat compromised by the trade‐off between the quadratic and quartic moveout terms. The largest uncertainty is observed in the parameter η(3) , which influences only long‐spread moveout in off‐symmetry directions. For stratified orthorhombic models with depth‐dependent symmetry‐plane azimuths, the moveout equation has to be modified by allowing the orientation of the effective NMO ellipse to differ from the principal azimuthal direction of the effective quartic moveout term. The algorithm was successfully tested on wide‐azimuth P‐wave reflections recorded at the Weyburn Field in Canada. Taking azimuthal anisotropy into account increased the semblance values for most long‐offset reflection events in the overburden, which indicates that fracturing is not limited to the reservoir level. The inverted symmetry‐plane directions are close to the azimuths of the off‐trend fracture sets determined from borehole data and shear‐wave splitting analysis. The effective moveout parameters estimated by our algorithm provide input for P‐wave time imaging and geometrical‐spreading correction in layered orthorhombic media. 相似文献
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Inspired by the linear filter method introduced by D. P. Ghosh in 1970 we have developed a general theory for numerical evaluation of integrals of the Hankel type: Replacing the usual sine interpolating function by sinsh (x) =a· sin (ρx)/sinh (aρx), where the smoothness parameter a is chosen to be “small”, we obtain explicit series expansions for the sinsh-response or filter function H*. If the input function f(λ exp (iω)) is known to be analytic in the region o < λ < ∞, |ω|≤ω0 of the complex plane, we can show that the absolute error on the output function is less than (K(ω0)/r) · exp (?ρω0/Δ), Δ being the logarthmic sampling distance. Due to the explicit expansions of H* the tails of the infinite summation ((m?n)Δ) can be handled analytically. Since the only restriction on the order is ν > ? 1, the Fourier transform is a special case of the theory, ν=± 1/2 giving the sine- and cosine transform, respectively. In theoretical model calculations the present method is considerably more efficient than the Fast Fourier Transform (FFT). 相似文献
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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
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Breakthrough characteristics, kinetics, and dose‐effect in defluoridation with bauxite, gypsum, magnesite, and their composites were determined. The aim was to identify optimum filter and configuration viable for groundwater defluoridation. Bed depth service time (BDST) design model and empty bed residence time (EBRT) optimization model were employed to characterize breakthrough. Higher doses obtained lower loading capacities but higher sorption percentages and breakthrough times. Breakthrough times obtained were 50 400, 32 400, 25 200, and 19 800 s for 150, 120, 75, and 45 g, respectively. The equation ? = 1.0 × 10?4 δ2 ?0.022 δ + 1.5053 defined the operating line with ?, adsorbent exhaustion rate, in g L?1 and δ, EBRT, in seconds. A critical bed depth (Zo) of 6.56 cm was obtained. Second order kinetic rate constants were 0.73, 1.17, and 1.81 g mg?1 s?1 for magnesite, gypsum, and bauxite, respectively. The composite, gypsum and bauxite decreased water pH but magnesite increased pH in water defluoridation. Experimental data did not fit the two‐parameter logistics model; model values were significantly different from experimental values. Optimum defluoridation characteristics were obtained in fixed bed. Despite high residual sulphates and apparent color, fixed‐bed defluoridation with raw composites of these materials, treated in this manner, is viable. 相似文献
10.
It is advantageous to postulate the phenomenological equivalence of chargeability with a slight increase in resistivities rather than a similar reduction in the conductivities. Substitution of these increments in the expression for the total differential of apparent resistivity leads directly to Seigel's formula. Included also are (i) an equally simple demonstration that, for a homogeneously chargeable ground with arbitrary resistivity distribution, the apparent chargeability ma, equals the true homogeneous value m, and (ii) a direct derivation of the completely general resistivity relation where the symbols have the usual meanings. 相似文献
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Analysis of Thomsen parameters for finely layered VTI media 总被引:2,自引:0,他引:2
James G. Berryman Vladimir Y. Grechka & Patricia A. Berge 《Geophysical Prospecting》1999,47(6):959-978
Since the work of Postma and Backus, much has been learned about elastic constants in vertical transversely isotropic (VTI) media when the anisotropy is due to fine layering of isotropic elastic materials. Nevertheless, there has continued to be some uncertainty about the possible range of Thomsen's anisotropy parameters ε and δ for such media. We use both Monte Carlo studies and detailed analysis of Backus' equations for both two- and three-component layered media to establish the results presented. We show that ε lies in the range ?3/8 ε ½[〈v2p〉〈v?2p〉?1], for finely layered media; smaller positive and all negative values of ε occur for media with large fluctuations in the Lamé parameter λ in the component layers. We show that δ can also be either positive or negative, and that for constant density media, sign (δ) = sign (〈v?2p〉 ? 〈v?2s〉〈v2s/v2p〉). Monte Carlo simulations show that among all theoretically possible random media, positive and negative δ are equally likely in finely layered media. (Of course, the δs associated with real earth materials may span some smaller subset of those that are theoretically possible, but answering this important question is beyond our present scope.) Layered media having large fluctuations in λ are those most likely to have positive δ. This is somewhat surprising since ε is often negative or a small positive number for such media, and we have the general constraint that ε ? δ > 0 for layered VTI media. Since Gassmann's results for fluid-saturated porous media show that the mechanical effects of fluids influence only the Lamé parameter λ, not the shear modulus μ, these results suggest that small positive δ occurring together with small positive ε (but somewhat larger than δ) may be indicative of changing fluid content in a layered earth. 相似文献
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A major complication caused by anisotropy in velocity analysis and imaging is the uncertainty in estimating the vertical velocity and depth scale of the model from surface data. For laterally homogeneous VTI (transversely isotropic with a vertical symmetry axis) media above the target reflector, P‐wave moveout has to be combined with other information (e.g. borehole data or converted waves) to build velocity models for depth imaging. The presence of lateral heterogeneity in the overburden creates the dependence of P‐wave reflection data on all three relevant parameters (the vertical velocity VP0 and the Thomsen coefficients ε and δ) and, therefore, may help to determine the depth scale of the velocity field. Here, we propose a tomographic algorithm designed to invert NMO ellipses (obtained from azimuthally varying stacking velocities) and zero‐offset traveltimes of P‐waves for the parameters of homogeneous VTI layers separated by either plane dipping or curved interfaces. For plane non‐intersecting layer boundaries, the interval parameters cannot be recovered from P‐wave moveout in a unique way. Nonetheless, if the reflectors have sufficiently different azimuths, a priori knowledge of any single interval parameter makes it possible to reconstruct the whole model in depth. For example, the parameter estimation becomes unique if the subsurface layer is known to be isotropic. In the case of 2D inversion on the dip line of co‐orientated reflectors, it is necessary to specify one parameter (e.g. the vertical velocity) per layer. Despite the higher complexity of models with curved interfaces, the increased angle coverage of reflected rays helps to resolve the trade‐offs between the medium parameters. Singular value decomposition (SVD) shows that in the presence of sufficient interface curvature all parameters needed for anisotropic depth processing can be obtained solely from conventional‐spread P‐wave moveout. By performing tests on noise‐contaminated data we demonstrate that the tomographic inversion procedure reconstructs both the interfaces and the VTI parameters with high accuracy. Both SVD analysis and moveout inversion are implemented using an efficient modelling technique based on the theory of NMO‐velocity surfaces generalized for wave propagation through curved interfaces. 相似文献
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S.A. Horne 《Geophysical Prospecting》2013,61(4):817-826
Mudrocks, defined to be fine‐grained siliclastic sedimentary rocks such as siltstones, claystones, mudstones and shales, are often anisotropic due to lamination and microscopic alignments of clay platelets. The resulting elastic anisotropy is often non‐negligible for many applications in the earth sciences such as wellbore stability, well stimulation and seismic imaging. Anisotropic elastic properties reported in the open literature have been compiled and statistically analysed. Correlations between elastic parameters are observed, which will be useful in the typical case that limited information on a rock's elastic properties is known. For example, it is observed that the highest degree of correlation is between the horizontal elastic stiffnesses C11 and C66. The results of statistical analysis are generally consistent with prior observations. In particular, it is observed that Thomsen's ? and γ parameters are almost always positive, Thomsen's ? and γ parameters are well correlated, Thomsen's δ is most frequently small and Thomsen's ? is generally larger than Thomsen's δ. These observations suggest that the typical range for the elastic properties of mudrocks span a sub‐space less than the five elastic constants required to fully define a Vertical Transversel Isotropic medium. Principal component analysis confirms this and that four principal components can be used to span the space of observed elastic parameters. 相似文献
14.
A Bremmer Series decomposition of the solution y(t) to the lossless wave equation in layered media is where the yj(t) are physically meaningful constituents (i.e., y1(t) are primaries, y2(t) are secondaries, etc.). This paper reviews Mendel's state space models for generating the constituents; reviews Bremmer's integral equation models for generating the constituents; and demonstrates how Mendel's state space models can be obtained by a careful decomposition of Bremmer's integral equation models. It shows that Mendel's equations can be viewed as approximate numerical solutions of Bremmer's integral equations. In a lossless homogeneous medium, the approximations become exact. 相似文献
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A. TARANTOLA 《Geophysical Prospecting》1984,32(6):998-1015
This is the first of a series of papers giving the solution of the inverse problem in seismic exploration. The acoustic approximation is used together with the assumption that the velocity field has the form . The forward problem is then linearized (thus neglecting multiple reflected waves) and the inverse problem of estimating δ is set up. Its rigorous solution can be obtained using an iterative algorithm, each step consisting of a classical Kirchhoff migration (hyperbola summation) plus a classical forward modeling step (circle summation). 相似文献
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Fluid permeability in fractured rocks is sensitive to pore-pressure changes. This dependence can have large effects on the flow of fluids through rocks. We define the permeability compliance γ= 1/k(k/δpp)pc, which is the sensitivity of the permeability k to the pore pressure pp at a constant confining pressure pc, and solve the specific problems of constant pressure at the boundary of a half-space, a cylindrical cavity and a spherical cavity. The results show that when the magnitude of permeability compliance is large relative to other compliances, diffusion is masked by a piston-like pressure profile. We expect this phenomenon to occur in highly fractured and compliant rock systems where γ may be large. The pressure profile moves rapidly when fluids are pumped into the rock and very slowly when fluids are pumped out. Consequently, fluid pressure, its history and distribution around injection and production wells may be significantly different from pressures predicted by the linear diffusion equation. The propagation speed of the pressure profile, marked by the point where δpp/δx is a maximum, decreases with time approximately as and the amplitude of the profile also dissipates with time (or distance). The effect of permeability compliance can be important for fluid injection into and withdrawal from reservoirs. For example, excessive drawdown could cause near-wellbore flow suffocation. Also, estimates of the storage capacity of reservoirs may be greatly modified when γ is large. The large near-wellbore pressure gradients caused during withdrawal by large γ can cause sanding and wellbore collapse due to excessive production rates. 相似文献
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Based on the theory of anisotropic elasticity and observation of static mechanic measurement of transversely isotropic hydrocarbon source rocks or rock‐like materials, we reasoned that one of the three principal Poisson's ratios of transversely isotropic hydrocarbon source rocks should always be greater than the other two and they should be generally positive. From these relations, we derived tight physical constraints on c13, Thomsen parameter δ, and anellipticity parameter η. Some of the published data from laboratory velocity anisotropy measurement are lying outside of the constraints. We analysed that they are primarily caused by substantial uncertainty associated with the oblique velocity measurement. These physical constraints will be useful for our understanding of Thomsen parameter δ, data quality checking, and predicting δ from measurements perpendicular and parallel to the symmetrical axis of transversely isotropic medium. The physical constraints should also have potential application in anisotropic seismic data processing. 相似文献
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I. Introduction In this section the problem is stated, its physical and mathematical difficulties are indicated, and the way the authors try to overcome them are briefly outlined. Made up of a few measurements of limited accuracy, an electrical sounding does not define a unique solution for the variation of the earth resistivities, even in the case of an isotropic horizontal layering. Interpretation (i.e. the determination of the true resistivities and thicknesses of the ground-layers) requires, therefore, additional information drawn from various more or less reliable geological or other geophysical sources. The introduction of such information into an automatic processing is rather difficult; hence the authors developped a two-stage procedure:
- a) the field measurements are automatically processed, without loss of information, into more easily usable data;
- b) some additional information is then introduced, permitting the determination of several geologically conceivable solutions.
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Velocity model updating in prestack Kirchhoff time migration for PS converted waves: Part I – Theory
A velocity model updating approach is developed based on moveout analysis of the diffraction curve of PS converted waves in prestack Kirchhoff time migration. The diffraction curve can be expressed as a product of two factors: one factor depending on the PS converted‐wave velocity only, and the other factor depending on all parameters. The velocity‐dependent factor represents the hyperbolic behaviour of the moveout and the other is a scale factor that represents the non‐hyperbolic behaviour of the moveout. This non‐hyperbolic behaviour of the moveout can be corrected in prestack Kirchhoff time migration to form an inverse normal‐moveout common‐image‐point gather in which only the hyperbolic moveout is retained. This hyperbolic moveout is the moveout that would be obtained in an isotropic equivalent medium. A hyperbolic velocity is then estimated from this gather by applying hyperbolic moveout analysis. Theoretical analysis shows that for any given initial velocity, the estimated hyperbolic velocity converges by an iterative procedure to the optimal velocity if the velocity ratio is optimal or to a value closer to the optimal velocity if the velocity ratio is not optimal. The velocity ratio (VP/VS) has little effect on the estimation of the velocity. Applying this technique to a synthetic seismic data set confirms the theoretical findings. This work provides a practical method to obtain the velocity model for prestack Kirchhoff time migration. 相似文献