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1.
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2.
Simultaneous estimation of velocity gradients and anisotropic parameters from seismic reflection data is one of the main challenges in transversely isotropic media with a vertical symmetry axis migration velocity analysis. In migration velocity analysis, we usually construct the objective function using the l2 norm along with a linear conjugate gradient scheme to solve the inversion problem. Nevertheless, for seismic data this inversion scheme is not stable and may not converge in finite time. In order to ensure the uniform convergence of parameter inversion and improve the efficiency of migration velocity analysis, this paper develops a double parameterized regularization model and gives the corresponding algorithms. The model is based on the combination of the l2 norm and the non‐smooth l1 norm. For solving such an inversion problem, the quasi‐Newton method is utilized to make the iterative process stable, which can ensure the positive definiteness of the Hessian matrix. Numerical simulation indicates that this method allows fast convergence to the true model and simultaneously generates inversion results with a higher accuracy. Therefore, our proposed method is very promising for practical migration velocity analysis in anisotropic media.  相似文献   

3.
Multiparameter inversion for pre‐stack seismic data plays a significant role in quantitative estimation of subsurface petrophysical properties. However, it remains a complicated problem due to the non‐unique results and unstable nature of the processing; the pre‐stack seismic inversion problem is ill‐posed and band‐limited. Combining the full Zoeppritz equation and additional assumptions with edge‐preserving regularisation can help to alleviate these problems. To achieve this, we developed an inversion method by constructing a new objective function that includes edge‐preserving regularisation and soft constraints based on anisotropic Markov random fields and is intended especially for layered formations. We applied a fast simulated annealing algorithm to solve the nonlinear optimisation problem. The method directly obtains reflectivity RPP values using the full Zoeppritz equation instead of its approximations and effectively controls the stability of the multiparameter inversion by assuming a sectionally constant S‐ and P‐wave velocity ratio and using the generalised Gardner equation. We substituted the inverted parameters, i.e., the P‐wave velocity, the fitting deviation of S‐wave velocity, and the density were inverted instead of the P‐wave velocity, the S‐wave velocity, and the density, and the generalised Gardner equation was applied as a constraint. Test results on two‐dimensional synthetic data indicated that our substitution obtained improved results for multiparameter inversion. The inverted results could be improved by utilising high‐order anisotropic Markov random field neighbourhoods at early stages and low‐order anisotropic Markov random field neighbourhoods in the later stages. Moreover, for layered formations, using a large horizontal weighting coefficient can preserve the lateral continuity of layers, and using a small vertical weighting coefficient allows for large longitudinal gradients of the interlayers. The inverted results of the field data revealed more detailed information about the layers and matched the logging curves at the wells acceptably over most parts of the curves.  相似文献   

4.
Seismic inversion plays an important role in reservoir modelling and characterisation due to its potential for assessing the spatial distribution of the sub‐surface petro‐elastic properties. Seismic amplitude‐versus‐angle inversion methodologies allow to retrieve P‐wave and S‐wave velocities and density individually allowing a better characterisation of existing litho‐fluid facies. We present an iterative geostatistical seismic amplitude‐versus‐angle inversion algorithm that inverts pre‐stack seismic data, sorted by angle gather, directly for: density; P‐wave; and S‐wave velocity models. The proposed iterative geostatistical inverse procedure is based on the use of stochastic sequential simulation and co‐simulation algorithms as the perturbation technique of the model parametre space; and the use of a genetic algorithm as a global optimiser to make the simulated elastic models converge from iteration to iteration. All the elastic models simulated during the iterative procedure honour the marginal prior distributions of P‐wave velocity, S‐wave velocity and density estimated from the available well‐log data, and the corresponding joint distributions between density versus P‐wave velocity and P‐wave versus S‐wave velocity. We successfully tested and implemented the proposed inversion procedure on a pre‐stack synthetic dataset, built from a real reservoir, and on a real pre‐stack seismic dataset acquired over a deep‐water gas reservoir. In both cases the results show a good convergence between real and synthetic seismic and reliable high‐resolution elastic sub‐surface Earth models.  相似文献   

5.
Elastic full waveform inversion of seismic reflection data represents a data‐driven form of analysis leading to quantification of sub‐surface parameters in depth. In previous studies attention has been given to P‐wave data recorded in the marine environment, using either acoustic or elastic inversion schemes. In this paper we exploit both P‐waves and mode‐converted S‐waves in the marine environment in the inversion for both P‐ and S‐wave velocities by using wide‐angle, multi‐component, ocean‐bottom cable seismic data. An elastic waveform inversion scheme operating in the time domain was used, allowing accurate modelling of the full wavefield, including the elastic amplitude variation with offset response of reflected arrivals and mode‐converted events. A series of one‐ and two‐dimensional synthetic examples are presented, demonstrating the ability to invert for and thereby to quantify both P‐ and S‐wave velocities for different velocity models. In particular, for more realistic low velocity models, including a typically soft seabed, an effective strategy for inversion is proposed to exploit both P‐ and mode‐converted PS‐waves. Whilst P‐wave events are exploited for inversion for P‐wave velocity, examples show the contribution of both P‐ and PS‐waves to the successful recovery of S‐wave velocity.  相似文献   

6.
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   

7.
By applying seismic inversion, we can derive rock impedance from seismic data. Since it is an interval property, impedance is valuable for reservoir characterization. Furthermore, the decomposition of the impedance into two fundamental properties, i.e. velocity and density, provides a link to the currently available rock‐physics applications to derive quantitative reservoir properties. However, the decomposition is a challenging task due to the strong influence of noise, especially for seismic data with a maximum offset angle of less than 30°. We present a method of impedance decomposition using three elastic impedance data derived from the seismic inversion of angle stacks, where the far‐stack angle is 23.5°. We discuss the effect of noise on the analysis as being the most significant cause of making the decomposition difficult. As the result, the offset‐consistent component of noise mostly affects the determination of density but not the velocities (P‐ and S‐wave), whereas the effect of the random component of noise occurs equally in the determination of the velocities and density. The effect is controlled by the noise enhancement factor 1/A, which is determined by a combination of stack angles. Based on the results of the analysis, we show an innovative method of decomposition incorporating rock‐physics bounds as constraints for the analysis. The method is applied to an actual data set from an offshore oilfield; we demonstrate the result of analysis for sandbody detection.  相似文献   

8.
A series of time‐lapse seismic cross‐well and single‐well experiments were conducted in a diatomite reservoir to monitor the injection of CO2 into a hydrofracture zone, based on P‐ and S‐wave data. A high‐frequency piezo‐electric P‐wave source and an orbital‐vibrator S‐wave source were used to generate waves that were recorded by hydrophones as well as 3‐component geophones. During the first phase the set of seismic experiments was conducted after the injection of water into the hydrofractured zone. The set of seismic experiments was repeated after a time period of seven months during which CO2 was injected into the hydrofractured zone. The questions to be answered ranged from the detectability of the geological structure in the diatomic reservoir to the detectability of CO2 within the hydrofracture. Furthermore, it was intended to determine which experiment (cross‐well or single‐well) is best suited to resolve these features. During the pre‐injection experiment, the P‐wave velocities exhibited relatively low values between 1700 and 1900 m/s, which decreased to 1600–1800 m/s during the post‐injection phase (?5%). The analysis of the pre‐injection S‐wave data revealed slow S‐wave velocities between 600 and 800 m/s, while the post‐injection data revealed velocities between 500 and 700 m/s (?6%). These velocity estimates produced high Poisson's ratios between 0.36 and 0.46 for this highly porous (～50%) material. Differencing post‐ and pre‐injection data revealed an increase in Poisson's ratio of up to 5%. Both velocity and Poisson's ratio estimates indicate the dissolution of CO2 in the liquid phase of the reservoir accompanied by an increase in pore pressure. The single‐well data supported the findings of the cross‐well experiments. P‐ and S‐wave velocities as well as Poisson's ratios were comparable to the estimates of the cross‐well data. The cross‐well experiment did not detect the presence of the hydrofracture but appeared to be sensitive to overall changes in the reservoir and possibly the presence of a fault. In contrast, the single‐well reflection data revealed an arrival that could indicate the presence of the hydrofracture between the source and receiver wells, while it did not detect the presence of the fault, possibly due to out‐of‐plane reflections.  相似文献   

9.
AVO investigations of shallow marine sediments   总被引：2，自引：0，他引：2  
Amplitude‐variation‐with‐offset (AVO) analysis is based on the Zoeppritz equations, which enable the computation of reflection and transmission coefficients as a function of offset or angle of incidence. High‐frequency (up to 700 Hz) AVO studies, presented here, have been used to determine the physical properties of sediments in a shallow marine environment (20 m water depth). The properties that can be constrained are P‐ and S‐wave velocities, bulk density and acoustic attenuation. The use of higher frequencies requires special analysis including careful geometry and source and receiver directivity corrections. In the past, marine sediments have been modelled as elastic materials. However, viscoelastic models which include absorption are more realistic. At angles of incidence greater than 40°, AVO functions derived from viscoelastic models differ from those with purely elastic properties in the absence of a critical angle of incidence. The influence of S‐wave velocity on the reflection coefficient is small (especially for low S‐wave velocities encountered at the sea‐floor). Thus, it is difficult to extract the S‐wave parameter from AVO trends. On the other hand, P‐wave velocity and density show a considerably stronger effect. Attenuation (described by the quality factor Q) influences the reflection coefficient but could not be determined uniquely from the AVO functions. In order to measure the reflection coefficient in a seismogram, the amplitudes of the direct wave and the sea‐floor reflection in a common‐midpoint (CMP) gather are determined and corrected for spherical divergence as well as source and streamer directivity. At CMP locations showing the different AVO characteristics of a mud and a boulder clay, the sediment physical properties are determined by using a sequential‐quadratic‐programming (SQP) inversion technique. The inverted sediment physical properties for the mud are: P‐wave velocity α=1450±25 m/s, S‐wave velocity β=90±35 m/s, density ρ=1220±45 kg/m3, quality factor for P‐wave QP=15±200, quality factor for S‐wave QS=10±30. The inverted sediment physical properties for the boulder clay are: α=1620±45 m/s,β=360±200 m/s,ρ=1380±85 kg/m3,QP=790±660,QS=25±10.  相似文献   

10.
The quantitative explanation of the potential field data of three‐dimensional geological structures remains one of the most challenging issues in modern geophysical inversion. Obtaining a stable solution that can simultaneously resolve complicated geological structures is a critical inverse problem in the geophysics field. I have developed a new method for determining a three‐dimensional petrophysical property distribution, which produces a corresponding potential field anomaly. In contrast with the tradition inverse algorithm, my inversion method proposes a new model norm, which incorporates two important weighting functions. One is the L0 quasi norm (enforcing sparse constraints), and the other is depth‐weighting that counteracts the influence of source depth on the resulting potential field data of the solution. Sparseness constraints are imposed by using the L0 quasinorm on model parameters. To solve the representation problem, an L0 quasinorm minimisation model with different smooth approximations is proposed. Hence, the data space (N) method, which is much smaller than model space (M), combined with the gradient‐projected method, and the model space, combined with the modified Newton method for L0 quasinorm sparse constraints, leads to a computationally efficient method by using an N × N system versus an M × M one because N ? M. Tests on synthetic data and real datasets demonstrate the stability and validity of the L0 quasinorm spare norms inversion method. With the aim of obtaining the blocky results, the inversion method with the L0 quasinorm sparse constraints method performs better than the traditional L2 norm (standard Tikhonov regularisation). It can obtain the focus and sparse results easily. Then, the Bouguer anomaly survey data of the salt dome, offshore Louisiana, is considered as a real case study. The real inversion result shows that the inclusion the L0 quasinorm sparse constraints leads to a simpler and better resolved solution, and the density distribution is obtained in this area to reveal its geological structure. These results confirm the validity of the L0 quasinorm sparse constraints method and indicate its application for other potential field data inversions and the exploration of geological structures.  相似文献   

11.
We investigated the seismic attenuation of compressional (P‐) and converted shear (S‐) waves through stacked basalt flows using short‐offset vertical seismic profile (VSP) recordings from the Brugdan (6104/21–1) and William (6005/13–1A) wells in the Faroe‐Shetland Trough. The seismic quality factors (Q) were evaluated with the classical spectral ratio method and a root‐mean‐square time‐domain amplitude technique. We found the latter method showed more robust results when analysing signals within the basalt sequence. For the Brugdan well we calculated effective Q estimates of 22–26 and 13–17 for P‐ and S‐waves, respectively, and 25–33 for P‐waves in the William well. An effective QS/QP ratio of 0.50–0.77 was found from a depth interval in the basalt flow sequence where we expect fully saturated rocks. P‐wave quality factor estimates are consistent with results from other VSP experiments in the North Atlantic Margin, while the S‐wave quality factor is one of the first estimates from a stacked basalt formation using VSP data. Synthetic modelling demonstrates that seismic attenuation for P‐ and S‐waves in the stacked basalt flow sequence is mainly caused by one‐dimensional scattering, while intrinsic absorption is small.  相似文献   

12.
Filters for migrated offset substacks are designed by partial coherence analysis to predict ‘normal’ amplitude variation with offset (AVO) in an anomaly free area. The same prediction filters generate localized prediction errors when applied in an AVO‐anomalous interval. These prediction errors are quantitatively related to the AVO gradient anomalies in a background that is related to the minimum AVO anomaly detectable from the data. The prediction‐error section is thus used to define a reliability threshold for the identification of AVO anomalies. Coherence analysis also enables quality control of AVO analysis and inversion. For example, predictions that are non‐localized and/or do not show structural conformity may indicate spatial variations in amplitude–offset scaling, seismic wavelet or signal‐to‐noise (S/N) ratio content. Scaling and waveform variations can be identified from inspection of the prediction filters and their frequency responses. S/N ratios can be estimated via multiple coherence analysis. AVO inversion of seismic data is unstable if not constrained. However, the use of a constraint on the estimated parameters has the undesirable effect of introducing biases into the inverted results: an additional bias‐correction step is then needed to retrieve unbiased results. An alternative form of AVO inversion that avoids additional corrections is proposed. This inversion is also fast as it inverts only AVO anomalies. A spectral coherence matching technique is employed to transform a zero‐offset extrapolation or near‐offset substack into P‐wave impedance. The same technique is applied to the prediction‐error section obtained by means of partial coherence, in order to estimate S‐wave velocity to P‐wave velocity (VS/VP) ratios. Both techniques assume that accurate well ties, reliable density measurements and P‐wave and S‐wave velocity logs are available, and that impedance contrasts are not too strong. A full Zoeppritz inversion is required when impedance contrasts that are too high are encountered. An added assumption is made for the inversion to the VS/VP ratio, i.e. the Gassmann fluid‐substitution theory is valid within the reservoir area. One synthetic example and one real North Sea in‐line survey illustrate the application of the two coherence methods.  相似文献   

13.
To provide a guide for future deep (<1.5 km) seismic mineral exploration and to better understand the nature of reflections imaged by surface reflection seismic data in two mining camps and a carbonatite complex of Sweden, more than 50 rock and ore samples were collected and measured for their seismic velocities. The samples are geographically from the northern and central parts of Sweden, ranging from metallic ore deposits, meta‐volcanic and meta‐intrusive rocks to deformed and metamorphosed rocks. First, ultrasonic measurements of P‐ and S‐wave velocities at both atmospheric and elevated pressures, using 0.5 MHz P‐ and S‐wave transducers were conducted. The ultrasonic measurements suggest that most of the measured velocities show positive correlation with the density of the samples with an exception of a massive sulphide ore sample that shows significant low P‐ and S‐wave velocities. The low P‐ and S‐wave velocities are attributed to the mineral texture of the sample and partly lower pyrite content in comparison with a similar type sample obtained from Norway, which shows significantly higher P‐ and S‐wave velocities. Later, an iron ore sample from the central part of Sweden was measured using a low‐frequency (0.1–50 Hz) apparatus to provide comparison with the ultrasonic velocity measurements. The low‐frequency measurements indicate that the iron ore sample has minimal dispersion and attenuation. The iron ore sample shows the highest acoustic impedance among our samples suggesting that these deposits are favourable targets for seismic methods. This is further demonstrated by a real seismic section acquired over an iron ore mine in the central part of Sweden. Finally, a laser‐interferometer device was used to analyse elastic anisotropy of five rock samples taken from a major deformation zone in order to provide insights into the nature of reflections observed from the deformation zone. Up to 10% velocity‐anisotropy is estimated and demonstrated to be present for the samples taken from the deformation zone using the laser‐interferometery measurements. However, the origin of the reflections from the major deformation zone is attributed to a combination of anisotropy and amphibolite lenses within the deformation zone.  相似文献   

14.
Elastic rock properties can be estimated from prestack seismic data using amplitude variation with offset analysis. P‐wave, S‐wave and density ‘reflectivities’, or contrasts, can be inverted from angle‐band stacks. The ‘reflectivities’ are then inverted to absolute acoustic impedance, shear impedance and density. These rock properties can be used to map reservoir parameters through all stages of field development and production. When P‐wave contrast is small, or gas clouds obscure reservoir zones, multicomponent ocean‐bottom recording of converted‐waves (P to S or Ps) data provides reliable mapping of reservoir boundaries. Angle‐band stacks of multicomponent P‐wave (Pz) and Ps data can also be inverted jointly. In this paper Aki‐Richards equations are used without simplifications to invert angle‐band stacks to ‘reflectivities’. This enables the use of reflection seismic data beyond 30° of incident angles compared to the conventional amplitude variation with offset analysis. It, in turn, provides better shear impedance and density estimates. An important input to amplitude variation with offset analysis is the Vs/Vp ratio. Conventional methods use a constant or a time‐varying Vs/Vp model. Here, a time‐ and space‐varying model is used during the computation of the ‘reflectivities’. The Vs/Vp model is generated using well log data and picked horizons. For multicomponent data applications, the latter model can also be generated from processing Vs/Vp models and available well data. Reservoir rock properties such as λρ, μρ, Poisson's ratio and bulk modulus can be computed from acoustic impedance, shear impedance and density for pore fill and lithology identification. λ and μ are the Lamé constants and ρ is density. These estimations can also be used for a more efficient log property mapping. Vp/Vs ratio or Poisson's ratio, λρ and weighted stacks, such as the one computed from λρ and λ/μ, are good gas/oil and oil/water contact indicators, i.e., pore fill indicators, while μρ mainly indicates lithology. μρ is also affected by pressure changes. Results from a multicomponent data set are used to illustrate mapping of gas, oil and water saturation and lithology in a Tertiary sand/shale setting. Whilst initial log crossplot analysis suggested that pore fill discrimination may be possible, the inversion was not successful in revealing fluid effects. However, rock properties computed from acoustic impedance, shear impedance and density estimates provided good lithology indicators; pore fill identification was less successful. Neural network analysis using computed rock properties provided good indication of sand/shale distribution away from the existing wells and complemented the results depicted from individual rock property inversions.  相似文献   

15.
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   

16.
Converted-wave imaging in anisotropic media: theory and case studies   总被引：1，自引：0，他引：1  
Common‐conversion‐point binning associated with converted‐wave (C‐wave) processing complicates the task of parameter estimation, especially in anisotropic media. To overcome this problem, we derive new expressions for converted‐wave prestack time migration (PSTM) in anisotropic media and illustrate their applications using both 2D and 3D data examples. The converted‐wave kinematic response in inhomogeneous media with vertical transverse isotropy is separated into two parts: the response in horizontally layered vertical transverse isotrophy media and the response from a point‐scatterer. The former controls the stacking process and the latter controls the process of PSTM. The C‐wave traveltime in horizontally layered vertical transverse isotrophy media is determined by four parameters: the C‐wave stacking velocity VC2, the vertical and effective velocity ratios γ0 and γeff, and the C‐wave anisotropic parameter χeff. These four parameters are referred to as the C‐wave stacking velocity model. In contrast, the C‐wave diffraction time from a point‐scatterer is determined by five parameters: γ0, VP2, VS2, ηeff and ζeff, where ηeff and ζeff are, respectively, the P‐ and S‐wave anisotropic parameters, and VP2 and VS2 are the corresponding stacking velocities. VP2, VS2, ηeff and ζeff are referred to as the C‐wave PSTM velocity model. There is a one‐to‐one analytical link between the stacking velocity model and the PSTM velocity model. There is also a simple analytical link between the C‐wave stacking velocities VC2 and the migration velocity VCmig, which is in turn linked to VP2 and VS2. Based on the above, we have developed an interactive processing scheme to build the stacking and PSTM velocity models and to perform 2D and 3D C‐wave anisotropic PSTM. Real data applications show that the PSTM scheme substantially improves the quality of C‐wave imaging compared with the dip‐moveout scheme, and these improvements have been confirmed by drilling.  相似文献   

17.
With ill‐posed inverse problems such as Full‐Waveform Inversion, regularization schemes are needed to constrain the solution. Whereas many regularization schemes end up smoothing the model, an undesirable effect with FWI where high‐resolution maps are sought, blocky regularization does not: it identifies and preserves strong velocity contrasts leading to step‐like functions. These models might be needed for imaging with wave‐equation based techniques such as Reverse Time Migration or for reservoir characterization. Enforcing blockiness in the model space amounts to enforcing a sparse representation of discontinuities in the model. Sparseness can be obtained using the ?1 norm or Cauchy function which are related to long‐tailed probability density functions. Detecting these discontinuities with vertical and horizontal gradient operators helps constraining the model in both directions. Blocky regularization can also help recovering higher wavenumbers that the data used for inversion would allow, thus helping controlling the cost of FWI. While the Cauchy function yields blockier models, both ?1 and Cauchy attenuate illumination and inversion artifacts.  相似文献   

18.
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   

19.
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   

20.
Predicting the shear‐wave (S‐wave) velocity is important in seismic modelling, amplitude analysis with offset, and other exploration and engineering applications. Under the low‐frequency approximation, the classical Biot–Gassmann theory relates the Biot coefficient to the bulk modulus of water‐saturated sediments. If the Biot coefficient under in situ conditions can be estimated, the shear modulus or the S‐wave velocity can be calculated. The Biot coefficient derived from the compressional‐wave (P‐wave) velocity of water‐saturated sediments often differs from and is less than that estimated from the S‐wave velocity, owing to the interactions between the pore fluid and the grain contacts. By correcting the Biot coefficients derived from P‐wave velocities of water‐saturated sediments measured at various differential pressures, an accurate method of predicting S‐wave velocities is proposed. Numerical results indicate that the predicted S‐wave velocities for consolidated and unconsolidated sediments agree well with measured velocities.  相似文献   

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