共查询到20条相似文献，搜索用时 30 毫秒
1.
Up–down wavefield decomposition is effectuated by a scaled addition or subtraction of the pressure and vertical particle velocity, generally on horizontal or vertical surfaces, and works well for data given on such surfaces. The method, however, is not applicable to decomposing a wavefield when it is given at one instance in time, i.e. on snapshots. Such situations occur when a wavefield is modelled with methods like finite-difference techniques, for the purpose of, for example, reverse time migration, where the entire wavefield is determined per time instance. We present an alternative decomposition method that is exact when working on snapshots of an acoustic wavefield in a homogeneous medium, but can easily be approximated to heterogeneous media, and allows the wavefield to be decomposed in arbitrary directions. Such a directional snapshot wavefield decomposition is achieved by recasting the acoustic system in terms of the time derivative of the pressure and the vertical particle velocity, as opposed to the vertical derivative in up–down decomposition for data given on a horizontal surface. As in up–down decomposition of data given at a horizontal surface, the system can be eigenvalue decomposed and the inverse of the eigenvector matrix decomposes the wavefield snapshot into fields of opposite directions, including up–down decomposition. As the vertical particle velocity can be rotated at will, this allows for decomposition of the wavefield into any spatial direction; even spatially varying directions are possible. We show the power and effectiveness of the method by synthetic examples and models of increasing complexity. 相似文献
2.
Seismic wave propagation in transversely isotropic (TI) media is commonly described by a set of coupled partial differential equations, derived from the acoustic approximation. These equations produce pure P‐wave responses in elliptically anisotropic media but generate undesired shear‐wave components for more general TI anisotropy. Furthermore, these equations suffer from instabilities when the anisotropy parameter ε is less than δ. One solution to both problems is to use pure acoustic anisotropic wave equations, which can produce pure P‐waves without any shear‐wave contaminations in both elliptical and anelliptical TI media. In this paper, we propose a new pure acoustic transversely isotropic wave equation, which can be conveniently solved using the pseudospectral method. Like most other pure acoustic anisotropic wave equations, our equation involves complicated pseudo‐differential operators in space which are difficult to handle using the finite difference method. The advantage of our equation is that all of its model parameters are separable from the spatial differential and pseudo‐differential operators; therefore, the pseudospectral method can be directly applied. We use phase velocity analysis to show that our equation, expressed in a summation form, can be properly truncated to achieve the desired accuracy according to anisotropy strength. This flexibility allows us to save computational time by choosing the right number of summation terms for a given model. We use numerical examples to demonstrate that this new pure acoustic wave equation can produce highly accurate results, completely free from shear‐wave artefacts. This equation can be straightforwardly generalized to tilted TI media. 相似文献
3.
Anatoly A. Nikitin Boris D. Plyushchenkov Arkady Yu. Segal 《Geophysical Prospecting》2016,64(5):1335-1349
We derived the velocity and attenuation of a generalized Stoneley wave being a symmetric trapped mode of a layer filled with a Newtonian fluid and embedded into either a poroelastic or a purely elastic rock. The dispersion relation corresponding to a linearized Navier–Stokes equation in a fracture coupling to either Biot or elasticity equations in the rock via proper boundary conditions was rigorously derived. A cubic equation for wavenumber was found that provides a rather precise analytical approximation of the full dispersion relation, in the frequency range of 10?3 Hz to 103 Hz and for layer width of less than 10 cm and fluid viscosity below 0.1 Pa· s [100 cP]. We compared our results to earlier results addressing viscous fluid in either porous rocks with a rigid matrix or in a purely elastic rock, and our formulae are found to better match the numerical solution, especially regarding attenuation. The computed attenuation was used to demonstrate detectability of fracture tip reflections at wellbore, for a range of fracture lengths and apertures, pulse frequencies, and fluid viscosity. 相似文献
4.
Acoustic transversely isotropic models are widely used in seismic exploration for P‐wave processing and analysis. In isotropic acoustic media only P‐wave can propagate, while in an acoustic transversely isotropic medium both P and S waves propagate. In this paper, we focus on kinematic properties of S‐wave in acoustic transversely isotropic media. We define new parameters better suited for S‐wave kinematics analysis. We also establish the travel time and relative geometrical spreading equations and analyse their properties. To illustrate the behaviour of the S‐wave in multi‐layered acoustic transversely isotropic media, we define the Dix‐type equations that are different from the ones widely used for the P‐wave propagation. 相似文献
5.
In an acoustic transversely isotropic medium, there are two waves that propagate. One is the P-wave and another one is the S-wave (also known as S-wave artefact). This paper is devoted to analyse the S-wave in two-dimensional acoustic transversely isotropic media with a tilted symmetry axis. We derive the S-wave slowness surface and traveltime function in a homogeneous acoustic transversely isotropic medium with a tilted symmetry axis. The S-wave traveltime approximations in acoustic transversely isotropic media with a tilted symmetry axis can be mapped from the counterparts for acoustic transversely isotropic media with a vertical symmetry axis. We consider a layered two-dimensional acoustic transversely isotropic medium with a tilted symmetry axis to analyse the S-wave moveout. We also illustrate the behaviour of the moveout for reflected S-wave and converted waves. 相似文献
6.
Wave‐induced fluid flow at microscopic and mesoscopic scales arguably constitutes the major cause of intrinsic seismic attenuation throughout the exploration seismic and sonic frequency ranges. The quantitative analysis of these phenomena is, however, complicated by the fact that the governing physical processes may be dependent. The reason for this is that the presence of microscopic heterogeneities, such as micro‐cracks or broken grain contacts, causes the stiffness of the so‐called modified dry frame to be complex‐valued and frequency‐dependent, which in turn may affect the viscoelastic behaviour in response to fluid flow at mesoscopic scales. In this work, we propose a simple but effective procedure to estimate the seismic attenuation and velocity dispersion behaviour associated with wave‐induced fluid flow due to both microscopic and mesoscopic heterogeneities and discuss the results obtained for a range of pertinent scenarios. 相似文献
7.
Alexey Yurikov Maxim Lebedev Marina Pervukhina Boris Gurevich 《Geophysical Prospecting》2019,67(4):984-996
Shales play an important role in many engineering applications such as nuclear waste, CO2 storage and oil or gas production. Shales are often utilized as an impermeable seal or an unconventional reservoir. For both situations, shales are often studied using seismic waves. Elastic properties of shales strongly depend on their hydration, which can lead to substantial structural changes. Thus, in order to explore shaly formations with seismic methods, it is necessary to understand the dependency of shale elastic properties on variations in hydration. In this work, we investigate structural changes in Opalinus shale at different hydration states using laboratory measurements and X-ray micro-computed tomography. We show that the shale swells with hydration and shrinks with drying with no visible damage. The pore space of the shale deforms, exhibiting a reduction in the total porosity with drying and an increase in the total porosity with hydration. We study the elastic properties of the shale at different hydration states using ultrasonic velocities measurements. The elastic moduli of the shale show substantial changes with variations in hydration, which cannot be explained with a single driving mechanism. We suggest that changes of the elastic moduli with variations in hydration are driven by multiple competing factors: (1) variations in total porosity, (2) substitution of pore-filling fluid, (3) change in stiffness of contacts between clay particles and (4) chemical hardening/softening of clay particles. We qualitatively and quantitatively analyse and discuss the influence of each of these factors on the elastic moduli. We conclude that depending on the microstructure and composition of a particular shale, some of the factors dominate over the others, resulting in different dependencies of the elastic moduli on hydration. 相似文献
8.
W.A. Mulder 《Geophysical Prospecting》2020,68(9):2857-2866
Simulations of wave propagation in the Earth usually require truncation of a larger domain to the region of interest to keep computational cost acceptable. This introduces artificial boundaries that should not generate reflected waves. Most existing boundary conditions are not able to completely suppress all the reflected energy, but suffice in practice except when modelling subtle events such as interbed multiples. Exact boundary conditions promise better performance but are usually formulated in terms of the governing wave equation and, after discretization, still may produce unwanted artefacts. Numerically exact non-reflecting boundary conditions are instead formulated in terms of the discretized wave equation. They have the property that the numerical solution computed on a given domain is the same as one on a domain enlarged to the extent that waves reflected from the boundary do not have the time to reach the original truncated domain. With a second- or higher-order finite-difference scheme for the one-dimensional wave equation, these boundary conditions follow from a recurrence relation. In its generalization to two or three dimensions, a recurrence relation was only found for a single non-reflecting boundary on one side of the domain or two of them at opposing ends. The other boundaries should then be zero Dirichlet or Neumann. If two non-reflecting boundaries meet at a corner, translation invariance is lost and a simple recurrence relation could not be found. Here, a workaround is presented that restores translation invariance by imposing classic, approximately non-reflecting boundary conditions on the other sides and numerically exact ones on the two opposing sides that otherwise would create the strongest reflected waves with the classic condition. The exact ones can also be applied independently. As a proof of principle, the method is applied to the two-dimensional acoustic wave equation, discretized on a rectangular domain with a second-order finite-difference scheme and first-order Enquist–Majda boundary conditions as approximate ones. The method is computationally costly but has the advantage that it can be reused on a sequence of problems as long as the time step and the sound speed values next to the boundary are kept fixed. 相似文献
9.
In recent years, a variety of Marchenko methods for the attenuation of internal multiples has been developed. These methods have been extensively tested on two-dimensional synthetic data and applied to two-dimensional field data, but only little is known about their behaviour on three-dimensional synthetic data and three-dimensional field data. Particularly, it is not known whether Marchenko methods are sufficiently robust for sparse acquisition geometries that are found in practice. Therefore, we start by performing a series of synthetic tests to identify the key acquisition parameters and limitations that affect the result of three-dimensional Marchenko internal multiple prediction and subtraction using an adaptive double-focusing method. Based on these tests, we define an interpolation strategy and use it for the field data application. Starting from a wide azimuth dense grid of sources and receivers, a series of decimation tests are performed until a narrow azimuth streamer geometry remains. We evaluate the effect of the removal of sail lines, near offsets, far offsets and outer cables on the result of the adaptive double-focusing method. These tests show that our method is most sensitive to the limited aperture in the crossline direction and the sail line spacing when applying it to synthetic narrow azimuth streamer data. The sail line spacing can be interpolated, but the aperture in the crossline direction is a limitation of the acquisition. Next, we apply the adaptive Marchenko double-focusing method to the narrow azimuth streamer field data from the Santos Basin, Brazil. Internal multiples are predicted and adaptively subtracted, thereby improving the geological interpretation of the target area. These results imply that our adaptive double-focusing method is sufficiently robust for the application to three-dimensional field data, although the key acquisition parameters and limitations will naturally differ in other geological settings and for other types of acquisition. 相似文献
10.
In this paper, we deduced the corresponding first-order velocity–stress equation for curvilinear coordinates from the first-order velocity–stress equation based on the modified Biot/squirt model for a two-dimensional two-phase medium. The equations are then numerically solved by an optimized high-order non-staggered finite difference scheme, that is, the dispersion relation preserving/optimization MacCormack scheme. To implement undulating free-surface topography, we derive an analytical relationship between the derivatives of the particle velocity components and use the compact finite-difference scheme plus a traction-image method. In the undulating free surface and the undulating subsurface interface of two-phase medium, the complex reflected wave and transmitted wave can be clearly recognized in the numerical simulation results. The simulation results show that the curvilinear-grid finite-difference method, which uses a body-conforming grid to describe the undulating surface, can accurately reduce the numerical scattering effect of seismic wave propagation caused by the use of ladder-shaped grid to fit the surfaces when undulating topography is present in a two-phase isotropic medium. 相似文献
11.
A fast and robust method for two-point ray tracing in one-dimensional layered media is presented. This method is applicable to layered models with constant or linearly varying isotropic layer velocity. For given model properties and source and receiver positions, a ray path can be uniquely determined once its ray parameter (i.e. horizontal slowness) is known. The ray parameter can be obtained by numerically solving the nonlinear offset (i.e. source–receiver horizontal distance) equation using Newton's method, which generally works well at near and mid offsets. However, Newton's method becomes hard to converge at large offsets due to the oversensitivity of offset to ray parameter. Based on the analysis of the characteristic of the offset equation, a modified ray parameter is proposed and used to replace the generic ray parameter in numerical calculation. Numerical experiments show that the iteration process becomes stable and converges rapidly with the modified ray parameter. Moreover, a rational function that asymptotically approximates the shape of the offset equation is introduced for obtaining good initial estimates of the modified ray parameter. Numerical tests show that this method is robust in any situation, and an accurate ray parameter can be obtained within two or three iterations for a wide range of model velocity structure and source–receiver distance. Furthermore, the proposed two-point ray tracing method is easy to implement. 相似文献
12.
Flavio Poletto Cinzia Bellezza Kees Wapenaar Aronne Craglietto 《Geophysical Prospecting》2012,60(5):838-854
We formulate the Kirchhoff‐Helmholtz representation theory for the combination of seismic interferometry signals synthesized by cross‐correlation and by cross‐convolution in acoustic media. The approach estimates the phase of the virtual reflections from the boundary encompassing a volume of interest and subtracts these virtual reflections from the total seismic‐interferometry wavefield. The reliability of the combination result, relevant for seismic exploration, depends on the stationary‐phase and local completeness in partial coverage regions. The analysis shows the differences in the phase of the corresponding seismic interferometry (by cross‐correlation) and virtual reflector (by cross‐convolution) signals obtained by 2D and 3D formulations, with synthetic examples performed to remove water layer multiples in ocean bottom seismic (OBS) acoustic data. 相似文献
13.
14.
Reverse time migration of multiples can be used to construct subsurface structures where primaries cannot illuminate well. However, the images generated using multiples suffer from severe artefacts due to the cross-talks created by interference among unrelated multiples. We developed a migration approach using water-bottom-related multiples to reduce these cross-talk artefacts. This approach first isolates primaries from the original data and predicts water-column primaries. The nth-order water-column multiples can be obtained by auto-convolving the water-column primaries n times, followed by convolving the nth-order water-column multiples with the primaries to extract the (n+1)th-order water-bottom-related multiples. The approach takes the nth-order water-column multiples as the secondary source and regards the (n+1)th-order water-bottom-related multiples as the receiver wavefield, followed by a cross-correlation imaging condition. Numerical examples from synthetic and field data sets reveal that our approach can provide images with substantially fewer cross-talk artefacts than conventional reverse time migration using multiples, as well as greatly improving shallow imaging compared with reverse time migration of primaries. 相似文献
15.
Pure-mode wave propagation is important for applications ranging from imaging to avoiding parameter tradeoff in waveform inversion. Although seismic anisotropy is an elastic phenomenon, pseudo-acoustic approximations are routinely used to avoid the high computational cost and difficulty in decoupling wave modes to obtain interpretable seismic images. However, such approximations may result in inaccuracies in characterizing anisotropic wave propagation. We propose new pure-mode equations for P- and S-waves resulting in an artefact-free solution in transversely isotropic medium with a vertical symmetry axis. Our approximations are more accurate than other known approximations as they are not based on weak anisotropy assumptions. Therefore, the S-wave approximation can reproduce the group velocity triplications in strongly anisotropic media. The proposed approximations can be used for accurate modelling and imaging of pure P- and S-waves in transversely isotropic media. 相似文献
16.
In this work, an experimental study was carried out with the aim of reconciling static and dynamic stiffness of Opalinus Clay. The static and dynamic stiffness of core plugs from a shaly and a sandy facies of Opalinus Clay were characterized at two different stress states. The measurements included undrained quasi-static loading–unloading cycles from which the static stiffness was derived, dynamic stiffness measurement at seismic frequencies (0.5–150 Hz) and ultrasonic velocity measurements (500 kHz) probing the dynamic stiffness at ultrasonic frequencies. The experiments were carried out in a special triaxial low-frequency cell. The obtained results demonstrate that the difference between static and dynamic stiffness is due to both dispersion and non-elastic effects: Both sandy and shaly facies of Opalinus Clay exhibit large dispersion, that is, a large frequency dependence of dynamic stiffness and acoustic velocities. Especially dynamic Young's moduli exhibit very high dispersion; between seismic and ultrasonic frequencies they may change by more than a factor 2. P-wave velocities perpendicular to bedding are by more than 200 m/s higher at ultrasonic frequencies than at seismic frequencies. The static undrained stiffness of both sandy and shaly facies is strongly influenced by non-elastic effects, resulting in significant softening during both loading and unloading with increasing stress amplitude. The zero-stress extrapolated static undrained stiffness, however, reflects the purely elastic response and agrees well with the dynamic stiffness at seismic frequency. 相似文献
17.
Over the last years, full-waveform inversion has become an important tool in the list of processing and imaging technologies available to the industry. For marine towed-streamer data, full-waveform inversion is typically applied using an acoustic approximation because S-waves do not propagate in water and elastic effects in recorded data are generally assumed to be small. We compare acoustic and elastic modelling and full-waveform inversion for a field data set acquired offshore Angola over sediments containing a salt body with significant topology. Forward modelling tests reveal that such geological structures lead to significant mode conversions at interfaces and, consequently, to significant relative amplitude differences when elastically and acoustically modelled traces are compared. Using an acoustic approach for modelling in full-waveform inversion therefore leads to problems matching the synthetic data with the field data, even for recorded pressure data and with trace normalization applied. Full-waveform inversion is unable to find consistent model updates. Applying elastic full-waveform inversion leads to more consistent and reliable model updates with less artefacts, at the expense of additional computation cost. Although two-dimensional marine towed-streamer data are least favourable for the application of full-waveform inversion compared to three-dimensional data or ocean-bottom data, it is recommended to check on the existence of elastic effects before deciding on the final processing and imaging approach. 相似文献
18.
Under certain circumstances, seismic propagation within porous media may be associated to the conversion of mechanical energy to electromagnetic energy, which is known as a seismo‐electromagnetic phenomenon. The propagation of fast compressional P‐waves is more specifically associated to the manifestations of a seismoelectric field linked to the fluid flows within the pores. The analysis of seismoelectric phenomena, which requires the combination of the theory of electrokinetics and Biot's theory of poroelasticity, provides us with transfer function that links the coseismic seismoelectric field E to the seismic acceleration . To measure the transfer function, we have developed an experimental setup enabling seismoelectric laboratory observation in unconsolidated quartz sand within the kilohertz range. The investigation focused on the impact of fluid conductivity and water saturation over the coseismic seismoelectric field. During the experiment, special attention was given to the accuracy of electric field measurements. We concluded that, to obtain a reliable estimate of the electric field amplitude, the dipole from which the potential differences are measured should be of much smaller length than the wavelength of the propagating seismic field. Time‐lapse monitoring of the seismic velocities and seismoelectric transfer functions were performed during imbibition and drainage experiments. In all cases, the quantitative analysis of the seismoelectric transfer function was in good agreement with theoretical predictions. While investigating saturation variations from full to residual water saturation, we showed that the ratio undergoes a switch in polarity at a particular saturation , which also implies a sign change of the filtration, traducing a reversal of the relative fluid displacement with respect to the frame. This sign change at critical saturation stresses a particular behaviour of the poroelastic medium: the dropping of the coseismic electric field to zero traduces the absence of relative pore/fluid displacements representative of a Biot dynamically compatible medium. We concluded from our experimental study in loose sand that the measurements of the coseismic seismoelectric coupling may provide information on fluid distribution within the pores and that the reversal of the seismoelectric field may be used as an indicator of the dynamically compatible state of the medium. 相似文献
19.
Radon transform is a powerful tool with many applications in different stages of seismic data processing, because of its capability to focus seismic events in the transform domain. Three-parameter Radon transform can optimally focus and separate different seismic events, if its basis functions accurately match the events. In anisotropic media, the conventional hyperbolic or shifted hyperbolic basis functions lose their accuracy and cannot preserve data fidelity, especially at large offsets. To address this issue, we propose an accurate traveltime approximation for transversely isotropic media with vertical symmetry axis, and derive two versions of Radon basis functions, time-variant and time-invariant. A time-variant basis function can be used in time domain Radon transform algorithms while a time-invariant version can be used in, generally more efficient, frequency domain algorithms. Comparing the time-variant and time-invariant Radon transform by the proposed basis functions, the time-invariant version can better focus different seismic events; it is also more accurate, especially in presence of vertical heterogeneity. However, the proposed time-invariant basis functions are suitable for a specific type of layered anisotropic media, known as factorized media. We test the proposed methods and illustrate successful applications of them for trace interpolation and coherent noise attenuation. 相似文献
20.
Valentin Tschannen Norman Ettrich Matthias Delescluse Janis Keuper 《Geophysical Prospecting》2020,68(3):830-844
Diffracted waves carry high-resolution information that can help interpreting fine structural details at a scale smaller than the seismic wavelength. However, the diffraction energy tends to be weak compared to the reflected energy and is also sensitive to inaccuracies in the migration velocity, making the identification of its signal challenging. In this work, we present an innovative workflow to automatically detect scattering points in the migration dip angle domain using deep learning. By taking advantage of the different kinematic properties of reflected and diffracted waves, we separate the two types of signals by migrating the seismic amplitudes to dip angle gathers using prestack depth imaging in the local angle domain. Convolutional neural networks are a class of deep learning algorithms able to learn to extract spatial information about the data in order to identify its characteristics. They have now become the method of choice to solve supervised pattern recognition problems. In this work, we use wave equation modelling to create a large and diversified dataset of synthetic examples to train a network into identifying the probable position of scattering objects in the subsurface. After giving an intuitive introduction to diffraction imaging and deep learning and discussing some of the pitfalls of the methods, we evaluate the trained network on field data and demonstrate the validity and good generalization performance of our algorithm. We successfully identify with a high-accuracy and high-resolution diffraction points, including those which have a low signal to noise and reflection ratio. We also show how our method allows us to quickly scan through high dimensional data consisting of several versions of a dataset migrated with a range of velocities to overcome the strong effect of incorrect migration velocity on the diffraction signal. 相似文献