For microseisimic monitoring it is difficult to determine wave modes and their propagation velocity. In this paper, we propose a new method for automatically inverting in real time the source characteristics of micros...For microseisimic monitoring it is difficult to determine wave modes and their propagation velocity. In this paper, we propose a new method for automatically inverting in real time the source characteristics of microseismic events in mine engineering without wave mode identification and velocities. Based on the wave equation in a spherical coordinate system, we derive a tomographic imaging equation and formulate a scanning parameter selection criterion by which the microseisimic event maximum energy and corresponding parameters can be determined. By determining the maximum energy positions inside a given risk district, we can indentify microseismic events inside or outside the risk districts. The synthetic and field examples demonstrate that the proposed tomographic imaging method can automatically position microseismic events by only knowing the risk district dimensions and range of velocities without identifying the wavefield modes and accurate velocities. Therefore, the new method utilizes the full wavefields to automatically monitor microseismic events.展开更多
In multi-component seismic exploration, the horizontal and vertical components both contain P- and SV-waves. The P- and SV-wavefields in a seismic record can be separated by their horizontal and vertical displacements...In multi-component seismic exploration, the horizontal and vertical components both contain P- and SV-waves. The P- and SV-wavefields in a seismic record can be separated by their horizontal and vertical displacements when upgoing P- and SV-waves arrive at the sea floor. If the sea floor P wave velocity, S wave velocity, and density are known, the separation can be achieved in ther-p domain. The separated wavefields are then transformed to the time domain. A method of separating P- and SV-wavefields is presented in this paper and used to effectively separate P- and SV-wavefields in synthetic and real data. The application to real data shows that this method is feasible and effective. It also can be used for free surface data.展开更多
Seismic anisotropy has been extensively acknowledged as a crucial element that influences the wave propagation characteristic during wavefield simulation,inversion and imaging.Transversely isotropy(TI)and orthorhombic...Seismic anisotropy has been extensively acknowledged as a crucial element that influences the wave propagation characteristic during wavefield simulation,inversion and imaging.Transversely isotropy(TI)and orthorhombic anisotropy(OA)are two typical categories of anisotropic media in exploration geophysics.In comparison of the elastic wave equations in both TI and OA media,pseudo-acoustic wave equations(PWEs)based on the acoustic assumption can markedly reduce computational cost and complexity.However,the presently available PWEs may experience SV-wave contamination and instability when anisotropic parameters cannot satisfy the approximated condition.Exploiting pure-mode wave equations can effectively resolve the above-mentioned issues and generate pure P-wave events without any artifacts.To further improve the computational accuracy and efficiency,we develop two novel pure qP-wave equations(PPEs)and illustrate the corresponding numerical solutions in the timespace domain for 3D tilted TI(TTI)and tilted OA(TOA)media.First,the rational polynomials are adopted to estimate the exact pure qP-wave dispersion relations,which contain complicated pseudo-differential operators with irrational forms.The polynomial coefficients are produced by applying a linear optimization algorithm to minimize the objective function difference between the expansion formula and the exact one.Then,the developed optimized PPEs are efficiently implemented using the finite-difference(FD)method in the time-space domain by introducing a scalar operator,which can help avoid the problem of spectral-based algorithms and other calculation burdens.Structures of the new equations are concise and corresponding implementation processes are straightforward.Phase velocity analyses indicate that our proposed optimized equations can lead to reliable approximation results.3D synthetic examples demonstrate that our proposed FD-based PPEs can produce accurate and stable P-wave responses,and effectively describe the wavefield features in complicated TTI and TOA media.展开更多
To reduce the spatial simulation error generated by the finite difference method,previous researchers compute the optimal finite-difference weights always by minimizing the error of spatial dispersion relation.However...To reduce the spatial simulation error generated by the finite difference method,previous researchers compute the optimal finite-difference weights always by minimizing the error of spatial dispersion relation.However,we prove that the spatial simulation error of the finite difference method is associated with the dot product of the spatial dispersion relation of the finite-difference weights and the spectrum of the seismic wavefield.Based on the dot product relation,we construct a L_(2) norm cost function to minimize spatial simulation error.For solving this optimization problem,the seismic wavefield infor-mation in wavenumber region is necessary.Nevertheless,the seismic wavefield is generally obtained by costly forward modeling techniques.To reduce the computational cost,we substitute the spectrum of the seismic wavelet for the spectrum of the seismic wavefield,as the seismic wavelet plays a key role in determining the seismic wavefield.In solving the optimization problem,we design an exhaustive search method to obtain the solution of the L_(2) norm optimization problem.After solving the optimization problem,we are able to achieve the finite-difference weights that minimize spatial simulation error.In theoretical error analyses,the finite-difference weights from the proposed method can output more accurate simulation results compared to those from previous optimization algorithms.Furthermore,we validate our method through numerical tests with synthetic models,which encompass homogenous/inhomogeneous media as well as isotropic and anisotropic media.展开更多
Internal multiple interference,affecting both seismic data processing and interpretation,has been observed for long time.Although great progress has been achieved in developing a variety of internal-multiple-eliminati...Internal multiple interference,affecting both seismic data processing and interpretation,has been observed for long time.Although great progress has been achieved in developing a variety of internal-multiple-elimination(IME)methods,how to increase accuracy and reduce cost of IME still poses a significant challenge.A new method is proposed to effectively and efficiently eliminate internal multi-ples,along with its application in internal-multiple-eliminated-migration(IMEM),addressing this issue.This method stems from two-way wave equation depth-extrapolation scheme and associated up/down wavefield separation,which can accomplish depth-extrapolation of both up-going and down-going wavefields simultaneously,and complete internal-multiple-elimination processing,adaptively and effi-ciently.The proposed method has several features:(1)input data is same as that for conventional migration:source signature(used for migration only),macro velocity model,and receiver data,without additional requirements for source/receiver sampling;(2)method is efficient,without need of iterative calculations(which are typically needed for most of IME algorithms);and(3)method is cost effective:IME is completed in the same depth-extrapolation scheme of IMEM,without need of a separate pro-cessing and additional cost.Several synthesized data models are used to test the proposed method:one-dimensional model,horizontal layered model,multi-layer model with one curved layer,and SEG/EAGE Salt model.Additionally,we perform a sensitivity analysis of velocity using smoothed models.This analysis reveals that although the accuracy of velocity measurements impacts our proposed method,it significantly reduces internal multiple false imaging compared to traditional RTM techniques.When applied to actual seismic data from a carbonate reservoir zone,our method demonstrates superior clarity in imaging results,even in the presence of high-velocity carbonate formations,outperforming conven-tional migration methods in deep strata.展开更多
P-and S-wave separation plays an important role in elastic reverse-time migration.It can reduce the artifacts caused by crosstalk between different modes and improve image quality.In addition,P-and Swave separation ca...P-and S-wave separation plays an important role in elastic reverse-time migration.It can reduce the artifacts caused by crosstalk between different modes and improve image quality.In addition,P-and Swave separation can also be used to better understand and distinguish wave types in complex media.At present,the methods for separating wave modes in anisotropic media mainly include spatial nonstationary filtering,low-rank approximation,and vector Poisson equation.Most of these methods require multiple Fourier transforms or the calculation of large matrices,which require high computational costs for problems with large scale.In this paper,an efficient method is proposed to separate the wave mode for anisotropic media by using a scalar anisotropic Poisson operator in the spatial domain.For 2D problems,the computational complexity required by this method is 1/2 of the methods based on solving a vector Poisson equation.Therefore,compared with existing methods based on pseudoHelmholtz decomposition operators,this method can significantly reduce the computational cost.Numerical examples also show that the P and S waves decomposed by this method not only have the correct amplitude and phase relative to the input wavefield but also can reduce the computational complexity significantly.展开更多
Stability is the key to inverse Q-filtering. In this paper we present a stable approach to inverse Q-filtering, based on the theory of wavefield downward continuation. It is implemented in a layered manner, assuming a...Stability is the key to inverse Q-filtering. In this paper we present a stable approach to inverse Q-filtering, based on the theory of wavefield downward continuation. It is implemented in a layered manner, assuming a layered-earth Q model. For each individual constant Q layer, the seismic wavefield recorded at the surface is first extrapolated down to the top of the current layer and a constant Q inverse filter is then applied to the current layer. When extrapolating within the overburden, a stable wavefield continuation algorithm in combination with a stabilization factor is applied. This avoids accumulating inverse Q-filter errors within the overburden. Within the current constant Q layer, we use Gabor spectral analysis on the signals to pick time-variant gain-constrained frequencies and then deduce the corresponding gain-constrained amplitudes to stabilize the inverse Q-filtering algorithm. The algorithm is tested and verified application to field data.展开更多
We propose a symplectic partitioned Runge-Kutta （SPRK） method with eighth-order spatial accuracy based on the extended Hamiltonian system of the acoustic waveequation. Known as the eighth-order NSPRK method, this te...We propose a symplectic partitioned Runge-Kutta （SPRK） method with eighth-order spatial accuracy based on the extended Hamiltonian system of the acoustic waveequation. Known as the eighth-order NSPRK method, this technique uses an eighth-orderaccurate nearly analytic discrete （NAD） operator to discretize high-order spatial differentialoperators and employs a second-order SPRK method to discretize temporal derivatives.The stability criteria and numerical dispersion relations of the eighth-order NSPRK methodare given by a semi-analytical method and are tested by numerical experiments. We alsoshow the differences of the numerical dispersions between the eighth-order NSPRK methodand conventional numerical methods such as the fourth-order NSPRK method, the eighth-order Lax-Wendroff correction （LWC） method and the eighth-order staggered-grid （SG）method. The result shows that the ability of the eighth-order NSPRK method to suppress thenumerical dispersion is obviously superior to that of the conventional numerical methods. Inthe same computational environment, to eliminate visible numerical dispersions, the eighth-order NSPRK is approximately 2.5 times faster than the fourth-order NSPRK and 3.4 timesfaster than the fourth-order SPRK, and the memory requirement is only approximately47.17% of the fourth-order NSPRK method and 49.41% of the fourth-order SPRK method,which indicates the highest computational efficiency. Modeling examples for the two-layermodels such as the heterogeneous and Marmousi models show that the wavefields generatedby the eighth-order NSPRK method are very clear with no visible numerical dispersion.These numerical experiments illustrate that the eighth-order NSPRK method can effectivelysuppress numerical dispersion when coarse grids are adopted. Therefore, this methodcan greatly decrease computer memory requirement and accelerate the forward modelingproductivity. In general, the eighth-order NSPRK method has tremendous potential value forseismic exploration and seismology research.展开更多
Prestack reverse time migration（PSTM） is a common imaging method; however low-frequency noises reduce the structural imaging precision. Thus, the suppression of migration noises must be considered. The generation me...Prestack reverse time migration（PSTM） is a common imaging method; however low-frequency noises reduce the structural imaging precision. Thus, the suppression of migration noises must be considered. The generation mechanism of low-frequency noises is analyzed and the up-, down-, left-, and right-going waves are separated using the Poynting vector of the acoustic wave equation. The computational complexity and memory capacitance of the proposed method are far smaller than that required when using the conventional separation algorithm of 2D Fourier transform. The normalized wavefield separation crosscorrelation imaging condition is used to suppress low-frequency noises in reverse time migration and improve the imaging precision. Numerical experiments using the Marmousi model are performed and the results show that the up-, down-, left-, and right-going waves are well separated in the continuation of the wavefield using the Poynting vector. We compared the imaging results with the conventional method, Laplacian filtering, and wavefield separation with the 2D Fourier transform. The comparison shows that the migration noises are well suppressed using the normalized wavefield separation cross-correlation imaging condition and higher precision imaging results are obtained.展开更多
Wavefields in porous media saturated by two immiscible fluids are simulated in this paper.Based on the sealed system theory,the medium model considers both the relative motion between the fluids and the solid skeleton...Wavefields in porous media saturated by two immiscible fluids are simulated in this paper.Based on the sealed system theory,the medium model considers both the relative motion between the fluids and the solid skeleton and the relaxation mechanisms of porosity and saturation（capillary pressure）.So it accurately simulates the numerical attenuation property of the wavefields and is much closer to actual earth media in exploration than the equivalent liquid model and the unsaturated porous medium model on the basis of open system theory.The velocity and attenuation for different wave modes in this medium have been discussed in previous literature but studies of the complete wave-field have not been reported.In our work,wave equations with the relaxation mechanisms of capillary pressure and the porosity are derived.Furthermore,the wavefield and its characteristics are studied using the numerical finite element method.The results show that the slow P3-wave in the non-wetting phase can be observed clearly in the seismic band.The relaxation of capillary pressure and the porosity greatly affect the displacement of the non-wetting phase.More specifically,the displacement decreases with increasing relaxation coefficient.展开更多
Solving the wave equation is one of the most(if not the most)fundamental problems we face as we try to illuminate the Earth using recorded seismic data.The Helmholtz equation provides wavefield solutions that are dime...Solving the wave equation is one of the most(if not the most)fundamental problems we face as we try to illuminate the Earth using recorded seismic data.The Helmholtz equation provides wavefield solutions that are dimensionally reduced,per frequency,compared to the time domain,which is useful for many applications,like full waveform inversion.However,our ability to attain such wavefield solutions depends often on the size of the model and the complexity of the wave equation.Thus,we use here a recently introduced framework based on neural networks to predict functional solutions through setting the underlying physical equation as a loss function to optimize the neural network(NN)parameters.For an input given by a location in the model space,the network learns to predict the wavefield value at that location,and its partial derivatives using a concept referred to as automatic differentiation,to fit,in our case,a form of the Helmholtz equation.We specifically seek the solution of the scattered wavefield considering a simple homogeneous background model that allows for analytical solutions of the background wavefield.Providing the NN with a reasonable number of random points from the model space will ultimately train a fully connected deep NN to predict the scattered wavefield function.The size of the network depends mainly on the complexity of the desired wavefield,with such complexity increasing with increasing frequency and increasing model complexity.However,smaller networks can provide smoother wavefields that might be useful for inversion applications.Preliminary tests on a two-box-shaped scatterer model with a source in the middle,as well as,the Marmousi model with a source at the surface demonstrate the potential of the NN for this application.Additional tests on a 3D model demonstrate the potential versatility of the approach.展开更多
Wavefield separation of multicomponent seismic data to image subsurface structures can be realized in either the space domain or the wavenumber domain. However, as the particle velocity components used in the wavenumb...Wavefield separation of multicomponent seismic data to image subsurface structures can be realized in either the space domain or the wavenumber domain. However, as the particle velocity components used in the wavenumber-domain wavefield separation are not defined at the same grid point with the staggered-grid finite-difference method for elastic wavefield simulation, we propose the wavenumber-domain interpolation method to estimate the required values at the common grid points prior to the wavenumber-domain true-amplitude wavefield separation. Moreover, numerical experiments show that the wavenumber-domain interpolation method has high interpolation accuracy and the trueamplitude wavefield separation method shows good amplitude preservation. The application of the proposed methodology to elastic reverse-time migration can obtain good amplitudepreserved images even in the case of some velocity error.展开更多
With increased computational power, reverse-time prestack depth migration（RT-PSDM） has become a preferred imaging tool in seismic exploration, yet its use has remained relatively limited in ground-penetrating radar...With increased computational power, reverse-time prestack depth migration（RT-PSDM） has become a preferred imaging tool in seismic exploration, yet its use has remained relatively limited in ground-penetrating radar（GPR） applications. Complex topography alters the wavefield kinematics making for a challenging imaging problem. Model simulations show that topographic variation can substantially distort reflection amplitudes due to irregular wavefield spreading, attenuation anomalies due to irregular path lengths, and focusing and defocusing effects at the surface. The effects are magnified when the topographic variations are on the same order as the depth of investigation––a situation that is often encountered in GPR investigations. Here, I use a full wave-equation RT-PSDM algorithm to image GPR data in the presence of large topographic variability relative to the depth of investigation. The source and receiver wavefields are propagated directly from the topographic surface and this approach inherently corrects for irregular kinematics, spreading and attenuation. The results show that when GPR data are acquired in areas of extreme topography, RT-PSDM can accurately reconstruct reflector geometry as well as reflection amplitude.展开更多
Compared to towed streamers, ocean-bottom seismometers(OBS) obtain both S-wave data and richer wavefield information. In this paper, the induced polarization method is used to conduct wavefield separation on OBS data ...Compared to towed streamers, ocean-bottom seismometers(OBS) obtain both S-wave data and richer wavefield information. In this paper, the induced polarization method is used to conduct wavefield separation on OBS data obtained from the Shenhu area in the South China Sea. A comparison of the changes in P-and S-waves, and a comprehensive analysis of geological factors within the area, enable analysis and description of the occurrence of natural gas hydrate in the study area. Results show an increase in P-wave velocity when natural gas hydrate exists in the formation, whereas the S-wave velocity remains almost constant, as S-waves can only propagate through the rock skeleton. Therefore, the bottom-simulating reflection(BSR) response of the P-wave is better than that of the S-wave in the frequency analysis profile. In a wide-angle section, the refractive wave of the hydrate layer is evident when using P-wave components but identification is difficult with S-wave components. This velocity model illustrates the sensitivity of Pand S-wave components to gas hydrate. The use of this polarization method and results of analysis provide technical and theoretical support for research on hydrate deposits and other geological features in the Shenhu area.展开更多
The Pre-Stack Depth Migration （PSDM） method based on wavefield continuation is the most reliable method for imaging complex structure in the subsurface, although there are large computational costs and poorly adapti...The Pre-Stack Depth Migration （PSDM） method based on wavefield continuation is the most reliable method for imaging complex structure in the subsurface, although there are large computational costs and poorly adaptive geometry. Plane wave shot migration is another method to perform exact wave equation prestack imaging with high computational efficiency and without the migration aperture problem. Moreover, wavefield energy can be compensated at the target zone by controlled illumination. In this paper, plane wave shot PSDM was implemented by the control of the plane down-going wavefield and selection of number and range of the raypaths in order to optimize the imaging effect. In addition, controlled illumination techniques are applied to enhance the imaging precision of interesting areas at different depths. Numerical calculation indicates that plane wave shot imaging is a rapid and efficient method with less computational cost and easy parallel computation compared to the single-square-root operator imaging for common shot gathers and double- square-root operator imaging for common midpoint gathers.展开更多
Imaging the PP- and PS-wave for the elastic vector wave reverse-time migration requires separating the P- and S-waves during the wave field extrapolation. The amplitude and phase of the P- and S-waves are distorted wh...Imaging the PP- and PS-wave for the elastic vector wave reverse-time migration requires separating the P- and S-waves during the wave field extrapolation. The amplitude and phase of the P- and S-waves are distorted when divergence and curl operators are used to separate the P- and S-waves. We present a P- and S-wave amplitude-preserving separation algorithm for the elastic wavefield extrapolation. First, we add the P-wave pressure and P-wave vibration velocity equation to the conventional elastic wave equation to decompose the P- and S-wave vectors. Then, we synthesize the scalar P- and S-wave from the vector P- and S-wave to obtain the scalar P- and S-wave. The amplitude-preserved separated P- and S-waves are imaged based on the vector wave reverse-time migration (RTM). This method ensures that the amplitude and phase of the separated P- and S-wave remain unchanged compared with the divergence and curl operators. In addition, after decomposition, the P-wave pressure and vibration velocity can be used to suppress the interlayer reflection noise and to correct the S-wave polarity. This improves the image quality of P- and S-wave in multicomponent seismic data and the true-amplitude elastic reverse time migration used in prestack inversion.展开更多
With the development of seismic exploration,passive-source seismic data has attracted increasing attention.Ambient noise passive seismic sources exists widely in nature and industrial production.Passive seismic data i...With the development of seismic exploration,passive-source seismic data has attracted increasing attention.Ambient noise passive seismic sources exists widely in nature and industrial production.Passive seismic data is important in logging while drilling(LWD),large-scale structural exploration,etc.In this paper,we proposed a passive multiple reverse time migration imaging(PMRTMI)method based on wavefield decomposition and normalized imaging conditions method.This method differs from seismic interferometry in that it can use raw passive seismic data directly in RTM imaging without reconstruction of virtual active gather,and we use the wavefield decomposition method to eliminate the low frequency noise in RTM.Further,the energy normalized imaging condition is used in full wavefield decomposition,which can not only enhance the image quality of both edge and deep information but also overcome the wrong energy problem caused by uneven distribution of passive sources;furthermore,this method exhibits high efficiency.Finally,numerical examples with the Marmousi model show the effectiveness of the method.展开更多
Reverse-time migration has attracted more and more attention owing to the advantages of high imaging accuracy, no dip restriction, and adaptation to complex velocity models. Cross-correlation imaging method is typical...Reverse-time migration has attracted more and more attention owing to the advantages of high imaging accuracy, no dip restriction, and adaptation to complex velocity models. Cross-correlation imaging method is typically used in conventional reverse-time migration that produces images with strong low-frequency noise. Wavefield decomposition imaging can suppress such noise; however, some residual noise persists in the imaging results. We propose a 2D multidirectional wavefield decomposition method based on the traditional wavefield decomposition method. First, source wavefields and receiver wavefields are separated into eight subwavefields, respectively. Second, cross-correlation imaging is applied to selected subwavefields to produce subimages. Finally, the subimages are stacked to generate the final image. Numerical examples suggest that the proposed method can eliminate the low-frequency noise effectively and produce high-quality imaging profiles.展开更多
When topography and low velocity zone differences vary greatly, conventional vertical static time shifts will cause wavefield distortion and influence wave equation seismic imaging for seismic data acquired on a compl...When topography and low velocity zone differences vary greatly, conventional vertical static time shifts will cause wavefield distortion and influence wave equation seismic imaging for seismic data acquired on a complex near surface. In this paper, we propose an approach to datum correction that combines a joint tomography inversion with wavefield continuation to solve the static problem for seismic data on rugged acquisition topography. First, the near surface model is obtained by refracted wave tomography inversion. Second, the wavefield of sources and receivers are continued downward and upward to accomplish datum correction starting from a flat surface and locating the datum above topography. Based on the reciprocal theorem, Huygens＇ and Fresnel principles, the location of sources and receivers, and regarding the recorded data on the surface as a secondary emission, the sources and receivers are upward-continued to the datum above topography respectively. Thus, the datum correction using joint tomography inversion and wavefield continuation with the condition of a complex near surface is accomplished.展开更多
Fracture-cave reservoirs in carbonate rocks are characterized by a large difference in fracture and cavity size,and a sharp variation in lithology and velocity,thereby resulting in complex diffraction responses.Some s...Fracture-cave reservoirs in carbonate rocks are characterized by a large difference in fracture and cavity size,and a sharp variation in lithology and velocity,thereby resulting in complex diffraction responses.Some small-scale fractures and caves cause weak diffraction energy and would be obscured by the continuous reflection layer in the imaging section,thereby making them difficult to identify.This paper develops a diffraction wave imaging method in the dip domain,which can improve the resolution of small-scale diffractors in the imaging section.Common imaging gathers(CIGs)in the dip domain are extracted by Gaussian beam migration.In accordance with the geometric differences of the diffraction being quasilinear and the reflection being quasiparabolic in the dip-domain CIGs,we use slope analysis technique to filter waves and use Hanning window function to improve the diffraction wave separation level.The diffraction dip-domain CIGs are stacked horizontally to obtain diffraction imaging results.Wavefield separation analysis and numerical modeling results show that the slope analysis method,together with Hanning window filtering,can better suppress noise to obtain the diffraction dip-domain CIGs,thereby improving the clarity of the diffractors in the diffraction imaging section.展开更多
基金support jointly by projects of the National Natural Science Fund Project (40674017 and 50774012)the National Key Basic Research and Development Plan 973 (2010CB226803)
文摘For microseisimic monitoring it is difficult to determine wave modes and their propagation velocity. In this paper, we propose a new method for automatically inverting in real time the source characteristics of microseismic events in mine engineering without wave mode identification and velocities. Based on the wave equation in a spherical coordinate system, we derive a tomographic imaging equation and formulate a scanning parameter selection criterion by which the microseisimic event maximum energy and corresponding parameters can be determined. By determining the maximum energy positions inside a given risk district, we can indentify microseismic events inside or outside the risk districts. The synthetic and field examples demonstrate that the proposed tomographic imaging method can automatically position microseismic events by only knowing the risk district dimensions and range of velocities without identifying the wavefield modes and accurate velocities. Therefore, the new method utilizes the full wavefields to automatically monitor microseismic events.
基金This research is sponsored by National Natural Science Foundation of China （No. 40272041） and Innovative Foundation of CNPC （N0. 04E702）.
文摘In multi-component seismic exploration, the horizontal and vertical components both contain P- and SV-waves. The P- and SV-wavefields in a seismic record can be separated by their horizontal and vertical displacements when upgoing P- and SV-waves arrive at the sea floor. If the sea floor P wave velocity, S wave velocity, and density are known, the separation can be achieved in ther-p domain. The separated wavefields are then transformed to the time domain. A method of separating P- and SV-wavefields is presented in this paper and used to effectively separate P- and SV-wavefields in synthetic and real data. The application to real data shows that this method is feasible and effective. It also can be used for free surface data.
基金supported by the National Key R&D Program of China(2021YFA0716902)National Natural Science Foundation of China(NSFC)under contract number 42374149 and 42004119National Science and Technology Major Project(2024ZD1002907)。
文摘Seismic anisotropy has been extensively acknowledged as a crucial element that influences the wave propagation characteristic during wavefield simulation,inversion and imaging.Transversely isotropy(TI)and orthorhombic anisotropy(OA)are two typical categories of anisotropic media in exploration geophysics.In comparison of the elastic wave equations in both TI and OA media,pseudo-acoustic wave equations(PWEs)based on the acoustic assumption can markedly reduce computational cost and complexity.However,the presently available PWEs may experience SV-wave contamination and instability when anisotropic parameters cannot satisfy the approximated condition.Exploiting pure-mode wave equations can effectively resolve the above-mentioned issues and generate pure P-wave events without any artifacts.To further improve the computational accuracy and efficiency,we develop two novel pure qP-wave equations(PPEs)and illustrate the corresponding numerical solutions in the timespace domain for 3D tilted TI(TTI)and tilted OA(TOA)media.First,the rational polynomials are adopted to estimate the exact pure qP-wave dispersion relations,which contain complicated pseudo-differential operators with irrational forms.The polynomial coefficients are produced by applying a linear optimization algorithm to minimize the objective function difference between the expansion formula and the exact one.Then,the developed optimized PPEs are efficiently implemented using the finite-difference(FD)method in the time-space domain by introducing a scalar operator,which can help avoid the problem of spectral-based algorithms and other calculation burdens.Structures of the new equations are concise and corresponding implementation processes are straightforward.Phase velocity analyses indicate that our proposed optimized equations can lead to reliable approximation results.3D synthetic examples demonstrate that our proposed FD-based PPEs can produce accurate and stable P-wave responses,and effectively describe the wavefield features in complicated TTI and TOA media.
基金supported by the Marine S&T Fund of Shandong Province for Pilot National Laboratory for Marine Science and Technology(No.2021QNLM020001)the Major Scientific and Technological Projects of Shandong Energy Group(No.SNKJ2022A06-R23)+1 种基金the Funds of Creative Research Groups of China(No.41821002)the Major Scientific and Technological Projects of CNPC(No.ZD2019-183-003).
文摘To reduce the spatial simulation error generated by the finite difference method,previous researchers compute the optimal finite-difference weights always by minimizing the error of spatial dispersion relation.However,we prove that the spatial simulation error of the finite difference method is associated with the dot product of the spatial dispersion relation of the finite-difference weights and the spectrum of the seismic wavefield.Based on the dot product relation,we construct a L_(2) norm cost function to minimize spatial simulation error.For solving this optimization problem,the seismic wavefield infor-mation in wavenumber region is necessary.Nevertheless,the seismic wavefield is generally obtained by costly forward modeling techniques.To reduce the computational cost,we substitute the spectrum of the seismic wavelet for the spectrum of the seismic wavefield,as the seismic wavelet plays a key role in determining the seismic wavefield.In solving the optimization problem,we design an exhaustive search method to obtain the solution of the L_(2) norm optimization problem.After solving the optimization problem,we are able to achieve the finite-difference weights that minimize spatial simulation error.In theoretical error analyses,the finite-difference weights from the proposed method can output more accurate simulation results compared to those from previous optimization algorithms.Furthermore,we validate our method through numerical tests with synthetic models,which encompass homogenous/inhomogeneous media as well as isotropic and anisotropic media.
基金supported by the National Natural Science Foundation of China(Grant No.42004103)Sichuan Science and Technology Program(2023NSFSC0257)the CNPC Innovation Found(2022DQ02-0306).
文摘Internal multiple interference,affecting both seismic data processing and interpretation,has been observed for long time.Although great progress has been achieved in developing a variety of internal-multiple-elimination(IME)methods,how to increase accuracy and reduce cost of IME still poses a significant challenge.A new method is proposed to effectively and efficiently eliminate internal multi-ples,along with its application in internal-multiple-eliminated-migration(IMEM),addressing this issue.This method stems from two-way wave equation depth-extrapolation scheme and associated up/down wavefield separation,which can accomplish depth-extrapolation of both up-going and down-going wavefields simultaneously,and complete internal-multiple-elimination processing,adaptively and effi-ciently.The proposed method has several features:(1)input data is same as that for conventional migration:source signature(used for migration only),macro velocity model,and receiver data,without additional requirements for source/receiver sampling;(2)method is efficient,without need of iterative calculations(which are typically needed for most of IME algorithms);and(3)method is cost effective:IME is completed in the same depth-extrapolation scheme of IMEM,without need of a separate pro-cessing and additional cost.Several synthesized data models are used to test the proposed method:one-dimensional model,horizontal layered model,multi-layer model with one curved layer,and SEG/EAGE Salt model.Additionally,we perform a sensitivity analysis of velocity using smoothed models.This analysis reveals that although the accuracy of velocity measurements impacts our proposed method,it significantly reduces internal multiple false imaging compared to traditional RTM techniques.When applied to actual seismic data from a carbonate reservoir zone,our method demonstrates superior clarity in imaging results,even in the presence of high-velocity carbonate formations,outperforming conven-tional migration methods in deep strata.
基金supported by the National Key R&D Program of China(No.2018YFA0702505)the project of CNOOC Limited(Grant No.CNOOC-KJ GJHXJSGG YF 2022-01)+1 种基金R&D Department of China National Petroleum Corporation(Investigations on fundamental experiments and advanced theoretical methods in geophysical prospecting application,2022DQ0604-02)NSFC(Grant Nos.U23B20159,41974142,42074129,12001311)。
文摘P-and S-wave separation plays an important role in elastic reverse-time migration.It can reduce the artifacts caused by crosstalk between different modes and improve image quality.In addition,P-and Swave separation can also be used to better understand and distinguish wave types in complex media.At present,the methods for separating wave modes in anisotropic media mainly include spatial nonstationary filtering,low-rank approximation,and vector Poisson equation.Most of these methods require multiple Fourier transforms or the calculation of large matrices,which require high computational costs for problems with large scale.In this paper,an efficient method is proposed to separate the wave mode for anisotropic media by using a scalar anisotropic Poisson operator in the spatial domain.For 2D problems,the computational complexity required by this method is 1/2 of the methods based on solving a vector Poisson equation.Therefore,compared with existing methods based on pseudoHelmholtz decomposition operators,this method can significantly reduce the computational cost.Numerical examples also show that the P and S waves decomposed by this method not only have the correct amplitude and phase relative to the input wavefield but also can reduce the computational complexity significantly.
基金This research is sponsored by the National"973"Project(No.2007CB209603)the"863"Project(No.2006AA06Z108)
文摘Stability is the key to inverse Q-filtering. In this paper we present a stable approach to inverse Q-filtering, based on the theory of wavefield downward continuation. It is implemented in a layered manner, assuming a layered-earth Q model. For each individual constant Q layer, the seismic wavefield recorded at the surface is first extrapolated down to the top of the current layer and a constant Q inverse filter is then applied to the current layer. When extrapolating within the overburden, a stable wavefield continuation algorithm in combination with a stabilization factor is applied. This avoids accumulating inverse Q-filter errors within the overburden. Within the current constant Q layer, we use Gabor spectral analysis on the signals to pick time-variant gain-constrained frequencies and then deduce the corresponding gain-constrained amplitudes to stabilize the inverse Q-filtering algorithm. The algorithm is tested and verified application to field data.
基金This research was supported by the National Natural Science Foundation of China （Nos. 41230210 and 41204074）, the Science Foundation of the Education Department of Yunnan Province （No. 2013Z152）, and Statoil Company （Contract No. 4502502663）.
文摘We propose a symplectic partitioned Runge-Kutta （SPRK） method with eighth-order spatial accuracy based on the extended Hamiltonian system of the acoustic waveequation. Known as the eighth-order NSPRK method, this technique uses an eighth-orderaccurate nearly analytic discrete （NAD） operator to discretize high-order spatial differentialoperators and employs a second-order SPRK method to discretize temporal derivatives.The stability criteria and numerical dispersion relations of the eighth-order NSPRK methodare given by a semi-analytical method and are tested by numerical experiments. We alsoshow the differences of the numerical dispersions between the eighth-order NSPRK methodand conventional numerical methods such as the fourth-order NSPRK method, the eighth-order Lax-Wendroff correction （LWC） method and the eighth-order staggered-grid （SG）method. The result shows that the ability of the eighth-order NSPRK method to suppress thenumerical dispersion is obviously superior to that of the conventional numerical methods. Inthe same computational environment, to eliminate visible numerical dispersions, the eighth-order NSPRK is approximately 2.5 times faster than the fourth-order NSPRK and 3.4 timesfaster than the fourth-order SPRK, and the memory requirement is only approximately47.17% of the fourth-order NSPRK method and 49.41% of the fourth-order SPRK method,which indicates the highest computational efficiency. Modeling examples for the two-layermodels such as the heterogeneous and Marmousi models show that the wavefields generatedby the eighth-order NSPRK method are very clear with no visible numerical dispersion.These numerical experiments illustrate that the eighth-order NSPRK method can effectivelysuppress numerical dispersion when coarse grids are adopted. Therefore, this methodcan greatly decrease computer memory requirement and accelerate the forward modelingproductivity. In general, the eighth-order NSPRK method has tremendous potential value forseismic exploration and seismology research.
基金supported by the National Natural Science Foundation of China(No.41174087,41204089)the National Oil and Gas Major Project(No.2011ZX05005-005)
文摘Prestack reverse time migration（PSTM） is a common imaging method; however low-frequency noises reduce the structural imaging precision. Thus, the suppression of migration noises must be considered. The generation mechanism of low-frequency noises is analyzed and the up-, down-, left-, and right-going waves are separated using the Poynting vector of the acoustic wave equation. The computational complexity and memory capacitance of the proposed method are far smaller than that required when using the conventional separation algorithm of 2D Fourier transform. The normalized wavefield separation crosscorrelation imaging condition is used to suppress low-frequency noises in reverse time migration and improve the imaging precision. Numerical experiments using the Marmousi model are performed and the results show that the up-, down-, left-, and right-going waves are well separated in the continuation of the wavefield using the Poynting vector. We compared the imaging results with the conventional method, Laplacian filtering, and wavefield separation with the 2D Fourier transform. The comparison shows that the migration noises are well suppressed using the normalized wavefield separation cross-correlation imaging condition and higher precision imaging results are obtained.
基金supported by the 973 Program (Grant No.2007CB209505)the National Natural Science Foundation of China (Grant No.40674061,40704019)
文摘Wavefields in porous media saturated by two immiscible fluids are simulated in this paper.Based on the sealed system theory,the medium model considers both the relative motion between the fluids and the solid skeleton and the relaxation mechanisms of porosity and saturation（capillary pressure）.So it accurately simulates the numerical attenuation property of the wavefields and is much closer to actual earth media in exploration than the equivalent liquid model and the unsaturated porous medium model on the basis of open system theory.The velocity and attenuation for different wave modes in this medium have been discussed in previous literature but studies of the complete wave-field have not been reported.In our work,wave equations with the relaxation mechanisms of capillary pressure and the porosity are derived.Furthermore,the wavefield and its characteristics are studied using the numerical finite element method.The results show that the slow P3-wave in the non-wetting phase can be observed clearly in the seismic band.The relaxation of capillary pressure and the porosity greatly affect the displacement of the non-wetting phase.More specifically,the displacement decreases with increasing relaxation coefficient.
文摘Solving the wave equation is one of the most(if not the most)fundamental problems we face as we try to illuminate the Earth using recorded seismic data.The Helmholtz equation provides wavefield solutions that are dimensionally reduced,per frequency,compared to the time domain,which is useful for many applications,like full waveform inversion.However,our ability to attain such wavefield solutions depends often on the size of the model and the complexity of the wave equation.Thus,we use here a recently introduced framework based on neural networks to predict functional solutions through setting the underlying physical equation as a loss function to optimize the neural network(NN)parameters.For an input given by a location in the model space,the network learns to predict the wavefield value at that location,and its partial derivatives using a concept referred to as automatic differentiation,to fit,in our case,a form of the Helmholtz equation.We specifically seek the solution of the scattered wavefield considering a simple homogeneous background model that allows for analytical solutions of the background wavefield.Providing the NN with a reasonable number of random points from the model space will ultimately train a fully connected deep NN to predict the scattered wavefield function.The size of the network depends mainly on the complexity of the desired wavefield,with such complexity increasing with increasing frequency and increasing model complexity.However,smaller networks can provide smoother wavefields that might be useful for inversion applications.Preliminary tests on a two-box-shaped scatterer model with a source in the middle,as well as,the Marmousi model with a source at the surface demonstrate the potential of the NN for this application.Additional tests on a 3D model demonstrate the potential versatility of the approach.
基金supported by the National Science Foundation of China(No.41174100)the Large-scale Oil and Gas Field and Coalbed Methane Development Major Projects(No.2011ZX05019-008-08)the China National Petroleum Corporation(No.2014A-3609)
文摘Wavefield separation of multicomponent seismic data to image subsurface structures can be realized in either the space domain or the wavenumber domain. However, as the particle velocity components used in the wavenumber-domain wavefield separation are not defined at the same grid point with the staggered-grid finite-difference method for elastic wavefield simulation, we propose the wavenumber-domain interpolation method to estimate the required values at the common grid points prior to the wavenumber-domain true-amplitude wavefield separation. Moreover, numerical experiments show that the wavenumber-domain interpolation method has high interpolation accuracy and the trueamplitude wavefield separation method shows good amplitude preservation. The application of the proposed methodology to elastic reverse-time migration can obtain good amplitudepreserved images even in the case of some velocity error.
基金The Herbette Fondation at the University of Lausanne, Switzerland
文摘With increased computational power, reverse-time prestack depth migration（RT-PSDM） has become a preferred imaging tool in seismic exploration, yet its use has remained relatively limited in ground-penetrating radar（GPR） applications. Complex topography alters the wavefield kinematics making for a challenging imaging problem. Model simulations show that topographic variation can substantially distort reflection amplitudes due to irregular wavefield spreading, attenuation anomalies due to irregular path lengths, and focusing and defocusing effects at the surface. The effects are magnified when the topographic variations are on the same order as the depth of investigation––a situation that is often encountered in GPR investigations. Here, I use a full wave-equation RT-PSDM algorithm to image GPR data in the presence of large topographic variability relative to the depth of investigation. The source and receiver wavefields are propagated directly from the topographic surface and this approach inherently corrects for irregular kinematics, spreading and attenuation. The results show that when GPR data are acquired in areas of extreme topography, RT-PSDM can accurately reconstruct reflector geometry as well as reflection amplitude.
基金supported by the National Natural Science Foundation of China (Nos. 41304096, 41176077, 412303 18)the National Science and Technology Major Project of China (No. 2016ZX05024-001-002)+1 种基金the National Hightech R&D Program of China (863 Program) (Nos. 2013 AA092501, 2017YFC0307401)the Fundamental Research Funds for the Central Universities (No. 201762 019)
文摘Compared to towed streamers, ocean-bottom seismometers(OBS) obtain both S-wave data and richer wavefield information. In this paper, the induced polarization method is used to conduct wavefield separation on OBS data obtained from the Shenhu area in the South China Sea. A comparison of the changes in P-and S-waves, and a comprehensive analysis of geological factors within the area, enable analysis and description of the occurrence of natural gas hydrate in the study area. Results show an increase in P-wave velocity when natural gas hydrate exists in the formation, whereas the S-wave velocity remains almost constant, as S-waves can only propagate through the rock skeleton. Therefore, the bottom-simulating reflection(BSR) response of the P-wave is better than that of the S-wave in the frequency analysis profile. In a wide-angle section, the refractive wave of the hydrate layer is evident when using P-wave components but identification is difficult with S-wave components. This velocity model illustrates the sensitivity of Pand S-wave components to gas hydrate. The use of this polarization method and results of analysis provide technical and theoretical support for research on hydrate deposits and other geological features in the Shenhu area.
基金This project is sporspored by Fund item:the National Development and Innovation Committee Program (2005) 2372the National High-tech R&D Program (863 Program) 2006AA06Z241 of ChinaYouth Innovation Fund of CNPC (Program:Prestack Imaging Integral Study for Complex near Surface)
文摘The Pre-Stack Depth Migration （PSDM） method based on wavefield continuation is the most reliable method for imaging complex structure in the subsurface, although there are large computational costs and poorly adaptive geometry. Plane wave shot migration is another method to perform exact wave equation prestack imaging with high computational efficiency and without the migration aperture problem. Moreover, wavefield energy can be compensated at the target zone by controlled illumination. In this paper, plane wave shot PSDM was implemented by the control of the plane down-going wavefield and selection of number and range of the raypaths in order to optimize the imaging effect. In addition, controlled illumination techniques are applied to enhance the imaging precision of interesting areas at different depths. Numerical calculation indicates that plane wave shot imaging is a rapid and efficient method with less computational cost and easy parallel computation compared to the single-square-root operator imaging for common shot gathers and double- square-root operator imaging for common midpoint gathers.
基金supported by Special Research Grant for Non-profit Public Service(No.201511037)National Natural Science Foundation of China(No.41504109,41506084,and 41406071)+1 种基金China Postdoctoral Science Foundation(No.2015M582060)Qingdao Municipal Applied Research Projects(No.2015308)
文摘Imaging the PP- and PS-wave for the elastic vector wave reverse-time migration requires separating the P- and S-waves during the wave field extrapolation. The amplitude and phase of the P- and S-waves are distorted when divergence and curl operators are used to separate the P- and S-waves. We present a P- and S-wave amplitude-preserving separation algorithm for the elastic wavefield extrapolation. First, we add the P-wave pressure and P-wave vibration velocity equation to the conventional elastic wave equation to decompose the P- and S-wave vectors. Then, we synthesize the scalar P- and S-wave from the vector P- and S-wave to obtain the scalar P- and S-wave. The amplitude-preserved separated P- and S-waves are imaged based on the vector wave reverse-time migration (RTM). This method ensures that the amplitude and phase of the separated P- and S-wave remain unchanged compared with the divergence and curl operators. In addition, after decomposition, the P-wave pressure and vibration velocity can be used to suppress the interlayer reflection noise and to correct the S-wave polarity. This improves the image quality of P- and S-wave in multicomponent seismic data and the true-amplitude elastic reverse time migration used in prestack inversion.
基金sponsored by the Natural Science Foundation of China(No.41874139)the Natural Science Foundation of China(No.41674124)Jilin Province Foundation for Excellent Youths(No.20190103139JH)
文摘With the development of seismic exploration,passive-source seismic data has attracted increasing attention.Ambient noise passive seismic sources exists widely in nature and industrial production.Passive seismic data is important in logging while drilling(LWD),large-scale structural exploration,etc.In this paper,we proposed a passive multiple reverse time migration imaging(PMRTMI)method based on wavefield decomposition and normalized imaging conditions method.This method differs from seismic interferometry in that it can use raw passive seismic data directly in RTM imaging without reconstruction of virtual active gather,and we use the wavefield decomposition method to eliminate the low frequency noise in RTM.Further,the energy normalized imaging condition is used in full wavefield decomposition,which can not only enhance the image quality of both edge and deep information but also overcome the wrong energy problem caused by uneven distribution of passive sources;furthermore,this method exhibits high efficiency.Finally,numerical examples with the Marmousi model show the effectiveness of the method.
基金This work was supported by National Natural Science Foundation of China （No. 41474110） and the Scientific Research Starting Foundation of China University of Petroleum-Beijing at Karamay （No. RCYJ2018A-01-001）.
文摘Reverse-time migration has attracted more and more attention owing to the advantages of high imaging accuracy, no dip restriction, and adaptation to complex velocity models. Cross-correlation imaging method is typically used in conventional reverse-time migration that produces images with strong low-frequency noise. Wavefield decomposition imaging can suppress such noise; however, some residual noise persists in the imaging results. We propose a 2D multidirectional wavefield decomposition method based on the traditional wavefield decomposition method. First, source wavefields and receiver wavefields are separated into eight subwavefields, respectively. Second, cross-correlation imaging is applied to selected subwavefields to produce subimages. Finally, the subimages are stacked to generate the final image. Numerical examples suggest that the proposed method can eliminate the low-frequency noise effectively and produce high-quality imaging profiles.
基金the National Development and Innovation Committee Program (2005) 2372the National High-tech R&D Program (863 Program) 2006AA06Z241 of ChinaYouth Innovation Fund of CNPC’ Prestack Imaging Integral Study for Complex near Surface.
文摘When topography and low velocity zone differences vary greatly, conventional vertical static time shifts will cause wavefield distortion and influence wave equation seismic imaging for seismic data acquired on a complex near surface. In this paper, we propose an approach to datum correction that combines a joint tomography inversion with wavefield continuation to solve the static problem for seismic data on rugged acquisition topography. First, the near surface model is obtained by refracted wave tomography inversion. Second, the wavefield of sources and receivers are continued downward and upward to accomplish datum correction starting from a flat surface and locating the datum above topography. Based on the reciprocal theorem, Huygens＇ and Fresnel principles, the location of sources and receivers, and regarding the recorded data on the surface as a secondary emission, the sources and receivers are upward-continued to the datum above topography respectively. Thus, the datum correction using joint tomography inversion and wavefield continuation with the condition of a complex near surface is accomplished.
基金funded jointly by the National Natural Science Foundation of China(No.41104069)Shandong Province Higher Educational Science and Technology Program(No.J17KA197)+1 种基金Open Foundation of Shandong Provincial Key Laboratory of Depositional Mineralization&Sedimentary Minerals of Shandong University of Science and Technology(No.DMSM2018018)Chunhui Research Foundation of Shengli College,China University of Petroleum(No.KY2017007)。
文摘Fracture-cave reservoirs in carbonate rocks are characterized by a large difference in fracture and cavity size,and a sharp variation in lithology and velocity,thereby resulting in complex diffraction responses.Some small-scale fractures and caves cause weak diffraction energy and would be obscured by the continuous reflection layer in the imaging section,thereby making them difficult to identify.This paper develops a diffraction wave imaging method in the dip domain,which can improve the resolution of small-scale diffractors in the imaging section.Common imaging gathers(CIGs)in the dip domain are extracted by Gaussian beam migration.In accordance with the geometric differences of the diffraction being quasilinear and the reflection being quasiparabolic in the dip-domain CIGs,we use slope analysis technique to filter waves and use Hanning window function to improve the diffraction wave separation level.The diffraction dip-domain CIGs are stacked horizontally to obtain diffraction imaging results.Wavefield separation analysis and numerical modeling results show that the slope analysis method,together with Hanning window filtering,can better suppress noise to obtain the diffraction dip-domain CIGs,thereby improving the clarity of the diffractors in the diffraction imaging section.
