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- Volume 59, Issue 3, 2011
Geophysical Prospecting - Volume 59, Issue 3, 2011
Volume 59, Issue 3, 2011
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Caustics in a periodically layered transversely isotropic medium with vertical symmetry axis
Authors Y. Roganov and A. StovasABSTRACTWave propagation in a finely layered medium is a very important topic in seismic modelling and inversion. Here we analyse non‐vertical wave propagation in a periodically layered transversely isotropic (VTI) medium and show that the evanescent (attenuation) zones in the frequency‐horizontal slowness domain result in caustics in the group velocity domain. These caustics, which may appear for both the quasi‐compressional (qP) and quasi‐shear (qSV) wave surfaces are frequency dependent but display weak dependence at low frequencies. The caustics computed for a specific frequency differ from those observed at the low‐ and high‐frequency limits.
We illustrate these caustics with a few numerical examples and snapshots computed for both qP‐ and qSV‐wave types.
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3D acoustic waveform inversion in the Laplace domain using an iterative solver
Authors Sukjoon Pyun, Woohyun Son and Changsoo ShinABSTRACTIn this paper we propose a 3D acoustic full waveform inversion algorithm in the Laplace domain. The partial differential equation for the 3D acoustic wave equation in the Laplace domain is reformulated as a linear system of algebraic equations using the finite element method and the resulting linear system is solved by a preconditioned conjugate gradient method. The numerical solutions obtained by our modelling algorithm are verified through a comparison with the corresponding analytical solutions and the appropriate dispersion analysis. In the Laplace‐domain waveform inversion, the logarithm of the Laplace transformed wavefields mainly contains long‐wavelength information about the underlying velocity model. As a result, the algorithm smoothes a small‐scale structure but roughly identifies large‐scale features within a certain depth determined by the range of offsets and Laplace damping constants employed. Our algorithm thus provides a useful complementary process to time‐ or frequency‐domain waveform inversion, which cannot recover a large‐scale structure when low‐frequency signals are weak or absent. The algorithm is demonstrated on a synthetic example: the SEG/EAGE 3D salt‐dome model. The numerical test is limited to a Laplace‐domain synthetic data set for the inversion. In order to verify the usefulness of the inverted velocity model, we perform the 3D reverse time migration. The migration results show that our inversion results can be used as an initial model for the subsequent high‐resolution waveform inversion. Further studies are needed to perform the inversion using time‐domain synthetic data with noise or real data, thereby investigating robustness to noise.
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Diffraction‐limited imaging and beyond – the concept of super resolution‡
Authors Leiv‐J. Gelius and Endrias AsgedomABSTRACTIt is well‐known that experimental or numerical backpropagation of waves generated by a point‐source/‐scatterer will refocus on a diffraction‐limited spot with a size not smaller than half the wavelength. More recently, however, super‐resolution techniques have been introduced that apparently can overcome this fundamental physical limit. This paper provides a framework of understanding and analysing both diffraction‐limited imaging as well as super resolution.
The resolution analysis presented in the first part of this paper unifies the different ideas of backpropagation and resolution known from the literature and provides an improved platform to understand the cause of diffraction‐limited imaging. It is demonstrated that the monochromatic resolution function consists of both causal and non‐causal parts even for ideal acquisition geometries. This is caused by the inherent properties of backpropagation not including the evanescent field contributions. As a consequence, only a diffraction‐limited focus can be obtained unless there are ideal acquisition surfaces and an infinite source‐frequency band.
In the literature various attempts have been made to obtain images resolved beyond the classical diffraction limit, e.g., super resolution. The main direction of research has been to exploit the evanescent field components. However, this approach is not practical in case of seismic imaging in general since the evanescent waves are so weak – because of attenuation, they are masked by the noise. Alternatively, improvement of the image resolution of point like targets beyond the diffraction limit can apparently be obtained employing concepts adapted from conventional statistical multiple signal classification (MUSIC). The basis of this approach is the decomposition of the measurements into two orthogonal domains: signal and noise (nil) spaces. On comparison with Kirchhoff prestack migration this technique is showed to give superior results for monochromatic data. However, in case of random noise the super‐ resolution power breaks down when employing monochromatic data and a limited acquisition aperture. For such cases it also seems that when the source‐receiver lay out is less correlated, the use of a frequency band may restore the super‐resolution capability of the method.
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Angle gathers in wave‐equation imaging for transversely isotropic media
Authors Tariq Alkhalifah and Sergey FomelABSTRACTIn recent years, wave‐equation imaged data are often presented in common‐image angle‐domain gathers as a decomposition in the scattering angle at the reflector, which provide a natural access to analysing migration velocities and amplitudes. In the case of anisotropic media, the importance of angle gathers is enhanced by the need to properly estimate multiple anisotropic parameters for a proper representation of the medium. We extract angle gathers for each downward‐continuation step from converting offset‐frequency planes into angle‐frequency planes simultaneously with applying the imaging condition in a transversely isotropic with a vertical symmetry axis (VTI) medium. The analytic equations, though cumbersome, are exact within the framework of the acoustic approximation. They are also easily programmable and show that angle gather mapping in the case of anisotropic media differs from its isotropic counterpart, with the difference depending mainly on the strength of anisotropy. Synthetic examples demonstrate the importance of including anisotropy in the angle gather generation as mapping of the energy is negatively altered otherwise. In the case of a titled axis of symmetry (TTI), the same VTI formulation is applicable but requires a rotation of the wavenumbers.
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Refractor velocity analysis: a signal processing procedure
More LessABSTRACTThis paper presents a signal processing procedure to perform refractor velocity analysis. The procedure enables one to obtain the seismic velocity from the refracted wavefield without the picking of refracted arrival times. Two processing procedures are derived, one starting from a seismic interferometric approach and another, from the conventional reciprocal method and generalized reciprocal method approaches. The theoretical equivalence of the two approaches is also demonstrated.
The proposed processing procedure is applied to synthetic data in order to test the influence of some procedural parameters and its capability to reconstruct a known velocity model starting from refracted signals, without and with perturbations, in arrival times and noise; finally, it is applied to a field data set.
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Prestack Kirchhoff time migration of 3D coal seismic data from mining zones
Authors Yijun Yuan, Yuan Gao, Liying Bai and Zhanzu LiuABSTRACTConventional seismic data processing methods based on post‐stack time migration have been playing an important role in coal exploration for decades. However, post‐stack time migration processing often results in low‐quality images in complex geological environments. In order to obtain high‐quality images, we present a strategy that applies the Kirchhoff prestack time migration (PSTM) method to coal seismic data. In this paper, we describe the implementation of Kirchhoff PSTM to a 3D coal seam. Meanwhile we derive the workflow of 3D Kirchhoff PSTM processing based on coal seismic data. The processing sequence of 3D Kirchhoff PSTM includes two major steps: 1) the estimation of the 3D root‐mean‐square (RMS) velocity field; 2) Kirchhoff prestack time migration processing. During the construction of a 3D velocity model, dip moveout velocity is served as an initial migration velocity field. We combine 3D Kirchhoff PSTM with the continuous adjustment of a 3D RMS velocity field by the criteria of flattened common reflection point gathers. In comparison with post‐stack time migration, the application of 3D Kirchhoff PSTM to coal seismic data produces better images of the coal seam reflections.
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Seismic interferometry experiment in a shallow cased borehole using a seismic vibrator source‡
Authors Flavio Poletto, Lorenzo Petronio, Biancamaria Farina and Andrea SchleiferABSTRACTWe present the results of a seismic interferometry experiment in a shallow cased borehole. The experiment is an initial study for subsequent borehole seismic surveys in an instrumented well site, where we plan to test other surface/borehole seismic techniques. The purpose of this application is to improve the knowledge of the reflectivity sequence and to verify the potential of the seismic interferometry approach to retrieve high‐frequency signals in the single well geometry, overcoming the loss and attenuation effects introduced by the overburden. We used a walkaway vertical seismic profile (VSP) geometry with a seismic vibrator to generate polarized vertical and horizontal components along a surface seismic line and an array of 3C geophones cemented outside the casing. The recorded traces are processed to obtain virtual sources in the borehole and to simulate single‐well gathers with a variable source‐receiver offset in the vertical array. We compare the results obtained by processing the field data with synthetic signals calculated by numerical simulation and analyse the signal bandwidth and amplitude versus offset to evaluate near‐field effects in the virtual signals. The application provides direct and reflected signals with improved bandwidth after vibrator signal deconvolution. Clear reflections are detected in the virtual seismic sections in agreement with the geology and other surface and borehole seismic data recorded with conventional seismic exploration techniques.
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Preconditioned non‐linear conjugate gradient method for frequency domain full‐waveform seismic inversion
Authors W. Hu, A. Abubakar, T. M. Habashy and J. LiuABSTRACTWe present preconditioned non‐linear conjugate gradient algorithms as alternatives to the Gauss‐Newton method for frequency domain full‐waveform seismic inversion. We designed two preconditioning operators. For the first preconditioner, we introduce the inverse of an approximate sparse Hessian matrix. The approximate Hessian matrix, which is highly sparse, is constructed by judiciously truncating the Gauss‐Newton Hessian matrix based on examining the auto‐correlation and cross‐correlation of the Jacobian matrix. As the second preconditioner, we employ the approximation of the inverse of the Gauss‐Newton Hessian matrix. This preconditioner is constructed by terminating the iteration process of the conjugate gradient least‐squares method, which is used for inverting the Hessian matrix before it converges. In our preconditioned non‐linear conjugate gradient algorithms, the step‐length along the search direction, which is a crucial factor for the convergence, is carefully chosen to maximize the reduction of the cost function after each iteration. The numerical simulation results show that by including a very limited number of non‐zero elements in the approximate Hessian, the first preconditioned non‐linear conjugate gradient algorithm is able to yield comparable inversion results to the Gauss‐Newton method while maintaining the efficiency of the un‐preconditioned non‐linear conjugate gradient method. The only extra cost is the computation of the inverse of the approximate sparse Hessian matrix, which is less expensive than the computation of a forward simulation of one source at one frequency of operation. The second preconditioned non‐linear conjugate gradient algorithm also significantly saves the computational expense in comparison with the Gauss‐Newton method while maintaining the Gauss‐Newton reconstruction quality. However, this second preconditioned non‐linear conjugate gradient algorithm is more expensive than the first one.
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Characterization of fractured reservoirs using a consistent stiffness‐permeability model: focus on the effects of fracture aperture
Authors Ali Shahraini, Aamir Ali and Morten JakobsenABSTRACTIn this paper we propose a method for the characterization of naturally fractured reservoirs by quantitative integration of seismic and production data. The method is based on a consistent theoretical frame work to model both effective hydraulic and elastic properties of fractured porous media and a (non‐linear) Bayesian method of inversion that provides information about uncertainties as well as mean (or maximum likelihood) values. We model a fractured reservoir as a porous medium containing a single set of vertical fractures characterized by an unknown fracture density, azimuthal orientation and aperture. We then look at the problem of fracture parameter estimation as a non‐linear inverse problem and try to estimate the unknown fracture parameters by joint inversion of seismic amplitude versus angle and azimuth data and dynamic production data. Once the fracture parameters have been estimated the corresponding effective stiffness and permeability tensors can be estimated using consistent models. A synthetic example is provided to clearly explain and test the workflow. It shows that seismic and production data complement each other, in the sense that the seismic data resolve a non‐uniqueness in the fracture orientation and the production data help to recover the true fracture aperture and permeability, because production data are more sensitive to the fracture aperture than the seismic data.
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Pressure effects on the joint elastic‐electrical properties of reservoir sandstones
Authors Tongcheng Han, Angus I. Best, Jeremy Sothcott and Lucy M. MacGregorABSTRACTWe conducted a laboratory study of the joint elastic‐electrical properties of sixty‐three brine‐saturated sandstone samples to assess the likely impact of differential pressure (confining minus pore fluid pressures) in the range 8–60 MPa on the joint interpretation of marine seismic and controlled‐source electromagnetic survey data. The samples showed a wide range of petrophysical properties representative of most sandstone reservoirs. We found that a regression equation comprising both a constant and an exponential part gave a good fit to the pressure dependence of all five measured geophysical parameters (ultrasonic P‐ and S‐wave velocity, attenuation and electrical resistivity). Electrical resistivity was more pressure‐sensitive in clay‐rich sandstones with higher concentrations of low aspect ratio pores and micropores than in clean sandstones. Attenuation was more pressure‐sensitive in clean sandstones with large open pores (macropores) than in clay‐rich sandstones. Pore shape did not show any influence on the pressure sensitivity of elastic velocity. As differential pressure increases, the effect of the low aspect ratio pores and micropores on electrical resistivity becomes stronger than the effect of the macropores on attenuation. Further analysis of correlations among the five parameters as a function of pressure revealed potentially diagnostic relationships for geopressure prediction in reservoir sandstones.
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Joint elastic‐electrical properties of reservoir sandstones and their relationships with petrophysical parameters
Authors Tongcheng Han, Angus I. Best, Jeremy Sothcott and Lucy M. MacGregorABSTRACTWe measured in the laboratory ultrasonic compressional and shear‐wave velocity and attenuation (0.7–1.0 MHz) and low‐frequency (2 Hz) electrical resistivity on 63 sandstone samples with a wide range of petrophysical properties to study the influence of reservoir porosity, permeability and clay content on the joint elastic‐electrical properties of reservoir sandstones. P‐ and S‐wave velocities were found to be linearly correlated with apparent electrical formation factor on a semi‐logarithmic scale for both clean and clay‐rich sandstones; P‐ and S‐wave attenuations showed a bell‐shaped correlation (partial for S‐waves) with apparent electrical formation factor. The joint elastic‐electrical properties provide a way to discriminate between sandstones with similar porosities but with different clay contents. The laboratory results can be used to estimate sandstone reservoir permeability from seismic velocity and apparent formation factor obtained from co‐located seismic and controlled source electromagnetic surveys.
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Texture and anisotropy analysis of Qusaiba shales
More LessABSTRACTScanning and transmission electron microscopy, synchrotron X‐ray diffraction, microtomography and ultrasonic velocity measurements were used to characterize microstructures and anisotropy of three deeply buried Qusaiba shales from the Rub’al‐Khali basin, Saudi Arabia. Kaolinite, illite‐smectite, illite‐mica and chlorite show strong preferred orientation with (001) pole figure maxima perpendicular to the bedding plane ranging from 2.4–6.8 multiples of a random distribution (m.r.d.). Quartz, feldspars and pyrite crystals have a random orientation distribution. Elastic properties of the polyphase aggregate are calculated by averaging the single crystal elastic properties over the orientation distribution, assuming a nonporous material. The average calculated bulk P‐wave velocities are 6.2 km/s (maximum) and 5.5 km/s (minimum), resulting in a P‐wave anisotropy of 12%. The calculated velocities are compared with those determined from ultrasonic velocity measurements on a similar sample. In the ultrasonic experiment, which measures the effects of the shale matrix as well as the effects of porosity, velocities are smaller (P‐wave maximum 5.3 km/s and minimum 4.1 km/s). The difference between calculated and measured velocities is attributed to the effects of anisotropic pore structure and to microfractures present in the sample, which have not been taken into account in the matrix averaging.
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An algorithm for fast 3D inversion of surface electrical resistivity tomography data: application on imaging buried antiquities
Authors N.G. Papadopoulos, P. Tsourlos, C. Papazachos, G.N. Tsokas, A. Sarris and J.H. KimABSTRACTIn this work a new algorithm for the fast and efficient 3D inversion of conventional 2D surface electrical resistivity tomography lines is presented. The proposed approach lies on the assumption that for every surface measurement there is a large number of 3D parameters with very small absolute Jacobian matrix values, which can be excluded in advance from the Jacobian matrix calculation, as they do not contribute significant information in the inversion procedure. A sensitivity analysis for both homogeneous and inhomogeneous earth models showed that each measurement has a specific region of influence, which can be limited to parameters in a critical rectangular prism volume. Application of the proposed algorithm accelerated almost three times the Jacobian (sensitivity) matrix calculation for the data sets tested in this work. Moreover, application of the least squares regression iterative inversion technique, resulted in a new 3D resistivity inversion algorithm more than 2.7 times faster and with computer memory requirements less than half compared to the original algorithm. The efficiency and accuracy of the algorithm was verified using synthetic models representing typical archaeological structures, as well as field data collected from two archaeological sites in Greece, employing different electrode configurations. The applicability of the presented approach is demonstrated for archaeological investigations and the basic idea of the proposed algorithm can be easily extended for the inversion of other geophysical data.
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Gravity analysis of salt structures. An example from the El Kef‐Ouargha region (northern Tunisia)
Authors Mohamed Arfaoui, Mohamed Hédi Inoubli, Saïd Tlig and Rabeh AlouaniABSTRACTTriassic outcrops in the Atlassic zone of northern Tunisia may be modelled in two ways: salt bodies piercing through Cretaceous terrains or Triassic salt flows stratified within an Albian series. Both models find support from gravity data and are debatable. To evaluate the mass distribution changes with depth, the Bouguer anomaly of the El Kef‐Ouargha region was successively decomposed into regional and residual components to construct multiple pseudo‐depth slices and apparent density maps. Analyses of gravity lows clearly show a vertical continuity of less dense materials below the Triassic salt outcrops. These features can be explained by salt diapirism during Mesozoic and Cenozoic. Further, gravity data tend to indicate less dense materials below Aptian outcropping in Jebel Aite (Oued Bou Adila); thus suggesting Triassic materials occurring at depth. In addition, dense entities were recognized under Mio‐Pliocene and Quaternary deposits, which are thought to correspond to Cretaceous paleoshoals currently collapsed by non‐outcropping faults. Our findings lend support to a diapir model intruding overburden rather than the salt glacier model stratified in the Albian series proposed by some authors as the genetic structural model for Triassic material‐bearing series in the north of Tunisia.
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