Seismic Shear Energy Reflection By Radon-Fourier Transform

Low RCS targets detection is a challenging problem for marine radar in sea clutter. In this paper, a new detection algorithm is developed based on Radon and inverse Radon transform which accounts for the linear feature of the targets in sea clutter. After Radon transform the SCR is increased and clutter can be suppressed more easily in Radon domain. Then the data in Radon domain can be inverse Radon transformed into time-range domain, and the target track can be detected. The simulation results show that the proposed algorithm makes the detection of very small targets possible.

A simple shearlet-based 2D Radon inversion with an application to computed tomography

The basic requirements to recover plane layers of constant interval velocity, arbitrary dip and strike from common depth point (CDP) recordings are the following four quantities related to the primary event of each reflector at the common midpoint of a CDP profile: a) Two‐way normal time b) Normal moveout velocity within one arbitrary CDP profile c) Time slope of normally reflected rays within the profile d) Time slope of normally reflected rays in some other direction. The solution of the inverse problem is obtained directly. The moveout velocity is expressed in terms of seismic parameters along the normal incidence path in three dimensions and the direction of the profile within the free surface. A formula connecting dip and strike of the emerging normal ray with the measured time gradients is given and discussed. The method includes, as a special case, the Dix formulas for plane parallel layers.

The effectiveness of shallow high resolution ‘seismic reflection (i.e., resolution potential) to image geologic interfaces between about 70 and 750 ft at the Aberdeen Proving Grounds, Maryland (APG), appears to vary locally with the geometric complexity of the unconsolidated sediments that overlay crystalline bedrock. The bedrock surface (which represents the primary geologic target of this study) was imaged at each of three test areas on walkaway noise tests and CDP (common depth point) stacked data. Proven high resolution techniques were used to design and acquire data on this survey. Feasibility of the technique and minimum acquisition requirements were determined through evaluation and correlation of walkaway noise tests, CDP survey lines, and a downhole velocity check shot survey. Data processing and analysis revealed several critical attributes of shallow seismic data from APG that need careful consideration and compensation on reflection data sets. This survey determined: 1) the feasibility of the technique, 2) the resolution potential (both horizontal and vertical) of the technique, 3) the optimum source for this site, 4) the optimum acquisition geometries, 5) general processing flow, and 6) a basic idea of the acoustic variability across this site. Source testing involved an accelerated weight drop, land air gun, downhole black powder charge, sledge hammer/plate, and high frequency vibrator. Shallow seismic reflection profiles provided for a more detailed picture of the geometric complexity and variability of the distinct clay sequences (aquatards), previously inferred from drilling to be present, based on sparse drill holes and basewide conceptual models. The seismic data also reveal a clear explanation for the difficulties previously noted in correlating individual, borehole-identified sand or clay units over even short distances. Geologic cross-sections derived from CDP stacked data and borehole logs suggest locally complex geometries and horizontally variable geologic contacts.

X-ray computed tomography (CT) reconstruction with sparse projection views was proposed to reduce both the radiation dose and scan time. However, lacking of sufficient projection views may lead to severe artifacts for analytical reconstruction method such as the filtered back projection (FBP). Although the projection data is incomplete, we can generate the full-sampling system matrices according to the sufficient-sampling conditions [5]. Thus, we propose a novel iterative reconstruction model to fit the target images and the corresponding high resolution measurements in Radon domain by the full-sampling system matrices. Our proposed model is solved by the learned alternating minimization method, which accounts for a forward operator in deep neural network by the unrolling strategy. Numerical results demonstrate that the proposed approach outperforms some latest learning based reconstruction methods for the sparse-view CT problems.

The primary purpose of this paper is to show the benefits obtained from coordinating seismic and geologic information into an acceptable interpretation of the subsurface geologic conditions existing at a particular gas storage project. During 1974 and 1975, seismic explorations, utilizing the common depth point (CDP) technique and the Vibroseis energy method, were conducted at Northern Natural Gas Company's Dallas Center Aquifer Storage Prospect in central Iowa and Lyons Depleted Gas Field Storage Prospect in central Kansas. Although these two areas are geographically far removed from one another, the CDP technique is quite applicable to each of these geologic provinces. The petroleum engineer's need for detailed information about the configuration and integrity of the gas storage reservoir often surpasses the geologist's knowledge, based on a finite number of drill holes. The seismologist, working in close association with the geologist and utilizing modern field recording techniques, instruments and computer data enhancement, can add a new dimension to the understanding and thinking of both the petroleum engineer and geologist. Introduction The Dallas Center Anticline, located in Dallas County, Iowa, is 300 miles northeast of the Lyons Anticline, located in Rice County, Kansas. Both of these geologic structures have been evaluated by shallow and deep drill holes and by common depth point seismic work. The purpose of this evaluation was to prove their purpose of this evaluation was to prove their relative worth either as an aquifer gas storage prospect (Dallas Center) or to more accurately prospect (Dallas Center) or to more accurately define the boundary faults associated with an abandoned gas field (Lyons). Figure 1, an index map, shows the location of these two anticlines in relation to each other and to State and County boundaries, as well as major geologic features. Geologically, the two anticlines are in entirely different provinces. The Dallas Center Anticline is located at the extreme northern end of the Forest City Basin, eight miles east of the southeastern edge of the Mid-continent Gravity-Magnetic High. The Lyons Anticline is located on the southern half of the Genesco Uplift, the eastern most lobe of the larger Central Kansas Uplift. The Dallas Center Anticline was originally delineated by Northern Natural Gas Company from preliminary structural mapping of shallow farm preliminary structural mapping of shallow farm water well data.

The Common Depth Point (CDP) Method is a seismic data acquisition and processing technique which transforms field recordings from seismic surveys into pseudo-cross-sectional images of the earth's geologic layering beneath the survey line. Such images are the primary geophysical analysis tools used by explorationists to pinpoint likely drilling locations for oil and gas reservoirs. The CDP Method has evolved from an elementary data enhancement concept in the analog seismic era of the 1950s to a highly sophisticated digital imaging and parameter estimation technique in the 1980s. This paper reviews the history of the method, and its underlying mathematical-physical basis in terms of simple computer simulations of reflection seismic experiments. The method is illustrated with actual examples from several geologic provinces, and the paper closes with a discussion of some limitations of the CDP Stack and possible future directions in seismic imagery.

Multiple attenuation based on connected-component analysis and high-resolution parabolic Radon transform

Feasibility of detecting embedded cracks in concrete structures by reflection seismology

Summary Water column variations are an important source of non-repeatability in time-lapse marine surveys. In a deep water context, the physical property variations within the water layers can generate significant time-shifts between repeated time-lapse seismic data. We present a new methodology for estimating water velocity changes and correcting the 4D seismic datasets. Each sail line is migrated independently and Common Depth Point (CDP) gathers are produced for the overburden along a subsurface strip for both vintages. The 4D approach consists of performing cross-correlations using collocated CDPs for each sail lines pair. It creates water bottom “cross-image CDP gathers”. The cross-image CDP curvature along offsets is used to compute the water velocity difference between the two vintages. Once a water velocity is inverted for each sail line, the kinematic correction is performed on the pre-migrated datasets. The main difference with conventional approaches is the simultaneous usage of both 4D datasets for estimating the water velocity changes and therefore minimizing the seismic difference in the overburden. The methodology is significantly beneficial for deep-water 4D acquisitions. The correction for such small environmental variations improves the time-lapse data repeatability and is part of the effort for providing high resolution 4D images.

Seismic wave velocities, including effective velocities, play a critical role in the kinematic processing and interpretation of 2D and 3D seismic data. Along with other parameters of elastic waves, the geological efficiency of seismic exploration also depends on the level of knowledge of the velocity model of the medium, on the accuracy of information about velocities. The article briefly lists the main methods for determining the effective velocities according to the seismic wave field, developed and applied in the practice of seismic research. The methods used to determine the effective velocities of reflected waves can be divided into two groups: methods for determining the effective velocities based on automatic or visual tracking of the in-phase axes (i.e. hodographs) of reflected waves on seismic records, then their approximation by hyperbolas constitute the first group, and the second the group consists of methods based on the application of the analysis of the seismic wave field in controlled directions on the seismograms of a common depth point (CDP). Each proposed method for determining effective speeds has advantages and disadvantages. The article focuses on the industrial method, widely used at present, based on the analysis of the wave field in controlled directions, which do not provide sufficient information to solve the main problems of kinematic interpretation. The main disadvantages of the existing methods are indicated. The article describes a new method for determining the effective velocity, which is fundamentally different from the methods that are still used in the practice of seismic exploration. The fact is that in this method, seismic survey data of single and multiple profiling are not used separately, as it was in the methods used in seismic survey practice so far, but together. Formulas have been derived for determining the effective velocity based on the time gradients of the travel time curves of the CSP and CDP of reflected waves, which makes it possible to determine the speeds even from incomplete travel time curves. A technique for determining the effective speed has been developed and a sequence of procedures has been determined for solving the problem. The results of research are given on a specific example by solving the direct and inverse problems for the Sazhdag area between the Kura and Gabyrra rivers. The influence of errors in the values of the parameters included in the formula for calculating the effective speed on the final results is studied. At the end of the article, the main advantages of the proposed method are indicated.

Homomorphic filtering using the complex cepstrum has been used in many applications of one-dimensional (1D) signal processing, notably speech signal analysis and seismic signal analysis. Increasing attention is now being directed towards extension of cepstral filtering to the 2D domain. An application that we are particularly interested in is the extraction of texture elements or textons from an image with quasi-periodic or ordered texture. We show in this paper that 1D cepstral filtering techniques may be applied to the projections of textured images at various angles, i.e., in the Radon domain. The filtered projections may then be used to reconstruct an image of a single texton. Preliminary results with a synthetic image are presented to illustrate the application of the method. The technique should be easier to apply than 2D cepstral filtering techniques, and find applications in analysis of textured images and images obtained via reconstruction from projections.

The time-invariant Radon transform (RT) is commonly used to regularize and interpolate sparsely sampled or irregularly acquired prestack seismic data. The sparseness of the Radon model significantly influences the results of regularization. We have developed an effective and efficient method for the regularization and interpolation of 2D as well as 3D prestack seismic data. We used an accelerated sparse time-invariant RT in the mixed frequency-time domain to improve the performance of RT-based seismic data regularization. This 2D sparse RT incorporated the iterative 2D model shrinkage algorithm instead of the traditional iteratively reweighted least-squares (IRLS) algorithm in the time domain, and we computed the forward and inverse RTs in the frequency domain to solve the sparse inverse problem, which dramatically reduced the computational cost while obtaining a high-resolution result. The 2D synthetic and real data examples revealed that our 2D approach can better interpolate beyond aliasing a 2D prestack seismic record that contains a large gap, compared with the least-squares-based RT and the frequency-domain sparse RT methods. To extend the 2D technique to 3D more efficiently, we first formulate the 3D RT as a problem of solving a special matrix equation. Next, we use the iterative 3D model shrinkage algorithm to obtain a high-resolution 3D Radon model. The proposed 3D sparse RT method can be applied in the regularization of 3D prestack gathers, such as in the cable interpolation in a 3D marine survey. We achieved robustness and effectiveness with our 3D approach with successful applications to 3D synthetic and real data.

Rocks are far from being isotropic and elastic. Such simplifications in modeling the seismic response of real geological structures may lead to misinterpretations, or even worse, to overlooking useful information. It is useless to develop highly accurate modeling algorithms or to naively use amplitude information in inversion processes if the stress-strain relations are based on simplified rheologies. Thus, an accurate description of wave propagation requires a rheology that accounts for the anisotropic and anelastic behavior of rocks.This work presents a new constitutive relation and the corresponding time-domain wave equation to model wave propagation in inhomogeneous anisotropic and dissipative media. The rheological equation includes the generalized Hooke's law and Boltzmann's superposition principle to account for anelasticity. The attenuation properties in different directions, associated with the principal axes of the medium, are controlled by four relaxation functions of viscoelastic type. A dissipation model that is consistent with rock properties is the general standard linear solid. This is based on a spectrum of relaxation mechanisms and is suitable for wavefield calculations in the time domain.One relaxation function describes the anelastic properties of the quasi-dilatational mode and the other three model the anelastic properties of the shear modes. The convolutional relations are avoided by introducing memory variables, six for each dissipation mechanism in the 3-D case, two for the generalized SH-wave equation, and three for the qP - qSV wave equation. Two-dimensional wave equations apply to monoclinic and higher symmetries.A plane analysis derives expressions for the phase velocity, slowness, attenuation factor, quality factor and energy velocity (wavefront) for homogeneous viscoelastic waves. The analysis shows that the directional properties of the attenuation strongly depend on the values of the elasticities. In addition, the displacement formulation of the 3-D wave equation is solved in the time domain by a spectral technique based on the Fourier method. The examples show simulations in a transversely-isotropic clayshale and phenolic (orthorhombic symmetry).

Common depth point (CDP) recording, sometimes called common mid point (CMP), is a basic method in present day seismic exploration, whether that is the normal linear 2-D type or 3-D recording. However, to understand the concept fully, it is necessary to look back on the history of seismic exploration with respect, in the main, to the geometry of the recording spread and its effect on the processing and the interpretation of the recorded data. Some references to this topic have already been made, earlier in this book.