Shear-Wave Reflection Moveout For Azimuthally Anisotropic Media

The presence of azimuthal anisotropy causes shear wave propagation to split into fast and slow shear waves. The most common azimuthally anisotropic models used to describe fractured reservoirs are transverse isotropy with a horizontal axis of symmetry (HTI), and orthorhombic. In this paper, we study shear-wave reflection moveout in azimuthally anisotropic media with special attention paid to orthorhombic media with horizontal interfaces. In such cases the shear-wave reflection moveout is azimuthally variant and nonhyperbolic. We analyze the azimuthal dependence of normal moveout (NMO) velocity and we validate the accuracy of the conventional hyperbolic moveout equation. The azimuthal variation of NMO velocity is elliptical for both wave modes. In the presence of anisotropy-induced, nonhyperbolic moveout (NHMO), the hyperbolic moveout equation loses its accuracy with increasing offset (e.g., offset-to-depth ratio> 1). To study the azimuthal behavior of the NHMO for shear-wave reflections, we introduce an analytic representation for the quartic coefficient of the Taylor's series expansion of the two-way traveltime. In an orthorhombic medium the quartic coefficient for shearwave reflections has a relatively simple form, especially in comparison to P-wave. The reflection moveout for each shear-wave mode in a homogeneous orthorhombic medium is purely hyperbolic in the direction normal to the polarization. The nonhyperbolic portion of the moveout, on the other hand, reaches its maximum along the polarization direction, and it reduces rapidly away from the direction of pOlarization. As a result, the anisotropy-induced, nonhyperbolic reflection moveout is significant in the vicinity of the polarization directions (e.g., ±30° and for large offset-to-depth ratios). The implementation of the NHM0 equation and the utilization of the moveout coefficients allow for not only enhanced seismic imaging but also provide the link between seismic signatures and medium parameters.Saudi AramcoMassachusetts Institute of Technology. Borehole Acoustics and Logging ConsortiumMassachusetts Institute of Technology. Earth Resources Laboratory. Reservoir Delineation Consortiu

Nonhyperbolic reflection moveout for orthorhombic media

Reflection moveout in azimuthally anisotropic media is not only azimuthally dependent but it is also nonhyperbolic. As a result, the conventional hyperbolic normal moveout (NMO) equation parameterized by the exact NMO (stacking) velocity loses accuracy with increasing offset (i.e., spreadlength). This is true even for a single-homogeneous azimuthally anisotropic layer. The most common azimuthally anisotropic models used to describe fractured media are the horizontal transverse isotropy (HTI) and the orthorhombic (ORT). Here, we introduce an analytic representation for the quartic coefficient of the Taylor’s series expansion of the two-way traveltime for pure mode reflection (i.e., no conversion) in arbitrary anisotropic media with arbitrary strength of anisotropy. In addition, we present an analytic expression for the long-spread (large-offset) nonhyperbolic reflection moveout (NHMO). In this study, special attention is given to Pwave propagation in orthorhombic media with horizontal interfaces. The quartic coefficient, in general, has a relatively simple form, especially for shear wave propagation. The reflection moveout for each shear-wave mode in a homogeneous orthorhombic medium is purely hyperbolic in the direction normal to the polarization. In addition, the nonhyperbolic portion of the moveout for shear-wave propagation reaches its maximum along the polarization direction, and it decreases rapidly away from the direction of polarization. Hence, the anisotropy-induced nonhyperbolic reflection moveout for shear-wave propagation is significant in the vicinity of the polarization directions. In multilayered azimuthally anisotropic media, the NMO (stacking) velocity and the quartic moveout coefficient can be calculated with good accuracy using Dix-type averaging (e.g., the known averaging equations for VTI media). The interval NMO velocities and the interval quartic coefficients, however, are azimuthally dependent. This allows us to extend the nonhyperbolic moveout (NHMO) equation, originally designed for VTI media, to more general horizontally stratified azimuthally anisotropic media. Numerical examples from reflection moveout in orthorhombic media, the focus of this paper, show that this NHMO equation accurately describes the azimuthally-dependent P-wave reflection traveltimes, even on spreadlengths twice as large as the reflector depth. This work provides analytic insight into the behavior of nonhyperbolic moveout, and it has important applications in modeling and inversion of reflection moveout in azimuthally anisotropic media.Massachusetts Institute of Technology. Earth Resources LaboratorySaudi Aramc

Bis(2,6-diamino­pyridin-1-ium) hexa­aqua­cobalt(II) disulfate dihydrate

In the title compound, (C5H8N3)2[Co(H2O)6](SO4)2·2H2O, the complete complex cation is generated by crystallographic inversion symmetry, such that the CoII cation is octa­hedrally coordinated by six water mol­ecules. The organic cation is essentially planar, with a maximum deviation of 0.013 (1) Å. In the crystal structure, the ions and mol­ecules are linked into a pseudo-layered three-dimensional supra­molecular network via O—H⋯O and N—H⋯O hydrogen bonds. Weak inter­molecular π–π inter­actions further stabilize the crystal structure [centroid–centroid distance = 3.5231 (4) Å]

Aeolian And Fluvial Depositional Systems Discrimination In Wireline Logs: Unayzah Formation, Central Saudi Arabia

The objective of tills study is to discriminate between aeolian and fluvial deposits of the Permian Unayzah formation in Central Saudi Arabia by using wireline logs. The analysis is conducted on wire-line logs (field data): Density, sonic, gamma, and neutron, from two vertical wells (U1 and U2) in Central Saudi Arabia. Core data are available at well location U1 but not at U2. We apply an automated neural-network method to the wireline data for facies discrimination. Our analysis has been applied to the logs of well U2 after training the method on U1 logs using available core information. Results indicate that the Unayzah formation at well location U2 consists mainly of fluvial deposits (about 90%), which is consistent with previous studies and is supported by surface seismic images. We also investigate an analysis method based On the Fourier transform. We study the decay of the energy spectrum in the frequency domain and estimate the associated power-law exponent (i.e., the slope of the decay) for each depositional system. Analysis on the porosity logs (density, neutron, sonic, and shear), which are highly influenced by deposition composition and texture, has shown that the exponent is about the same for fluvial deposits at both well locations, while it is different for aeolian deposits.Massachusetts Institute of Technology. Borehole Acoustics and Logging ConsortiumMassachusetts Institute of Technology. Earth Resources Laboratory. Reservoir Delineation Consortiu

Diguanidinium bis­(μ-2-hydroxy­propane-1,2,3-tricarboxyl­ato)bis­[diaqua­zincate(II)] dihydrate

The asymmetric unit of the title compound, (CH6N3)2[Zn2(C6H5O7)2(H2O)2]·2H2O, contains one-half of a centrosymmetric dizinc(II) complex anion, one guanidinium cation and one water mol­ecule. Each ZnII ion is hexa­coordinated by two citrate anions, one in a bidentate fashion and the second monodentate, and two water mol­ecules in a distorted octa­hedral geometry. Intra­molecular O—H⋯O hydrogen bonds add further stability to the mol­ecular structure. In the crystal structure, mol­ecules are linked into a three-dimensional framework by inter­molecular N—H⋯O, O—H⋯O and C—H⋯O hydrogen bonds

Determination of Near-Surface Anisotropy From Surface Electromagnetic Data

Ground penetrating radar (GPR) signatures, such as reflection moveout, are sensitive to the presence of azimuthal anisotropy. Azimuthal anisotropy can occur as an intrinsic property of the medium and/or due to the presence of fractures. In such cases, the GPR normal moveout (NMO) velocity, along different orientations of common-midpoint (CMP) gathers, varies with azimuth. This fact is well known in surface reflection seismology. The azimuthal variation of the NMO velocity in an arbitrary medium is elliptical. Considering the analogy between seismic wave propagation in surface seismology and GPR sounding, we can transfer some of the ideas between both fields, including the ellipticity of the NMO velocity in a fractured medium. Here, we discuss briefly GPR reflection moveout in azimuthally anisotropic media. Our study focuses on the transverse mode of electromagnetic wave propagation in which the polarization is normal to the incidence plane of the CMP gathers. A field data example is presented in which three GPR CMP gathers are acquired along three different azimuths, 60° apart, over a fractured medium. Our data analysis demonstrates the azimuthal variation of the GPR NMO velocity, which is utilized to invert for the local orientation of the fracture system in the near surface. The results obtained from the field example agree with the information obtained from geology and near surface studies. This work has important applications in imaging near surface geologic structures and in the determination of tectonic-induced fractures in the near surface.Massachusetts Institute of Technology. Earth Resources LaboratorySaudi Aramc

Bis(2,6-diamino­pyridinium) bis­(hydrogen oxalate) monohydrate

The asymmetric unit of the title compound, 2C5H8N3 +·2C2HO4 −·H2O, contains two crystallographically independent 2,6-diamino­pyridinium cations, a pair of hydrogen oxalate anions and a water mol­ecule. Both 2,6-diamino­pyridinium cations are planar, with maximum deviations of 0.011 (2) and 0.015 (1) Å, and are protonated at the pyridine N atoms. The hydrogen oxalate anions adopt twisted conformations and the dihedral angles between the planes of their carboxyl groups are 31.01 (11) and 63.48 (11)°. In the crystal, the cations, anions and water mol­ecules are linked via O—H⋯O and N—H⋯O hydrogen bonds, forming a three-dimensional network

Analysis Of Deteriorating Inventory/Production Systems Using ALinearQuadratic Regulator

We consider an inventory-production system where items deteriorate at a constant rate. The objective is to develop an optimal production policy that minimizes the cost associated with inventory and production rate. The inventory problem is first modeledas a linear optimal control problem. Then linear quadratic regulator (LQR) technique is applied to the control problem in order to determine the optimal production policy.Examples are solved for three different demand functions. Sensitivity analysis is then conducted to study the effect of changing the cost parameters on the objective function. (C) 1998 Published by Elsevier Science B.V

Analysis Of Deteriorating Inventory/Production Systems Using ALinearQuadratic Regulator

We consider an inventory-production system where items deteriorate at a constant rate. The objective is to develop an optimal production policy that minimizes the cost associated with inventory and production rate. The inventory problem is first modeledas a linear optimal control problem. Then linear quadratic regulator (LQR) technique is applied to the control problem in order to determine the optimal production policy.Examples are solved for three different demand functions. Sensitivity analysis is then conducted to study the effect of changing the cost parameters on the objective function. (C) 1998 Published by Elsevier Science B.V