GRAVITY GRADIENT TENSORS DUE TO A POLYHEDRON WITH POLYGONAL FACETS1

Using the conjugate complex variables formulation, closed-form formulae for the gravity gradient tensors of the gravitational potential due to a homogeneous polyhedral body composed of polygonal facets are derived. The treatise considers the cases of the observation point being inside the polyhedron, on the surface of a facet, or outside the polyhedron.     

Inversion of normal moveout for monoclinic media1

Multiple vertical fracture sets, possibly combined with horizontal fine layering, produce an equivalent medium of monoclinic symmetry with a horizontal symmetry plane. Although monoclinic models may be rather common for fractured formations, they have hardly been used in seismic methods of fracture detection due to the large number of independent elements in the stiffness tensor. Here, we show that multicomponent wide-azimuth reflection data (combined with known vertical velocity or reflector depth) or multi-azimuth walkaway VSP surveys provide enough information to invert for all but one anisotropic parameters of monoclinic media. In order to facilitate the inversion procedure, we introduce a Thomsen-style parametrization for monoclinic media that includes the vertical velocities of the P-wave and one of the split S-waves and a set of dimensionless anisotropic coefficients. Our notation, defined for the coordinate frame associated with the polarization directions of the vertically propagating shear waves, captures the combinations of the stiffnesses responsible for the normal-moveout (NMO) ellipses of all three pure modes. The first group of the anisotropic parameters contains seven coefficients (ε^(1,2), δ^(1,2,3) and γ^(1,2)) analogous to those defined by Tsvankin for the higher-symmetry orthorhombic model. The parameters ε^(1,2), δ^(1,2) and γ^(1,2) are primarily responsible for the pure-mode NMO velocities along the coordinate axes x₁ and x₂ (i.e. in the shear-wave polarization directions). The remaining coefficient δ⁽³⁾ is not constrained by conventional-spread reflection traveltimes in a horizontal monoclinic layer. The second parameter group consists of the newly introduced coefficients ζ^(1,2,3) which control the rotation of the P-, S₁- and S₂-wave NMO ellipses with respect to the horizontal coordinate axes. Misalignment of the P-wave NMO ellipse and shear-wave polarization directions was recently observed on field data by Pérez et al. Our parameter-estimation algorithm, based on NMO equations valid for any strength of the anisotropy, is designed to obtain anisotropic parameters of monoclinic media by inverting the vertical velocities and NMO ellipses of the P-, S₁- and S₂-waves. A Dix-type representation of the NMO velocity of mode-converted waves makes it possible to replace the pure shear modes in reflection surveys with the PS₁- and PS₂-waves. Numerical tests show that our method yields stable estimates of all relevant parameters for both a single layer and a horizontally stratified monoclinic medium.     

倾斜裂隙介质反透射系数研究

自然界的裂隙排列并非都是直立的,在复杂地壳应力作用下裂隙排列很可能是倾斜的.本文从各向异性弹性动力学基本方程出发,在特征矩阵方法基础上提出了计算任意倾斜裂隙介质水平界面上的反射、透射系数的简单方法,并利用该方法计算了倾斜裂隙介质P-P波、P-SV波和P-SH波的反透射系数.结果表明,P-P波、P-SV波和P-SH波的反透射系数与倾斜裂隙的倾角、测线方位以及偏移距这些物理参数之间存在一定的依赖关系.此外我们计算了C波的零入射相角时的反射系数,发现该反射系数跟裂隙倾角、裂隙的方位角有着明显的对应规律,且各向异性越强时,该反射系数越大.这些研究对于深入了解倾斜裂隙的动力学特征具有一定的意义.     

Non-equilibrium compaction and abnormal pore-fluid pressures: effects on rock properties1

Knowledge of pore pressure using seismic data will help in planning the drilling process to control potentially dangerous abnormal pressures. Various physical processes cause anomalous pressures on an underground fluid. Non-equilibrium compaction is a significant process of overpressure generation. This occurs when the sedimentation rate is so rapid that the pore fluids do not have a chance to 'escape' from the pore space.
The model assumes a closed system and that the pore space is filled with water and hydrocarbon in a liquid state. Balancing mass and volume fractions yields the fluid pressure versus time of deposition and depth of burial. Thermal effects are taken into account. The pore pressure, together with the confining pressure, determines the effective pressure which, in turn, determines the bulk moduli of the rock matrix.
We assume a sandstone saturated with hydrocarbons and water, for which calibration of the model with experimental data is possible. The seismic velocities and attenuation factors are computed by using Biot's theory of dynamic poroelasticity and the generalized linear solid. The example shows that the formation can be overpressured or underpressured depending on the properties of the saturating fluid. Wave velocities and quality factors decrease with decreasing differential pressure. The effect is important below approximately 20 MPa. The model is in good agreement with experimental data for Berea sandstone and provides a tool for predicting pore pressure from seismic attributes.     

A generalized Biot–Gassmann model for the acoustic properties of shaley sandstones1

We obtain the wave velocities of clay-bearing sandstones as a function of clay content, porosity and frequency. Unlike previous theories, based simply on slowness and/or moduli averaging or two-phase models, we use a Biot-type three-phase theory that considers the existence of two solids (sand grains and clay particles) and a fluid. The theory, which is consistent with the critical porosity concept, uses three free parameters that determine the dependence of the dry-rock moduli of the sand and clay matrices as a function of porosity and clay content.
Testing of the model with laboratory data shows good agreement between predictions and measurements. In addition to a rock physics model that can be useful for petrophysical interpretation of wave velocities obtained from well logs and surface seismic data, the model provides the differential equation for computing synthetic seismograms in inhomogeneous media, from the seismic to the ultrasonic frequency bands.     

接收函数方法估计Moho倾斜地区的地壳速度比

造山带地区的复合力系作用往往使Moho界面发生变形,局部表现为倾斜状态.为了得到这些区域精确地壳速度比结构,本文基于H-κ方法发展了H-κ-θ方法.该方法不仅考虑了倾斜Moho层的响应,同时利用径向和切向接收函数信息,增加了对扫描的约束.利用该方法对青藏高原东南缘地壳厚度和速度比结构进行研究,结果表明：研究区内地壳明显存在不均匀性,松潘—甘孜地体平均地壳厚度约为60 km,四川盆地西缘约为47 km,扬子地台约为43 km,三江块体和扬子地台东南缘已接近正常地壳厚度;松潘—甘孜地体与扬子地台相邻部位地壳平均地震波速度比（V_p/V_s）普遍偏高,且四川盆地西侧发现一绕盆地边缘的弧形高V_p/V_s异常区（>1.88）,我们推测该异常可能由青藏高原向东逃逸的地壳流体受到高强度的四川盆地阻挡,在其西侧堆积所致.     

Petrogenetic grid for ultrahigh-pressure metamorphism in the model system CaO-MgO-SiO2-CO2-H2O

Abstract Petrogenetic grids for ultrahigh-pressure (UHP) metamorphism were calculated at different X_co2 conditions in the model system CaO-MgO-SiO₂-CO₂-H₂O involving coesite (Co), diopside (Di), dolomite (Do), enstatite (En), forsterite (Fo), magnesite (Ms), quartz (Qz), talc (Tc), tremolite (Tr) using a published internally consistent thermodynamic data set. Two P-T grids at X_co2= 0.01 and 0.5 are described. In the calculated P-T grid at X_co2= 0.01, four out of 10 stable invariant points, Co-En-Ms-Tc, Co-Di-En-Tc-Tr, Co-Di-Ms-Tc-Tr and Di-En-Ms-Tc-Tr lie within the stability field of coesite. If the fluid phase has X_co2= 0.5, no invariant point is stable under UHP conditions. Some magnesite-bearing assemblages are stabilized by the following three reactions: Di + Ms = Do + Fo + CO₂, Ms + Tr = Do + Fo + CO₂+ H₂O and Ms + Tc = Fo+ CO₂+ H₂O at X_co2= 0.01 and by reaction Ms + Tc = Fo + CO₂+ H₂O together with these three at X_co2= 0.5. Ten possible UHP assemblages for mafic and ultramafic compositions at very low X_co2 conditions include the following: Co-Do-Ms, Co-Di-Ms, Co-Di-Tc, Di-Ms-Tc, Di-En-Tc-, Di-En-Ms, Co-Di-En, Di-En-Fo, Di-Fo-Ms, Di-Do-Fo. Among them, talc-bearing assemblages are restricted to X_co2 < 0.02 and their high-P limit is 31.7 kb (749°C) at X_co2= 0.01. Dolomite-magnesite-silica assemblages have large P-T stability fields even if X_co2 is as low as 0.1, and could occur in cold subduction zones with very low geothermal gradients. Reported UHP coesite-dolomite assemblage is restricted only to a calc-silicate rock interlayered with marble where X_co2 is relatively higher; no such assemblage appears for mafic and ultramafic rocks with low X_co2 evidenced by the occurrence of diopside (or omphacite) at the expense of dolomite + coesite. The effect of X_co2 on the stability of coesite-dolomite-magnesite, diopside-enstatite-magnesite, diopside-talc assemblages is examined and the occurrence of coesite-dolomite, magnesite-bearing and talc-bearing assemblages in the Dabie UHP rocks are interpreted by employing the calculated P-T grids.     

Co2+ as a chemical analogue for Fe2+ in high-temperature experiments in basaltic systems

High-temperature experiments on ferromagnesian compositions have been hampered by the rapid absorption of up to 95% of the original iron by platinum and 40% by silver-palladium capsules. Molybdenum or iron capsule materials can decrease or alleviate iron loss, but restrict oxygen fugacities to values near the iron-wustite buffer. Because Co²⁺ is stable at f_O2 =HM and because the solubility of Co in platinum in this range of f_O2 is ～0.05% at temperatures to 1350°C, its use as an analogue for Fe²⁺ is possible. In addition, experiments simulating various Fe²⁺ ratios can be easily performed by choosing appropriate Co²⁺/Fe³⁺ ratios. The cobalt phases produced possess brilliant and distinctive colors which are valuable aids in optical identification of minute phases. The cobalt analogue hypothesis was tested with atmospheric pressure experiments in air on the cobalt analogue of the 1921 Kilauea basalt at three simulated Fe²⁺/Fe³⁺ ratios. The results were compared with those of R.E.T. Hill (1969) for the natural 1921 basalt. The phase relations were the same, with the cobalt system stability fields systematically shifted by about +50°C. Microprobe analysis of olivines and the coexisting glasses indicate that the distribution of Co²⁺ between olivine and melt is independent of temperature and liquid composition. Although the analogue liquid composition differs from the equilibrium composition of the natural system, it may be corrected be employing distribution coefficients (K_D = 0.61 for the Co system; K_D = 0.33 for the Fe system) to closely approximate what the natural system would yield if iron loss did not occur.     

230Th/234U and 14C dating of a lowstand coral reef beneath the insular shelf off Irabu Island, Ryukyus, southwestern Japan

Abstract   High-resolution seismic reflection profiles delineated the distribution of mound-shaped reflections, which were interpreted as reefs, beneath the insular shelf western off Irabu Island, Ryukyus, southwestern Japan. A sediment core through one of the mounded structures was recovered from the sea floor at a depth of −118.2 m by offshore drilling and was dated by radiometric methods. The lithology and coral fauna of the core indicate that the mounded structure was composed of coral–algal boundstone suggesting a small-scaled coral reef. High-precision α-spectrometric ²³⁰Th/²³⁴U dating coupled with calibrated accelerator mass spectrometric ¹⁴C ages of corals obtained reliable ages of this reef ranging from 22.18 ± 0.63 to 30.47 ± 0.98 ka. This proves that such a submerged reef was formed during the lowstand stage of marine oxygen isotope stages 3–2. The existence of low-Mg calcite in the aragonitic coral skeleton of 22.18 ± 0.63 ka provides evidence that the reef had once been exposed by lowering of the relative sealevel to at least −126 m during the last glacial maximum in the study area. There is no room for doubt that a coral reef grew during the last glacial period on the shelf off Irabu Island of Ryukyus in the subtropical region of western Pacific.     

Mt-field of H-polarization in models with dipping interfaces

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