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.     

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.     

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.     

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.     

Adaptive subtraction of multiples using the L1-norm

A strategy for multiple removal consists of estimating a model of the multiples and then adaptively subtracting this model from the data by estimating shaping filters. A possible and efficient way of computing these filters is by minimizing the difference or misfit between the input data and the filtered multiples in a least‐squares sense. Therefore, the signal is assumed to have minimum energy and to be orthogonal to the noise. Some problems arise when these conditions are not met. For instance, for strong primaries with weak multiples, we might fit the multiple model to the signal (primaries) and not to the noise (multiples). Consequently, when the signal does not exhibit minimum energy, we propose using the L₁‐norm, as opposed to the L₂‐norm, for the filter estimation step. This choice comes from the well‐known fact that the L₁‐norm is robust to ‘large’ amplitude differences when measuring data misfit. The L₁‐norm is approximated by a hybrid L₁/L₂‐norm minimized with an iteratively reweighted least‐squares (IRLS) method. The hybrid norm is obtained by applying a simple weight to the data residual. This technique is an excellent approximation to the L₁‐norm. We illustrate our method with synthetic and field data where internal multiples are attenuated. We show that the L₁‐norm leads to much improved attenuation of the multiples when the minimum energy assumption is violated. In particular, the multiple model is fitted to the multiples in the data only, while preserving the primaries.     

40Ar/ 39Ar and K–Ar geochronological age constraints for the inception and early evolution of the Izu–Bonin – Mariana arc system

K–Ar and ⁴⁰Ar/³⁹Ar dates are presented for locations in the Izu–Bonin – Mariana (IBM) forearc (Ocean Drilling Program (ODP) sites 786 & 782, Chichijima, Deep Sea Drilling Program (DSDP) sites 458 & 459, Saipan), and Palau on the remnant arc of the Kyushu–Palau Ridge. For a number of these locations, the ⁴⁰Ar/³⁹Ar plateau and ³⁶Ar/⁴⁰Ar versus ³⁹Ar/⁴⁰Ar isochrons give older ages than the K–Ar results. The most important results are: (i) at site 786, initial construction of the proto-IBM (now forearc) basement occurred at least by ca 47–45 Ma, consistent with the age of the immediately overlying sediments (middle Eocene nannofossil Zone CP13c); the younger pulse of construction dated at ca 35 Ma by K–Ar could not be confirmed by ⁴⁰Ar/³⁹Ar analysis; (ii) ⁴⁰Ar/³⁹Ar ages for the initial construction of the Mariana portion of the IBM system are as old as those of the Izu–Bonin portion, for example at site 458, initial construction commenced at least by ca 49 Ma and at ca 47 Ma at Saipan (Sankakayuma Formation); and (iii) a combination of K–Ar and ⁴⁰Ar/³⁹Ar ages indicate continued boninite magmatism in the Izu–Bonin forearc (and remnant arc at Palau) until ca 35 Ma. Subduction inception including boninite series rocks along most of the exposed length of the IBM system, clearly preceded by some 5 million years the Middle Eocene (ca 43.5 Ma) change in Pacific plate motion. Boninitic series magmatism persisted at locations now exposed in the forearc for ～ 15 million years after arc inception concurrently with low-K tholeiitic series eruptions from a subaerial arc system, established at ≥ 40 Ma, on the Kyushu–Palau Ridge. For the Mariana portion of the IBM system, reconstruction of the proto-arc places this activity adjacent to the concurrent but orthogonally spreading Central Basin Ridge of the West Philippine Basin. It is possible that a combination of subduction of a young North New Guinea Plate beneath newly created back-arc basin crust may account for some of the features of the Mariana system. It is clear, however, that the understanding of the processes of subduction initiation and early IBM arc development is incomplete.     

40Ar–39Ar analysis of phlogopite in the Horoman Peridotite Complex, Hokkaido, Japan and implications for its origin

Abstract ⁴⁰Ar–³⁹Ar analysis of phlogopite separated from a plagioclase lherzolite of the Horoman Peridotite Complex, Hokkaido, Japan, has yielded a plateau age of 20.6 ± 0.5 Ma in an environment where the metamorphic fluid was characterized by an almost atmospheric Ar isotopic ratio. The age spectrum is slightly saddle-shaped, implying some incorporation of excess ⁴⁰Ar during the formation of the phlogopite at a depth. As the phlogopite has been inferred to have formed in veins and/or interstitials during exhumation of the peridotite body, metasomatic fluids, to which ground- and sea water might have contributed, were probably involved in the formation of phlogopite in the crustal environment. A total ⁴⁰Ar–³⁹Ar age of 129 Ma of a whole rock sample of the plagioclase lherzolite, from which the phlogopite was separated and is representative of the main lithology of the Horoman Peridotite Complex, indicates the occurrence of excess ⁴⁰Ar. Hence, the age has no geological meaning.     

Characterization of dipping fractures in a transverselyisotropic background

Although it is believed that natural fracture sets predominantly have near‐vertical orientation, oblique stresses and some other mechanisms may tilt fractures away from the vertical. Here, we examine an effective medium produced by a single system of obliquely dipping rotationally invariant fractures embedded in a transversely isotropic with a vertical symmetry axis (VTI) background rock. This model is monoclinic with a vertical symmetry plane that coincides with the dip plane of the fractures. Multicomponent seismic data acquired over such a medium possess several distinct features that make it possible to estimate the fracture orientation. For example, the vertically propagating fast shear wave (and the fast converted PS‐wave) is typically polarized in the direction of the fracture strike. The normal‐moveout (NMO) ellipses of horizontal reflection events are co‐orientated with the dip and strike directions of the fractures, which provides an independent estimate of the fracture azimuth. However, the polarization vector of the slow shear wave at vertical incidence does not lie in the horizontal plane – an unusual phenomenon that can be used to evaluate fracture dip. Also, for oblique fractures the shear‐wave splitting coefficient at vertical incidence becomes dependent on fracture infill (saturation). A complete medium‐characterization procedure includes estimating the fracture compliances and orientation (dip and azimuth), as well as the Thomsen parameters of the VTI background. We demonstrate that both the fracture and background parameters can be obtained from multicomponent wide‐azimuth data using the vertical velocities and NMO ellipses of PP‐waves and two split SS‐waves (or the traveltimes of PS‐waves) reflected from horizontal interfaces. Numerical tests corroborate the accuracy and stability of the inversion algorithm based on the exact expressions for the vertical and NMO velocities.     

Depth versus (age)1/2: A perspective on mid-ocean rises

The straight-line relationship between depth and the square root of age predicted by recent variations of the thermal contraction model for ocean rise elevation is confirmed to an age of 80 m.y.We then examine this relationship in the immediate vicinity of the rise crest in an attempt to determine the sensitivity of the slopes thus obtained. Depth versus t^1/2 profiles from a variety of rise types ranging from the topographically smooth, fast-spreading Pacific-Antarctic rise to the rough, slow-spreading Mid-Atlantic rise are discussed, ages having been assigned using a finite rotation pole. Because of the variety of superimposed anomalous features concentrated within a limited and well-surveyed region, the Galapagos Spreading Center has provided a suitable arena for determining the precision with which the method can decompose such an agglomeration into distinctly recognizable components. Although topographic “noise” precludes precise quantification of the slopes, it is concluded that, by removing the first-order effect of thermal contraction, the method can be quite revealing when topography is examined in relation to other data. Slopes for several profiles across the Pacific-Antarctic and Pacific-Nazca rises reveal the pattern expected in the case of asymmetric spreading, a conclusion which has independently been derived from the magnetic anomalies. In the Galapagos region “jumps” of the spreading center, a basic compositional difference, and uplift from below are exposed by their predictable effect on the slopes obtained from the depth versus t^1/2 plots.     

A Geostatistically Based Ground Water Monitoring Study of Nonpoint Source No3--N Concentrations

Geostatistical interpretations of ground water monitoring data are presented to define the spatial distributions of NO₃^--N in the ground water at two demonstration test sites in the Idaho Snake River Plain. Sequential Gaussian simulation was used to delineate monthly ground water NO₃^--N changes during and after implementation of a prescribed crop rotation at test site 1. Trend surface analyses were used to illustrate monthly ground water NO₃^--N changes during and after a prescribed irrigation practice was implemented at test site 2. These evaluations suggest that geostatistically based ground water monitoring can be effective in the delineation of changes in ground water quality in shallow, unconfined aquifers in agricultural areas such as those in southern Idaho. Geostatistical methods showed spatial and temporal changes in ground water NO₃^--N inferred to be a result of the agricultural practices implemented.     

Stable Isotopes (δ18O, δ2H) of Pore Waters in Clay-Rich Aquitards: A Comparison and Evaluation of Measurement Techniques

Pore water collected from piezometers installed in a thick clay-rich till were used to compare and evaluate four techniques for obtaining δD and δ¹⁸O values in these media. The techniques included mechanical squeezing, centrifugation, azeotropic distillation, and a direct soil-water equilibration technique. Direct CO₂-core equilibration yielded sufficiently accurate and reproducible δ¹⁸O results of pore water in clay-rich tills. In addition, this method eliminated the need for labor-intensive complete extraction of water from the geologic media. Mechanical squeezing and centrifugation produced results similar to direct equilibration. However, both of these methods exhibited a greater degree of variability and were laborious and more time consuming. Small differences in δ¹⁸O values between piezometer water and equilibrated, squeezed, and centhfuged samples suggested that each method collected different fractions of the clay-water reservoir. Although these subtle differences were not conclusive, they did suggest the presence of weakly bound water and highlighted the difference between these three techniques for determining the stable isotopic composition of pore water in clay-rich aquitards. Azeotropic distillation produced a high level of discrepancy in δD andδ¹⁸O results compared to the other methods. Incomplete extraction was considered the most probable cause of this error. The results of this study suggested that direct equilibration is the best method for determining detailed δD and δ¹⁸O values of pore water in clay-rich aquitards.     

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.