Generalized Dix equation and analytic treatment of normal-moveout velocity for anisotropic media*

Despite the complexity of wave propagation in anisotropic media, reflection moveout on conventional common-midpoint (CMP) spreads is usually well described by the normal-moveout (NMO) velocity defined in the zero-offset limit. In their recent work, Grechka and Tsvankin showed that the azimuthal variation of NMO velocity around a fixed CMP location generally has an elliptical form (i.e. plotting the NMO velocity in each azimuthal direction produces an ellipse) and is determined by the spatial derivatives of the slowness vector evaluated at the CMP location. This formalism is used here to develop exact solutions for the NMO velocity in anisotropic media of arbitrary symmetry. For the model of a single homogeneous layer above a dipping reflector, we obtain an explicit NMO expression valid for all pure modes and any orientation of the CMP line with respect to the reflector strike. The contribution of anisotropy to NMO velocity is contained in the slowness components of the zero-offset ray (along with the derivatives of the vertical slowness with respect to the horizontal slownesses) — quantities that can be found in a straightforward way from the Christoffel equation. If the medium above a dipping reflector is horizontally stratified, the effective NMO velocity is determined through a Dix-type average of the matrices responsible for the ‘interval’ NMO ellipses in the individual layers. This generalized Dix equation provides an analytic basis for moveout inversion in vertically inhomogeneous, arbitrarily anisotropic media. For models with a throughgoing vertical symmetry plane (i.e. if the dip plane of the reflector coincides with a symmetry plane of the overburden), the semi-axes of the NMO ellipse are found by the more conventional rms averaging of the interval NMO velocities in the dip and strike directions. Modelling of normal moveout in general heterogeneous anisotropic media requires dynamic ray tracing of only one (zero-offset) ray. Remarkably, the expressions for geometrical spreading along the zero-offset ray contain all the components necessary to build the NMO ellipse. This method is orders of magnitude faster than multi-azimuth, multi-offset ray tracing and, therefore, can be used efficiently in traveltime inversion and in devising fast dip-moveout (DMO) processing algorithms for anisotropic media. This technique becomes especially efficient if the model consists of homogeneous layers or blocks separated by smooth interfaces. The high accuracy of our NMO expressions is illustrated by comparison with ray-traced reflection traveltimes in piecewise-homogeneous, azimuthally anisotropic models. We also apply the generalized Dix equation to field data collected over a fractured reservoir and show that P-wave moveout can be used to find the depth-dependent fracture orientation and to evaluate the magnitude of azimuthal anisotropy.     

3D waveform inversion of downhole microseismic data for transversely isotropic media

3D anisotropic waveform inversion could provide high-resolution velocity models and improved event locations for microseismic surveys. Here we extend our previously developed 2D inversion methodology for microseismic borehole data to 3D transversely isotropic media with a vertical symmetry axis. This extension allows us to invert multicomponent data recorded in multiple boreholes and properly account for vertical and lateral heterogeneity. Synthetic examples illustrate the performance of the algorithm for layer-cake and ‘hydraulically fractured’ (i.e. containing anomalies that simulate hydraulic fractures) models. In both cases, waveform inversion is able to reconstruct the areas which are sufficiently illuminated for the employed source-receiver geometry. In addition, we evaluate the sensitivity of the algorithm to errors in the source locations and to band-limited noise in the input displacements. We also present initial inversion results for a microseismic data set acquired during hydraulic fracturing in a shale reservoir.     

The origin of hydrous,high-δ<Superscript>18</Superscript>O voluminous volcanism: diverse oxygen isotope values and high magmatic water contents within the volcanic record of Klyuchevskoy volcano,Kamchatka, Russia

Klyuchevskoy volcano, in Kamchatka’s subduction zone, is one of the most active arc volcanoes in the world and contains some of the highest δ¹⁸O values for olivines and basalts. We present an oxygen isotope and melt inclusion study of olivine phenocrysts in conjunction with major and trace element analyses of ¹⁴C- and tephrochronologically-dated tephra layers and lavas spanning the eruptive history of Klyuchevskoy. Whole-rock and groundmass analyses of tephra layers and lava samples demonstrate that both high-Mg (7–12.5 wt% MgO) and high-Al (17–19 wt% Al₂O₃, 3–6.5 wt% MgO) basalt and basaltic andesite erupted coevally from the central vent and flank cones. Individual and bulk olivine δ¹⁸O range from normal MORB values of 5.1‰ to values as high as 7.6‰. Likewise, tephra and lava matrix glass have high-δ¹⁸O values of 5.8–8.1‰. High-Al basalts dominate volumetrically in Klyuchevskoy’s volcanic record and are mostly high in δ¹⁸O. High-δ¹⁸O olivines and more normal-δ¹⁸O olivines occur in both high-Mg and high-Al samples. Most olivines in either high-Al or high-Mg basalts are not in oxygen isotopic equilibrium with their host glasses, and Δ¹⁸O_{olivine–glass} values are out of equilibrium by up to 1.5‰. Olivines are also out of Fe–Mg equilibrium with the host glasses, but to a lesser extent. Water concentrations in olivine-hosted melt inclusions from five tephra samples range from 0.4 to 7.1 wt%. Melt inclusion CO₂ concentrations vary from below detection (<50 ppm) to 1,900 ppm. These values indicate depths of crystallization up to ~17 km (5 kbar). The variable H₂O and CO₂ concentrations likely reflect crystallization of olivine and entrapment of inclusions in ascending and degassing magma. Oxygen isotope and Fe–Mg disequilibria together with melt inclusion data indicate that olivine was mixed and recycled between high-Al and high-Mg basaltic melts and cumulates, and Fe–Mg and δ¹⁸O re-equilibration processes were incomplete. Major and trace elements in the variably high-δ¹⁸O olivines suggest a peridotite source for the parental magmas. Voluminous, highest in the world with respect to δ¹⁸O, and hydrous basic volcanism in Klyuchevskoy and other Central Kamchatka depression volcanoes is explained by a model in which the ascending primitive melts that resulted from the hydrous melt fluxing of mantle wedge peridotite, interacted with the shallow high-δ¹⁸O lithospheric mantle that had been extensively hydrated during earlier times when it was part of the Kamchatka forearc. Following accretion of the Eastern Peninsula terrains several million years ago, a trench jump eastward caused the old forearc mantle to be beneath the presently active arc. Variable interaction of ascending flux-melting-derived melts with this older, high-δ¹⁸O lithospheric mantle has produced mafic parental magmas with a spectrum of δ¹⁸O values. Differentiation of the higher δ¹⁸O parental magmas has created the volumetrically dominant high-Al basalt series. Both basalt types incessantly rise and mix between themselves and with variable in δ¹⁸O cumulates within dynamic Klyuchevskoy magma plumbing system, causing biannual eruptions and heterogeneous magma products. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Oxygen isotope and trace element evidence for three-stage petrogenesis of the youngest episode (260–79 ka) of Yellowstone rhyolitic volcanism

We report the first high-precision δ¹⁸O analyses of glass, δ¹⁸O of minerals, and trace element concentrations in glass and minerals for the 260–79 ka Central Plateau Member (CPM) rhyolites of Yellowstone, a >350 km³ cumulative volume of lavas erupted inside of 630 ka Lava Creek Tuff (LCT) caldera. The glass analyses of these crystal-poor rhyolites provide direct characterization of the melt and its evolution through time. The δ¹⁸O_glass values are low and mostly homogeneous (4.5 ± 0.14 ‰) within and in between lavas that erupted in four different temporal episodes during 200 ka of CPM volcanism with a slight shift to lower δ¹⁸O in the youngest episode (Pitchstone Plateau). These values are lower than Yellowstone basalts (5.7–6 ‰), LCT (5.5 ‰), pre-, and extracaldera rhyolites (~7–8 ‰), but higher than the earliest 550–450 ka post-LCT rhyolites (1–2 ‰). The glass δ¹⁸O value is coupled with new clinopyroxene analyses and previously reported zircon analyses to calculate oxygen isotope equilibration temperatures. Clinopyroxene records >900 °C near-liquidus temperatures, while zircon records temperatures <850 °C similar to zircon saturation temperature estimates. Trace element concentrations in the same glass analyzed for oxygen isotopes show evidence for temporal decreases in Ti, Sr, Ba, and Eu—related to Fe–Ti oxide and sanidine (±quartz) crystallization control, while other trace elements remain similar or are enriched through time. The slight temporal increase in glass Zr concentrations may reflect similar or higher temperature magmas (via zircon saturation) through time, while previosuly reported temperature decreases (e.g., Ti-in-quartz) might reflect changing Ti concentrations with progressive melt evolution. Multiple analyses of glass across single samples and in profiles across lava flow surfaces document trace element heterogeneity with compatible behavior of all analyzed elements except Rb, Nb, and U. These new data provide evidence for a three-stage geochemical evolution of these most recent Yellowstone rhyolites: (1) repeated batch melting events at the base of a homogenized low-δ¹⁸O intracaldera fill resulting in liquidus rhyolite melt and a refractory residue that sequesters feldspar-compatible elements over time. This melting may be triggered by conductive "hot plate" heating by basaltic magma intruding beneath the Yellowstone caldera resulting in contact rhyolitic melt that crystallizes early clinopyroxene and/or sanidine at high temperature. (2) Heterogeneity within individual samples and across flows reflects crystallization of these melts during preeruptive storage of magma at at lower, zircon-saturated temperatures. Compatible behavior and variations of most trace elements within individual lava flows are the result of sanidine, quartz, Fe–Ti oxide, zircon, and chevkinite crystallization at this stage. (3) Internal mixing immediately prior to and/or during eruption disrupts, these compositional gradients in each parental magma body that are preserved as melt domains distributed throughout the lava flows. These results based on the most recent and best-preserved volcanic products from the Yellowstone volcanic system provide new insight into the multiple stages required to generate highly fractionated hot spot and rift-related rhyolites. Our proposed model differs from previous interpretations that extreme Sr and Ba depletion result from long-term crystallization of a single magma body—instead we suggest that punctuated batch melting events generated a sanidine-rich refractory residue and a melt source region progressively depleted in Sr and Ba.     

Image-domain wavefield tomography for tilted transversely isotropic media

Transversely isotropic models with a tilted symmetry axis have become standard for imaging beneath dipping shale formations and in active tectonic areas. Here, we develop a methodology of wave-equation-based image-domain tomography for acoustic tilted transversely isotropic media. We obtain the gradients of the objective function using an integral wave-equation operator based on a separable dispersion relation that takes the symmetry-axis tilt into account. In contrast to the more conventional differential solutions, the integral operator produces only the P-wavefield without shear-wave artefacts, which facilitates both imaging and velocity analysis. The model is parameterized by the P-wave zero-dip normal-moveout velocity, the Thomsen parameter δ, anellipticity coefficient η and the symmetry-axis tilt θ. Assuming that the symmetry axis is orthogonal to reflectors, we study the influence of parameter errors on energy focusing in extended (space-lag) common-image gathers. Distortions in the anellipticity coefficient η introduce weak linear defocusing regardless of reflector dip, whereas δ influences both the energy focusing and depth scale of the migrated section. These results, which are consistent with the properties of the P-wave time-domain reflection moveout in tilted transversely isotropic media, provide important insights for implementation of velocity model-building in the image-domain. Then the algorithm is tested on a modified anticline section of the BP 2007 benchmark model.     

Complex coastal change in response to autogenic basin infilling: An example from a sub‐tropical Holocene strandplain

Thick bay‐fill sequences that often culminate in strandplain development serve as important sedimentary archives of land–ocean interaction, although distinguishing between internal and external forcings is an ongoing challenge. This study employs sediment cores, ground‐penetrating radar surveys, radiocarbon dates, palaeogeographic reconstructions and hydrodynamic modelling to explore the role of autogenic processes – notably a reduction in wave energy in response to coastal embayment infilling – in coastal evolution and shoreline morphodynamics. Following a regional 2 to 4 m highstand at ca 5·8 ka, the 75 km² Tijucas Strandplain in southern Brazil built from fluvial sediments deposited into a semi‐enclosed bay. Holocene regressive deposits are underlain by fluvial sands and a Pleistocene transgressive–regressive sequence, and backed by a highstand barrier‐island. The strandplain is immediately underlain by 5 to 16 m of seaward‐thickening, fluvially derived, Holocene‐age, basin‐fill mud. Several trends are observed from the landward (oldest) to the seaward (youngest) sections of the strandplain: (i) the upper shoreface and foreshore become finer and thinner and shift from sand‐dominated to mud‐dominated; (ii) beachface slopes decrease from >11° to ca 7°; and (iii) progradation rates increase from 0·4 to 1·8 m yr^?1. Hydrodynamic modelling demonstrates a correlation between progressive shoaling of Tijucas Bay driven by sea‐level fall and sediment infilling and a decrease in onshore wave‐energy transport from 18 to 4 kW m^?1. The combination of allogenic (sediment supply, falling relative sea‐level and geology) and autogenic (decrease in wave energy due to bay shoaling) processes drove the development of a regressive system with characteristics that are rare, if not unique, in the Holocene and rock records. These findings demonstrate the complexities in architecture styles of highstand and regressive systems tracts. Furthermore, this article highlights the diverse internal and external processes and feedbacks responsible for the development of these intricate marginal marine sedimentary systems.     

Partitioning of Mg, Ca, and Na between carbonatite melt and hydrous fluid at 0.1–0.2 GPa

Experimental studies of the element distribution between carbonatite melts and hydrous fluids are hampered by the fact that neither the fluid nor the melt can be isochemically quenched in conventional high-pressure vessels. In order to overcome this problem, we used a double-capsule technique to separate immiscible fluid and melt phases during and after the runs. The inner platinum capsules were charged with carbonate mixtures (CaCO₃, MgCO₃ and Na₂CO₃) and placed inside the outer capsules charged with distilled water and diamond powder. The latter was used as an inert trap for solids precipitating from the fluid on quenching. Carbonate melt and hydrous fluid equilibrated through a small hole left in the upper end of the inner capsule. The runs were performed in rapid-quench cold-seal pressure vessels at 0.1–0.2 GPa and 700–900 °C in the two-phase (fluid + melt) stability region. Both quenched melt and quenched fluid were dissolved in dilute HCl and analysed by inductively coupled plasma atomic emission spectroscopy. The results show that under all conditions investigated, fluid/melt partition coefficients for Ca and Mg are similar and several times smaller than those for Na. At 0.1 GPa and a water/carbonatite ratio of 1 (by weight), the partition coefficients are D_Na = 0.35 ± 0.02, D_Ca = 0.09 ± 0.02, and D_Mg = 0.13 ± 0.01. Between 700 and 900 °C, the effect of temperature on partitioning is negligible. However, D_Na increases significantly with decreasing water/carbonatite ratio in the system. Our data show that the release of a hydrous fluid enriched in sodium and simultaneous crystallisation of calcite can transform an alkaline, vapour-saturated carbonatite melt into a body of pure calcite surrounded by zones of sodium metasomatism. Thus, it is quite possible that carbonate magmas with substantial amounts of alkalies were common parental liquids of plutonic carbonatites. Received: 6 May 1999 / Accepted: 31 August 1999     

Phase equilibria in the silica-undersaturated part of the KAlSiO4– Mg2SiO4– Ca2SiO4– SiO2– F system at 1 atm and the larnite-normative trend of melt evolution

The evolution of nephelinitic melts in equilibrium with mica-bearing liquidus assemblages and melting relations have been studied on two silica-undersaturated joins of the KAlSiO₄– Mg₂SiO₄– Ca₂SiO₄– SiO₂– F system at atmospheric pressure by quench runs in sealed platinum capsules. Fluorine has been added to the batch compositions by the direct exchange of fluorine for oxygen (2F⁻ = O²⁻). The first join is the pseudo-ternary Forsterite – Diopside – KAlSiO₃F₂ system. Forsterite, diopside, F-phlogopite and leucite crystallisation fields and a fluoride-silicate liquid immiscibility solvus are present on the liquidus surface of the join. Sub-liquidus and sub-solidus phases include akermanite, cuspidine, spinel, fluorite and some other minor fluorine phases. The second system is the pseudo-binary Akermanite – F-phlogopite join that intersects the Forsterite – Diopside – KAlSiO₃F₂ join. Akermanite, forsterite, diopside, F-phlogopite, leucite and cuspidine are found to crystallise on the join. Forsterite (fo) and leucite (lc) are related to F-phlogopite (phl) by a reaction with the fluorine-bearing liquid: fo + lc + l = phl, and the reaction proceeds until forsterite or leucite are completely consumed. The reaction temperature and resulting phase association depend on batch composition. Thus, leucite is not stable in the sub-solidus of the Akermanite – F-phlogopite join, but is preserved in a part of the Forsterite – Diopside – KAlSiO₃F₂ system where forsterite reacts out, or does not crystallise at all. The phlogopite-in reaction has an important effect on the composition of the coexisting liquid. The liquids initially saturated in forsterite evolve to extremely Ca rich, larnite-normative residuals. The experimental data show that larnite-normative melilitolites can crystallise from evolved melilititic melts generated from “normal” melanephelinitic parental magmas with no normative larnite. The evolution towards melilitites requires fractionation of phlogopite-bearing assemblages under volatile pressure. Received: 3 June 1997 / Accepted: 5 January 1998