The One-Way Wave Equation: A Full-Waveform Tool for Modeling Seismic Body Wave Phenomena

The study of seismic body waves is an integral aspect in global, exploration and engineering scale seismology, where the forward modeling of waves is an essential component in seismic interpretation. Forward modeling represents the kernel of both migration and inversion algorithms as the Green’s function for wavefield propagation and is also an important diagnostic tool that provides insight into the physics of wave propagation and a means of testing hypotheses inferred from observational data. This paper introduces the one-way wave equation method for modeling seismic wave phenomena and specifically focuses on the so-called operator-root one-way wave equations. To provide some motivation for this approach, this review first summarizes the various approaches in deriving one-way approximations and subsequently discusses several alternative matrix narrow-angle and wide-angle formulations. To demonstrate the key strengths of the one-way approach, results from waveform simulation for global scale shear-wave splitting modeling, reservoir-scale frequency-dependent shear-wave splitting modeling and acoustic waveform modeling in random heterogeneous media are shown. These results highlight the main feature of the one-way wave equation approach in terms of its ability to model gradual vector (for the elastic case) and scalar (for the acoustic case) waveform evolution along the underlying wavefront. Although not strictly an exact solution, the one-way wave equation shows significant advantages (e.g., computational efficiency) for a range of transmitted wave three-dimensional global, exploration and engineering scale applications.     

Detecting the near-surface redox front in crystalline bedrock using fracture mineral distribution,geochemistry and U-series disequilibrium

Oxidizing conditions normally prevail in surface waters and near-surface groundwaters, but there is usually a change to reducing conditions in groundwater at greater depth. Dissolved O₂ originally present is consumed through biogenic and inorganic reactions along the flow paths. Fracture minerals participate in these reactions and the fracture mineralogy and geochemistry can be used to trace the redox front. An important task in the safety assessment of a potential repository for the disposal of nuclear waste in crystalline bedrock, at an approximate depth of 500 m in Sweden, is to demonstrate that reducing conditions can be maintained for a long period of time. Oxygen may damage the Cu canisters that host nuclear waste; additionally, in the event of a canister failure, oxidizing conditions may increase the mobility of some radionuclides. The present study of the near-surface redox front is based on mineralogical (redox-sensitive minerals), geochemical (redox-sensitive elements) and U-series disequilibrium investigations of mineral coatings along open fractures. The fractures have been sampled along drill cores from closely spaced, 100 m deep boreholes, which were drilled during the site investigation work in the Laxemar area, south-eastern Sweden, carried out by the Swedish Nuclear Fuel and Waste Management Co. (SKB). The distribution of the redox-sensitive minerals pyrite and goethite in open fractures shows that the redox front (switch from mainly goethite to mainly pyrite in the fractures) generally occurs at about 15–20 m depth. Calcite leaching by recharging water is indicated in the upper 20–30 m and positive Ce-anomalies suggest oxidation of Ce down to 20 m depth. The U-series radionuclides show disequilibrium in most of the samples, indicating mobility of U during the last 1 Ma. In the upper 20 m, U is mainly removed (due to oxidation) or has experienced complex removal and/or deposition. At depths of 35–55 m, both deposition and removal of U are indicated. Below 55 m, recent deposition of U is generally indicated which suggests removal of U near surface (oxidation) and deposition of U below the redox front. Scattered goethite occurrences below the general redox front (down to ca 80 m) and signs of U removal at 35–55 m mostly correlate with sections of high transmissivity (and/or high fracture frequencies). This shows that highly transmissive fractures are generally required to allow oxygenated groundwaters at depth greater than ca 30 m. Removal of U (oxidation) below 55 m within the last 300 ka is not observed. Although penetration of glacial waters to great depths has been confirmed in the study area, their potential O₂ load seems to have been reduced near the surface.     

Modelling converted seismic waveforms in isotropic and anisotropic 1-D gradients: discontinuous versus continuous gradient representations

Over the past decade, there have been numerous receiver function studies directed at imaging the lithosphere-asthenosphere boundary (LAB). Although it is generally accepted that receiver function phases observed in these studies are derived from physical mode conversions at depth within the lithosphere-asthenosphere transition, it is still debatable as to whether these phases are directly indicative of the LAB. This is because interpretation of receiver function LAB signals relies on understanding the elastic characteristics of the Earth??s outer thermal boundary layer. The main issues for receiver function imaging are the sharpness of the elastic material property transition and, more importantly, what specifically are the material gradients. To test the various transition models, a forward modelling approach is required that allows accurate waveform synthetics for a range of discontinuous and continuous gradients in anisotropic, elastic media. We present a derivation of the reflection and transmission response for continuous one-dimensional (1-D) gradients in generally anisotropic elastic media. We evaluate the influence of 1-D isotropic and anisotropic elastic gradients on the seismic waveform by comparing numerical results of models for discontinuous and continuous transitions. The results indicate that discontinuous representations using layers each with uniform parameters and with thicknesses on the order of approximately 1/3 to 1/8 of the dominant seismic wavelength can be used to accurately model P-to-S and S-to-P mode conversions due to continuous transitions of both isotropic and anisotropic elastic properties. From a practical point of view, when comparing synthetic modelling with observation, this constraint can be relaxed further. The presence of signal noise and/or the result of receiver function stacking techniques will likely obscure these subtle waveform e ff ects. Hence this study suggests that accurate synthetic waveforms for LAB transitions can be modelled with discontinuous gradient representations using a reasonable number of discrete transition layers with layer thicknesses no greater than 1/2 to 1/3 the dominant seismic wavelength.     

The influence of dunes on mixing in a migrating salt‐wedge: Fraser River estuary,Canada

Dune bedforms and salt‐wedge intrusions are common features in many estuaries with sand beds, and yet little is known about the interactions between the two. Flow visualization with an echosounder and velocity measurements with an acoustic Doppler current profiler over areas of flat‐bed and sand dunes in the highly‐stratified Fraser River estuary, Canada, were used to examine the effect of dunes on interfacial mixing. As the salt‐wedge migrates upstream over the flat‐bed, mixing is restricted to the lower portion of the water column. However, as the salt‐wedge migrates into the dune field from the flat bed, there is a dramatic change in the flow, and large internal in‐phase waves develop over each of the larger dunes, with water from the salt‐wedge reaching the surface of the estuary. The friction Richardson number shows that bed friction is more important in interfacial mixing over the dunes than over the flat‐bed, and a plot of internal Froude Number versus obstacle (dune) height shows that the salt‐wedge flow over the dunes is mainly supercritical. Such bedforms can be expected to cause similar effects in interfacial mixing in other estuaries and sediment‐laden density currents, and may thus be influential in fluid mixing and sediment transport. Copyright © 2010 John Wiley & Sons, Ltd.     

Integration of the life of field seismic data with the reservoir model at the Valhall Field‡

The frequent time‐lapse observations from the life of field seismic system across the Valhall field provide a wealth of information. The responses from the production and injection wells can be observed through time‐shift and amplitude changes. These observations can be compared to modelled synthetic seismic responses from a reservoir simulation model of the Valhall Field. The observed differences between the observations and the modelling are used to update and improve the history match of the reservoir model. The uncertainty of the resulting model is reduced and a more confident prediction of future reservoir performance is provided. A workflow is presented to convert the reservoir model to a synthetic seismic response and compare the results to the observed time‐lapse responses for any time range and area of interest. Correlation based match quality factors are calculated to quantify the visual differences. This match quality factor allows us to quantitatively compare alternative reservoir models to help identify the parameters that best match the seismic observations. Three different case studies are shown where this workflow has helped to reduce the uncertainty range associated with specific reservoir parameters. By updating various reservoir model parameters we have been able to improve the match to the observations and thereby improve the overall reservoir model predictability. The examples show positive results in a range of different reservoir modelling issues, which indicates the flexibility of this workflow and the ability to have an impact in most reservoir modelling challenges.     

Three‐dimensional gravity‐current flow within a subaqueous bend: Spatial evolution and force balance variations

The nature of three‐dimensional flow in submarine channel bends is poorly understood, largely due to the absence of detailed data from natural channels. Herein, data from density‐driven flows in a large reservoir on the Huanghe (Yellow) River are presented showing the spatio‐temporal variation of flow around a subaqueous bend. The data demonstrate for the first time that reversed helical flow, relative to that found in river channel bends, can occur from the centrifugal forcing of flow, even when the Coriolis force acts in the opposite direction. The data also suggest that reversed helical flow fields in submarine channels may be more frequent than currently estimated, notably for bends where Coriolis and centrifugal forces combine in the same direction. In addition, this study provides the first field evidence suggesting that sinuous submarine channels can exhibit an asymmetry in helical flow orientation between left and right‐turning bends, which will have major implications for the morphodynamics of submarine channels, their resultant patterns of sedimentation and, ultimately, the distribution of depositional units across submarine fan systems.     

The Oligocene Lund Tuff, Great Basin, USA: a very large volume monotonous intermediate

Unusual monotonous intermediate ignimbrites consist of phenocryst-rich dacite that occurs as very large volume (>1000 km³) deposits that lack systematic compositional zonation, comagmatic rhyolite precursors, and underlying plinian beds. They are distinct from countless, usually smaller volume, zoned rhyolite–dacite–andesite deposits that are conventionally believed to have erupted from magma chambers in which thermal and compositional gradients were established because of sidewall crystallization and associated convective fractionation. Despite their great volume, or because of it, monotonous intermediates have received little attention. Documentation of the stratigraphy, composition, and geologic setting of the Lund Tuff – one of four monotonous intermediate tuffs in the middle-Tertiary Great Basin ignimbrite province – provides insight into its unusual origin and, by implication, the origin of other similar monotonous intermediates.The Lund Tuff is a single cooling unit with normal magnetic polarity whose volume likely exceeded 3000 km³. It was emplaced 29.02±0.04 Ma in and around the coeval White Rock caldera which has an unextended north–south diameter of about 50 km. The tuff is monotonous in that its phenocryst assemblage is virtually uniform throughout the deposit: plagioclase>quartz≈hornblende>biotite>Fe–Ti oxides≈sanidine>titanite, zircon, and apatite. However, ratios of phenocrysts vary by as much as an order of magnitude in a manner consistent with progressive crystallization in the pre-eruption chamber. A significant range in whole-rock chemical composition (e.g., 63–71 wt% SiO₂) is poorly correlated with phenocryst abundance.These compositional attributes cannot have been caused wholly by winnowing of glass from phenocrysts during eruption, as has been suggested for the monotonous intermediate Fish Canyon Tuff. Pumice fragments are also crystal-rich, and chemically and mineralogically indistinguishable from bulk tuff. We postulate that convective mixing in a sill-like magma chamber precluded development of a zoned chamber with a rhyolitic top or of a zoned pyroclastic deposit. Chemical variations in the Lund Tuff are consistent with equilibrium crystallization of a parental dacitic magma followed by eruptive mixing of compositionally diverse crystals and high-silica rhyolite vitroclasts during evacuation and emplacement. This model contrasts with the more systematic withdrawal from a bottle-shaped chamber in which sidewall crystallization creates a marked vertical compositional gradient and a substantial volume of capping-evolved rhyolite magma. Eruption at exceptionally high discharge rates precluded development of an underlying plinian deposit.The generation of the monotonous intermediate Lund magma and others like it in the middle Tertiary of the western USA reflects an unusually high flux of mantle-derived mafic magma into unusually thick and warm crust above a subducting slab of oceanic lithosphere.     

The Western Irish Namurian Basin reassessed

ABSTRACT Current basin models for the Western Irish Namurian Basin (WINB) envisage an elongate trough along the line of the present‐day Shannon Estuary that was infilled with clastic sediments derived from a hinterland that lay to the W or NW. This paper argues for an alternative basin configuration with source areas to the SW supplying sediment to a basin where deepest water conditions were in northern County Clare. Rapid subsidence along the present‐day Shannon Estuary ponded sediment in this area throughout the early Namurian and, only with the rapid increase of sedimentation rates within the mid‐Namurian (Kinderscoutian Stage), were substantial amounts of sediment able to prograde to the NE of the basin. This alternative model better explains the overwhelming predominance of NE‐directed palaeocurrents in the Namurian infill, but requires fundamental revisions to most aspects of current depositional models. Deep‐water black shales (Clare Shale Formation) initially accumulated throughout the region and were progressively downlapped by an unconfined turbidite system (Ross Formation) prograding to the NE. This in turn was succeeded by an unstable, siltstone‐dominated slope system (Gull Island Formation) characterized by large‐scale soft‐sediment deformation, which also prograded to the NE. In the northern‐most basin outcrops, in northern County Clare, this early phase of basin infill was developed as a condensed succession of radiolarian‐rich black shales, minor turbiditic sandstones and undisturbed siltstones. The new basin model envisages the northern exposures of County Clare to be a distal, basin floor succession whereas the traditional model considers it a relatively shallow, winnowed, basin margin succession. Later stages of basin infill consist of a series of deltaic cycles that culminate in major, erosive‐based sandstone bodies (e.g. Tullig Sandstone) interpreted either as axial, deltaic feeder channels or incised valley fills genetically unrelated to the underlying deltaic facies. Within the context of the new basin model the former alternative is most likely and estimated channel depths within the Tullig Sandstone indicate that the basal erosive surface could have been generated by intrinsic fluvial scour without recourse to base‐level fall. The northerly flowing Tullig channels pass down‐dip into isolated channel sandbodies interbedded with wave‐dominated strata that suggest the deltas of the WINB were considerably more wave‐influenced than hitherto proposed. The retreat of the Tullig delta during sea‐level rise saw the rapid southerly retrogradation of parasequences, as may be expected if the basin margin lay to the SW of the present‐day outcrops.     

Comparing the transitional behaviour of kaolinite and bentonite suspension flows

Past research has demonstrated the dramatic effects that variations in suspended clay can have on the properties of flow by producing a range of transitional flows between turbulent and laminar states, depending on clay concentration and fluid shear. Past studies have been restricted to kaolinite flows, a clay mineral that has relatively weak cohesive properties. This paper extends these studies to suspension flows of bentonite, a clay mineral that attains higher viscosities at far lower volumetric concentrations within a flow. The results show that the types of transitional flow behaviour recognized in past studies can also be found in bentonite suspension flows, but at lower suspended sediment concentrations, thus demonstrating an even more dramatic effect on flow properties, and potentially on sediment transport and resulting bed morphology, than kaolinite flows. The paper proposes new stability diagrams for the phase space of bentonite flows and compares these to past work on kaolinite suspension flows. These new data suggest that the transitional‐flow Reynolds number can be used to delineate the types of transitional flow across different clay types and assess modern and ancient clay‐suspension flows. © 2016 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.