Hydrostatic pore water pressure revisited

Hydrostatic or “normal” pressure can be easily visualized as a water column with pressure given by ρgh and any departures classified as abnormal pressure. This is the basis for commonly used hydrostatic pressure depth trends in sedimentary basins that are constructed on assumptions of constant gradients and are datumed at mean sea level or ground level. But the straightforward water column concept does not upscale in a simple way to sedimentary basins where the zones of interest are several thousands of metres below the land or sea surface. Sedimentary basins are heterogeneous, including stacked, confined reservoirs and variations in pore water composition. It is possible to construct pressure-depth profiles that honour the geology and hydrostratigraphy of a basin and these give different hydrostatic baselines from simple constant gradients hung from familiar local datums such as ground level. Key steps are using a reservoir-specific datums such as the water table or potentiometric surface relevant to that unit, then building a pressure-depth trend that represents the pore fluid salinity variation and density profile throughout the reservoir unit. At a given depth, this version of hydrostatic may predict pressures several hundred psi different from a single density gradient hung from a datum local to the well, and exhibit a notched profile reflecting the geological and hydrological stratigraphy. This construct redefines normal and abnormal pore fluid pressures in sedimentary basins. The impacts of this alternative approach to sedimentary basin hydrostatics, even if data are limited and pressure profiles have to be framed probabilistically, extend to many aspects of studying and interacting with fluid systems in sedimentary basins including basin modelling, petroleum systems analysis, well planning and well operations.     

Dynamic ray tracing on Lagrangian manifolds

Summary. We show that Maslov's extension of the WKBJ method allows an extension of the dynamic ray tracing to wavefields involving caustics of arbitrary form. If the receiver lies off the caustics, then the synthetic seismogram can be obtained by integrating the DRT system along a single ray joining the receiver to the source which may touch caustics. If the receiver-lies in the vicinity of a caustic then DRT has to be carried out along a bunch of rays covering a neighbourhood of the receiver. Our approach encompasses pre-stressed and/or anisotropic media. Initial boundary conditions for a point source embedded in an anisotropic elastic medium are also presented.     

Caustics in seismology

Summary. Catastrophe optics provides insights into the structure of the caustics produced by seismic events. Two examples are given. The first is the caustic formed on the surface of the Earth between 10° and 30° from the event by P rays that have reached the transition zone of the mantle. This is organized by one or more approximately circular cusp lines; these are generally below the surface, but because of lateral (regional) variations, they are puckered. Where they intersect the surface they give rise to characteristic beak-to-beak and lips patterns. The second example is the caustic structure produced by refraction at the core–mantle boundary. There is a four-cusped figure at the antipodal point, and, in addition, it is suggested that the main 143° PKP caustic is actually cusped, the cusps being smeared out when radially symmetric earth models are used. The cusps arise from bumps on the core–mantle boundary. In general, the caustic, and its accompanying diffraction structure, associated with a bump can be understood as an unfolding of the parabolic umbilic catastrophe.     

Some remarks on the Gaussian beam summation method

Summary. Recently, a method using superposition of Gaussian beams has been proposed for the solution of high-frequency wave problems. The method is a potentially useful approach when the more usual techniques of ray theory fail: it gives answers which are finite at caustics, computes a nonzero field in shadow zones, and exhibits critical angle phenomena, including head waves. Subsequent tests by several authors have been encouraging, although some reported solutions show an unexplained dependence on the 'free' complex parameter ε which specifies the initial widths and phases of the Gaussian beams.
We use methods of uniform asymptotic expansions to explain the behaviour of the Gaussian beam method. We show how it computes correctly the entire caustic boundary layer of a caustic of arbitrary complexity, and computes correctly in a region of critical reflection. However, the beam solution for head waves and in edge-diffracted shadow zones are shown to have the correct asymptotic form, but with governing parameters that are explicitly ε-dependent. We also explain the mechanism by which the beam solution degrades when there are strong lateral inhomogeneities. We compare numerically our predictions for some representative, model problems, with exact solutions obtained by other means.     

Gaussian beams for surface waves in laterally slowly-varying media

Summary. Asymptotic ray theory is applied to surface waves in a medium where the lateral variations of structure are very smooth. Using ray-centred coordinates, parabolic equations are obtained for lateral variations while vertical structural variations at a given point are specified by eigenfunctions of normal mode theory as for the laterally homogeneous case. Final results on wavefields close to a ray can be expressed by formulations similar to those for elastic body waves in 2-D laterally heterogeneous media, except that the vertical dependence is described by eigenfunctions of 'local' Love or Rayleigh waves. The transport equation is written in terms of geometrical-ray spreading, group velocity and an energy integral. For the horizontal components there are both principal and additional components to describe the curvature of rays along the surface, as in the case of elastic body waves. The vertical component is decoupled from the horizontal components. With complex parameters the solutions for the dynamic ray tracing system correspond to Gaussian beams: the amplitude distribution is bell-shaped along the direction perpendicular to the ray and the solution is regular everywhere, even at caustics. Most of the characteristics of Gaussian beams for 2-D elastic body waves are also applicable to the surface wave case. At each frequency the solution may be regarded as a set of eigenfunctions propagating over a 2-D surface according to the phase velocity mapping.     

An explanation for USGS Station 6 record, 1979 Imperial Valley earthquake: a caustic induced by a sedimentary wedge

Summary. The largest earthquake-induced acceleration yet recorded occurred at the United States Geological Survey's (USGS) Strong Motion Array Station 6 during the 1979 October 15, Imperial Valley, California earthquake. This large acceleration (1.74 g, vertical component) is anomalously strong considering the low magnitude of the event ( M = 6.4), and the fact that receivers in the immediate neighbourhood of Station 6 recorded much lower accelerations. Previous studies of the records by other investigators have suggested a number of explanations for the anomaly, several of which implicate the near-receiver geological structure.
We present a detailed time and frequency domain analysis of the acceleration records at Stations 6, 5, 7, 8 and Diff Array to suggest that the anomalous acceleration is the consequence of the focusing of the incoming body waves by the lens-like effect of the sedimentary wedge between Imperial Valley and Brawley faults. The analyses include a detailed comparison of observed particle motions between neighbouring stations. Narrow band-pass filtered particle motions at Station 6 reveal the interaction of multipath arrivals as well as the frequency-dependent interference between them. Three-dimensional ray tracing experiments confirm the fact that the faulted sedimentary wedge is capable of focusing P -waves near Station 6. The interpretation that best combines theoretical and observed results is that amplification was due to the formation of an elliptic umbilic caustic with focus near the surface.     

Fluid flow in sedimentary basins: model of pore water flow in a vertical fracture

Open fractures provide high-permeability pathways for fluid flow in sedimentary basins. The potential for flow along permeable or open fractures and faults depends on the continuity of flow all the way to the surface except in the case of convective flow. Upward flowing fluid cools and may cause cementation due to the prograde solubility of quartz, but in the case of carbonates such flow may cause dissolution. The rate and duration of these processes depend on the mechanisms for sustaining fluid flow into the fracture, the geometries of fracture and sedimentary beds intersected, permeability, pressure and temperature gradients. Heat loss to the adjacent sediments causes sloping isotherms which can induce non-Rayleigh convection. To analyse these problems we have used a simple model in which a single fracture acts as a pathway for vertically moving fluid and there is no fluid transport across the walls of the fracture except near its inlet and outlet. Four mechanisms for fluid flow into the lower part of the fracture are considered: decompression of pore water; compaction of intersected overpressared sediments; focusing of compaction water derived from sediments beneath the fracture; and finally focusing of pore water moving through an aquifer. Water derived from the basement is not considered here. We find that sustained flow is unlikely to have velocities much higher than 1–100 m/yr, and the flow is laminar. The temperature of the fluid expelled at the top of the fracture increases by less than 1% and the vertical temperature gradient in the fracture remains close to the geothermal gradient. Where hot water is introduced from basement fractures (hydrothermal water) during tectonic deformation, much higher velocities may be sustained in the overlying sediments, but here also this depends on the permeability near the surface. Most of the cooling of water with (ore) mineral precipitation will then occur near the surface. In most cases, pore water decompression and sediment compaction will yield only very limited pore water flux with no significant potential for cementation or heating of the sediments adjacent to the fracture. Focusing of compaction water from sediments beneath the fracture or from an intersected aquifer can yield fluxes high enough to cement an open fracture significantly but the flow must be sustained for a very long time. For velocities of 1–100 m/yr, it takes typically 0.3–30 Myr to cement a fracture by 50%. The highest velocities may be obtained when a fracture extends all the way to the surface or sea floor. When a fracture does not reach the sediment surface, the flow velocity is reduced by the displacement of water in the sediments near the top of the fracture. The flow into the fracture from the sediments may often be rate limiting rather than the flow on the fracture. Sedimentary rocks only a few metres from the fracture will receive a much lower flux than the fracture. The fracture will therefore close due to cementation before significant amounts of silica can be introduced into adjacent sandstones. The isotherm slope in the adjacent sediments will in most cases be less than 10–20°. Non-Rayleigh convection velocities in the sediments adjacent to the fracture are too small to cause any significant diagenetic reactions such as quartz cementation. These quantifications of fluid flow in fractures in sedimentary basins are important in terms of constraining models for diagenesis, heat transport and formation of ore minerals in a compaction-driven system.     

Seismic waves in a stratified half space

Summary. For a buried source in a stratified elastic half space, the surface displacements are calculated by numerical integration of the Fourier–Bessel transform of the response. In the transform space this response is conveniently represented in terms of the reflection and transmission properties of the half space. For a layered medium this procedure avoids all problems associated with growing exponential terms in the evanescent regime. A slightly attenuative medium is assumed, so that the surface wave poles are shifted off the real slowness axis and thus a contour of integration along this axis may be employed. A general point source is represented by an arbitrary moment tensor.
The procedure is illustrated by calculations of three component seismograms including all P , SV and SH contributions for body and surface waves at moderate ranges. For local earthquakes we illustrate the striking effect of focal depth and also show the effect of sedimentary cover on strong ground motion.     

博鳌地区沙坝-泻湖沉积及探地雷达的应用

通过钻孔资料和探地雷达（GPR）反射剖面，揭示了海南岛东部博螯地区晚更新世以来沙坝-泻湖体系沉积序列和内部反射结构，探地雷达（GPR）给出了有关沙体厚度，岩性特征，潜水面深度，海水侵入范围以及沙体含水性等重要参数，是海岸带环境调查的有效手段。通过和钻孔资料的对比，在玉带滩海岸沙坝上部层序中识别出两套具有区域意义的反射波组，南岗村沙洲浅滩识别出一套反射波组，综合分析表明，博螯地区沙坝-泻湖体系晚更新世以来随海平面的上升经历了基岩侵蚀→河流，河漫滩相→泻湖→海岸沙坝，半封闭泻湖，河口湾的演化过程。     

Land subsidence pattern controlled by old alpine basement faults in the Kashmar Valley, northeast Iran: results from InSAR and levelling

Fluid storage systems, such as oil, gas, magma or water reservoirs, are often controlled by the host rock structure and faulted terrain. In sedimentary basins, where no direct information about underlying structure is available, the pattern of ground deformation may allow us to assess the buried fault arrangement. We provide an example in the semi-arid area of Iran, in the Kashmar Valley, a region subject to land subsidence due to water overexploitation. Geodetically determined subsidence rates in the Kashmar Valley exceed 15–30 cm yr⁻¹. The pattern of surface deformation is strongly non-uniform and displays NE–SW elongated bowls of subsidence. The trend resembles old Cretaceous-to-Tertiary faults that evolved during early alpine tectonic deformation. Although these early alpine structures are considered tectonically inactive in the present day, the observed land subsidence pattern indicates significant structural control on the geometry of the aquifer basin and its deformation during reservoir drainage.     

Regular spacing of drainage outlets from linear fault blocks

Outlets of river basins located on fault blocks often show a regular spacing. This regularity is most pronounced for fault blocks with linear ridge crests and a constant half-width, measured perpendicular to the ridge crest. The ratio of the half-width of the fault block and the outlet spacing is used in this study to characterize the average shape (or spacing ratio) of 31 sets of drainage basins. These fault-block spacing ratios are compared with similar data from small-scale flume experiments and large-scale mountain belts. Fault-block spacing ratios are much more variable than those measured for mountain belts. Differences between fault-block spacing ratios are attributed to variability in factors influencing the initial spacing of channel heads and subsequent rates of channel incision during the early stages of channel network growth (e.g. initial slope and uplift rate, precipitation, runoff efficiency and substrate erodibility). Widening or narrowing of fault blocks during ongoing faulting will also make spacing ratios more variable. It is enigmatic that some of these factors do not produce similar variability in mountain belt spacing ratios. Flume experiments in which drainage networks were grown on static topography show a strong correlation between spacing ratios and surface gradient. Spacing ratios on fault blocks are unaffected by variations in present-day gradients. Drainage basins on the Wheeler Ridge anticline in central California, which have formed on surfaces progressively uplifted by thrust faulting during the last 14 kyr, demonstrate that outlet spacing is likely to be determined during the early stages of drainage growth. This dependency on initial conditions may explain the lack of correlation between spacing ratios of fault blocks and slopes measured at the present day. Spacing ratios determine the location of sediment supply points to adjacent areas of deposition, and hence strongly influence the spatial scale of lateral facies variations in the proximal parts of sedimentary basins. Spacing ratios may be used to estimate this length scale in ancient sedimentary basins if the width of adjacent topography is known. Spacing ratio variability makes these estimates much less precise for fault blocks than for mountain belts.     

A New Model for Heat Flow in Extensional Basins: Estimating Radiogenic Heat Production

Radiogenic heat production (RHP) represents a significant fraction of surface heat flow, both on cratons and in sedimentary basins. RHP within continental crust—especially the upper crust—is high. RHP at any depth within the crust can be estimated as a function of crustal age. Mantle RHP, in contrast, is always low, contributing at most 1 to 2 mW/m² to total heat flow. Radiogenic heat from any noncrystalline basement that may be present also contributes to total heat flow. RHP from metamorphic rocks is similar to or slightly lower than that from their precursor sedimentary rocks. When extension of the lithosphere occurs—as for example during rifting—the radiogenic contribution of each layer of the lithosphere and noncrystalline basement diminishes in direct proportion to the degree of extension of that layer. Lithospheric RHP today is somewhat less than in the distant past, as a result of radioactive decay. In modeling, RHP can be varied through time by considering the half lives of uranium, thorium, and potassium, and the proportional contribution of each of those elements to total RHP from basement. RHP from sedimentary rocks ranges from low for most evaporites to high for some shales, especially those rich in organic matter. The contribution to total heat flow of radiogenic heat from sediments depends strongly on total sediment thickness, and thus differs through time as subsidence and basin filling occur. RHP can be high for thick clastic sections. RHP in sediments can be calculated using ordinary or spectral gamma-ray logs, or it can be estimated from the lithology.     

Lithospheric folding and sedimentary basin evolution: a review and analysis of formation mechanisms

Lithospheric folding is an important mode of basin formation in compressional intraplate settings. Basins formed by lithospheric folding are characterized by distinct features in subsidence history. A comparison with extensional basins, foreland basins, intracratonic basins and pull‐apart basins provides criteria for the discrimination between these modes of basin formation. These findings are important in deciphering the feedbacks between tectonics and surface processes. In addition, inferences on accommodation space and thermal regime have important consequences for hydrocarbon maturity. Lithospheric folding is coupled to compressional reactivation of basins and faults, and therefore, strongly affects reservoir characteristics of sedimentary basins.     

可可西里古近系含盐系地层沉积特征及古盐湖成盐模式讨论

可可西里是羌北—滇西构造域中重要的新生代沉积盆地,其古近系红层是认识中国陆相微陆块成盐作用的重要窗口。该区南部沱沱河盆地、北部错仁德加盆地古近系雅西措群地层中明显包含两套含盐系地层,两套层系形成的时代、古气候条件相同,但古地理条件、古盐湖盆地规模、成盐机制各异。渐新世时期沱沱河盆地属于封闭型的干盐湖沉积,错仁德加盆地属于开放型干盐湖沉积环境,预示着青藏高原中部渐新世大可可西里盆地并非相互连通,其中小型盆地的沉积成盐环境存在差异。     

The interaction between normal faulting and drainage in active extensional basins, with examples from the western United States and central Greece

Faulting exerts an important control upon drainage development in active extensional basins and thus helps determine the architecture of the sedimentary infill to a synrift basin. Examples of the interaction between faulting and drainage from the western United States and central Greece may be grouped into a relatively small number of classes based upon the structural position of a drainage catchment: footwall, hangingwall, fault offset and axial. Our examples illustrate the diversity of erosional effects that might arise because of variations in the spacing, orientation and segmentation of faults and their interactions. Where basement lithology is similar, footwall catchments are generally smaller, shorter and steeper than those of the hangingwall. Footwall-sourced alluvial fans and fan deltas are: generally smaller in area than those sourced from similar lithologies in the hangingwall. Wide fault offsets often give rise to large drainage catchments in the footwall. The development of axial drainage depends upon the breaching of transverse bedrock ridges by headward stream erosion or by lake overflow. Once breaching has occurred the direction of axial stream flow is controlled by the potential developed between basins of contrasting widths. Fault migration and propagation leads to the uplift, erosion and resedimentation of the sedimentary infill to formerly active basins, leading to the cutting of footwall unconformities. The outward sediment flux from structurally controlled catchments is modulated in an important way by lithology and runoff. The greatest contrasts in basement lithology arise when fault migration and propagation have occurred, such that the sedimentary fill to previously active basins is uplifted, incised and eroded by the establishment of large new drainage systems in the footwalls of younger faults. Drainage patterns in areas where faults interact can shed light on the relative timing of activity and therefore the occurrence of fault migration and propagation. Facies and palaeocurrent trends in ancient grabens may only be correctly interpreted when observations are made on a length scale of 10–20 km, comparable to that of the largest fault segments.     

Phase shift at caustics along rays in anisotropic media

In isotropic ray tracing, the ray approximation to the wavefield undergoes a phase shift when the ray crosses a caustic. The cumulative number of such phase shifts along a ray is usually called the KMAH index. The sign of these phase shifts is prescribed by the sign of the angular frequency in combination with the sign convention used for the Fourier transformation. In isotropic media the KMAH index always increases by one or by two, depending on the type of caustic crossed. For (quasi-)shear waves in anisotropic media the KMAH index may decrease. This is the case if the associated slowness sheet is locally concave in one or two of its principal directions of curvature.     

新疆农业地貌分类：以编制新疆1：100万农业地貌图为例

针对新疆地域辽阔，地形起伏巨大，山地层状地貌显著，盆地封闭、干旱，风成和流水地貌发育等特点，着眼于地貌与农业的关系，采用形态与成因相结合的分类原则，以地貌与农业关系密切的海拔高程、物质组成、相对高差、坡度等要素为指标，制定新疆农业地貌分类系统，划分农业地貌类型。     

A parabolic approximation for surface waves

Summary. A parabolic approximation to the equation of motion of elastic waves as a sum of surface modes and discovering a parabolic approximation be applied directly to surface waves. The approximation depends on the material properties varying slowly within a wavelength, whereas surface waves may travel in a surface wave guide whose depth is of the same order of magnitude as a wavelength. This difficulty is overcome by representing the waves as a sum of surface modes and discovering a parabolic approximation for the amplitudes as a function of position on the surface. The theory is applicable to the propagation of Love or Rayleigh waves in a structure which is vertically stratified in an arbitrary way, but varies slowly in any horizontal direction.     

A three-dimensional approach to fault seal analysis: fault-block juxtaposition & argillaceous smear modelling

Three‐dimensional (3D) numerical modelling of fault displacement enables the building of geological models to represent the complex 3D geometry and geological properties of faulted sedimentary basins. Using these models, cross‐fault juxtaposition relationships are predicted in 3D space and through time, based on the geometries of strata that are cut by faults. Forward modelling of fault development allows a 3D prediction of fault‐zone argillaceous smear using a 3D application of the Shale Gouge Ratio. Numerical models of the Artemis Field, Southern North Sea, UK and the Moab Fault, Utah, USA are used to demonstrate the developed techniques and compare them to traditional one‐ and two‐dimensional solutions. These examples demonstrate that a 3D analysis leads to significant improvements in the prediction of fault seal, the analysis of the interaction of the sealing properties of multiple faults, and the interpretation of fault seal within the context of sedimentary basin geometry.     

Statistical analysis of strong-motion accelerograms and its application to earthquake early-warning systems

In view of increasing damage due to earthquakes, and the current problems of earthquake prediction, real-time warning of strong ground motion is attracting more interest. In principle, it allows short-term warning of earthquakes while they are occurring. With warning times of up to tens of seconds it is possible to send alerts to potential areas of strong shaking before the arrival of the seismic waves and to mitigate the damage, but only if the seismic source parameters are determined rapidly. The major problem of an early-warning system is the real-time estimation of the earthquake's size.
We investigated digitized strong-motion accelerograms from 244 earthquakes that occurred in North and Central America between 1940 and 1986 to find out whether their initial portions reflected the size of the ongoing earthquake. Applying conventional methods of time-series analyses we calculate appropriate signal parameters and describe their uncertainties in relation to the magnitude and epicentral distance. The study reveals that the magnitude of an earthquake can be predicted from the first second of a single accelerogram within ±1.36 magnitude units. The uncertainty can be reduced to about ±0.5 magnitude units if a larger number (≥8) of accelerograms are available, which requires a dense network of seismic stations in areas of high seismic risk.