Acoustic and electromagnetic properties of soils saturated with salt water and NAPL

Electrical, seismic, and electromagnetic methods can be used for noninvasive determination of subsurface physical and chemical properties. In particular, we consider the evaluation of water salinity and the detection of surface contaminants. Most of the relevant properties are represented by electric conductivity, P-wave velocity, and dielectric permittivity. Hence, it is important to obtain relationships between these measurable physical quantities and soil composition, saturation, and frequency. Conductivity in the geoelectric frequency range is obtained with Pride's model for a porous rock. (The model considers salinity and permeability.) White's model of patchy saturation is used to calculate the P-wave velocity and attenuation. Four cases are considered: light nonaqueous phase liquid (LNAPL) pockets in water, dense nonaqueous phase liquid (DNAPL) pockets in water, LNAPL pockets in air, and DNAPL pockets in air. The size of the pockets (or pools), with respect to the signal wavelength, is modeled by the theory. The electromagnetic properties in the GPR frequency range are obtained by using the Hanai–Bruggeman equation for two solids (sand and clay grains) and two fluids (LNAPL or DNAPL in water or air). The Hanai–Bruggeman exponent (1/3 for spherical particles) is used as a fitting parameter and evaluated for a sand/clay mixture saturated with water.Pride's model predicts increasing conductivity for increasing salinity and decreasing permeability. The best-fit exponent of the Hanai–Bruggeman equation for a sand/clay mixture saturated with water is 0.61, indicating that the shape of the grains has a significant influence on the electromagnetic properties. At radar frequencies, it is possible to distinguish between a water-saturated medium and a NAPL-saturated medium, but LNAPL- and DNAPL-saturated media have very similar electromagnetic properties. The type of contaminant can be better distinguished from the acoustic properties. P-wave velocity increases with frequency, and has dissimilar behaviour for wet and dry soils.     

Onshore and offshore seismic and lithostratigraphic analysis of a deeply incised Quaternary buried valley system in the Northern Netherlands

High-resolution seismic data (onshore and offshore), geophysical borehole data as well as detailed lithofacies from airlift boreholes were acquired in northern Netherlands on and around the island of Ameland. Marine and land seismic data combined with information from land boreholes have been explored with the objective of providing a sedimentary model. Qualitative seismic facies analysis of the valley fill commonly shows a thin unit with high amplitude reflectors at the base. Thick units of variable seismic facies (transparent to high amplitude) occur higher up in the sequence. Onlap is common at mid–upper levels within the sandy valley fill (with clay in mm layering), and a transparent seismic facies, corresponding to firm clays, is common at the top. Almost all lithological unit boundaries recognised within core parameters correspond with seismic unconformities within error margins. Subunits contain multiple cyclical trends in gamma ray and grain size. Cyclical trends show lower order fluctuations in gamma radiation on a scale of less than 1 m. Gamma-ray pattern variability between units, e.g. in general coarsening-up or fining-up units, suggests migration of subaqueous outwash fans or ice margin fluctuations. Seismic results could support a headward excavation and backfilling process suggested by Praeg [Morphology, stratigraphy and genesis of buried Elsterian tunnel valleys in the southern North Sea basin [PhD thesis]: University of Edinburgh, 207 pp.; Journal of Applied Geophysics, (this volume)] as being responsible for the formation of buried valleys. On a lithological scale, a more complicated, detailed and cyclical pattern arises. Catastrophic processes are considered unlikely as being responsible for the infill sequence because of the observed small-scale facies variability and because of the presence of diamicton layers. Diamicton layers at the base of basal unconformities as well as higher in sequence could suggest subglacial deformation by grounded ice before and during the valley-fill process.     

Fermat's principle for seismic rays in elastic media

We prove that rays in linearly elastic anisotropic nonuniform media obey Fermat's principle of stationary traveltime. First, we formulate the concept of rays, which emerges from the Hamilton equations. Then, we show that these rays are solutions of the variational problem stated by Fermat's principle. This proof is valid for all rays except the ones associated with infection points on the phase-slowness surface.     

Practical VTI approximations: a systematic anatomy

Transverse isotropy (TI) with a vertical symmetry axis (VTI) often provides an appropriate earth model for prestack imaging of steep-dip reflection seismic data. Exact P-wave and SV-wave phase velocities in VTI media are described by complicated equations requiring four independent parameters. Estimating appropriate multiparameter earth models can be difficult and time-consuming, so it is often useful to replace the exact VTI equations with simpler approximations requiring fewer parameters. The accuracy limits of different previously published VTI approximations are not always clear, nor is it always obvious how these different approximations relate to each other. Here I present a systematic framework for deriving a variety of useful VTI approximations. I develop first a sequence of well-defined approximations to the exact P-wave and SV-wave phase velocities. In doing so, I show how the useful but physically questionable heuristic of setting shear velocities identically to zero can be replaced with a more precise and quantifiable approximation. The key here to deriving accurate approximations is to replace the stiffness a₁₃ with an appropriate factorization in terms of velocity parameters. Two different specific parameter choices lead to the P-wave approximations of Alkhalifah (Geophysics 63 (1998) 623) and Schoenberg and de Hoop (Geophysics 65 (2000) 919), but there are actually an infinite number of reasonable parametrizations possible. Further approximations then lead to a variety of other useful phase velocity expressions, including those of Thomsen (Geophysics 51 (1986) 1954), Dellinger et al. (Journal of Seismic Exploration 2 (1993) 23), Harlan (Stanford Exploration Project Report 89 (1995) 145), and Stopin (Stopin, A., 2001. Comparison of v(θ) equations in TI medium. 9th International Workshop on Seismic Anisotropy). Each P-wave phase velocity approximation derived this way can be paired naturally with a corresponding SV-wave approximation. Each P-wave or SV-wave phase velocity approximation can then be converted into an equivalent dispersion relation in terms of horizontal and vertical slownesses. A simple heuristic substitution also allows each phase velocity approximation to be converted into an explicit group velocity approximation. From these, in turn, travel time or moveout approximations can also be derived. The group velocity and travel time approximations derived this way include ones previously used by Byun et al. (Geophysics 54 (1989) 1564), Dellinger et al. (Journal of Seismic Exploration 2 (1993) 23), Tsvankin and Thomsen (Geophysics 59 (1994) 1290), Harlan (89 (1995) 145), and Zhang and Uren (Zhang, F. and Uren, N., 2001. Approximate explicit ray velocity functions and travel times for P-waves in TI media. 71st Annual International Meeting, Society of Exploration Geophysicists, Expanded Abstracts, 106–109).     

Seismic imaging of mid-Pleistocene tunnel-valleys in the North Sea Basin—high resolution from low frequencies

Seismic reflection methods provide continuous access both to stratigraphy (vertical) and to subsurface morphology (horizontal), for which the scales of interest may differ by orders of magnitude. Seismic surveys of Quaternary successions have generally sought to optimise vertical resolution, through the use of higher source frequency content. Here, I show that low-frequency bandwidth is not necessarily a limiting factor for the seismic resolution of glacigenic morpho-sedimentary features. Observations are presented from a buried network of large mid-Pleistocene (Elsterian) tunnel-valleys in the southern North Sea Basin, across a 100×130 km study area with water depths less than 30 m. Low-frequency 2D and 3D seismic multi-channel data, acquired for deeper hydrocarbon exploration, are compared with previously available high-frequency single- and multi-channel profiles (5–15 km grid spacing). The low-frequency data contribute to a new understanding of the basal morphology and fill stratigraphy of the tunnel-valleys, in part due to higher data densities (≥1 km grid spacing), but also to improved imaging of reflectors at depth. The tunnel-valleys are seen to be overdeepened troughs, shallow (≤0.5 km) relative to their widths (≤6 km). The basal unconformity defines a series of arborescent elements, convergent to the south; erosional overlap by younger elements to the north has resulted in anastomosing patterns in places. The fill is dominated by axially downlapping clinoforms, descending to the north, onlapped and overlain by subhorizontal reflectors. Well data show that sand-dominated glaciofluvial sediments are overlain by glaciolacustrine to marine muds. Better definition of the clinoforms on low- versus high-frequency multi-channel data is suggested to reflect the coarse spatial scale of the backset glaciofluvial strata. The results support a simple interpretation of time-transgressive tunnel-valley formation by coeval glaciofluvial erosion and backfill beneath the outer tens of kilometres of the northward receding Elsterian ice sheet margin. Comparable submarginal interpretations have been proposed for drainage features (tunnel-valleys and eskers) of the last deglaciation of both northern Europe and North America using integrated geomorphologic and stratigraphic methods. Commercial 2D and 3D seismic data are widely available from exploration areas such as the North Sea and are argued to constitute an underexploited resource for Quaternary research.     

Predictive instantaneous optimal control of elastic structures during earthquakes

A predictive instantaneous optimal control (PIOC) algorithm is proposed for controlling the seismic responses of elastic structures. This algorithm compensates for the time delay that happens in practical control applications by predicting the structural response over a period that equals the time delay, and by substituting the predicted response in the instantaneous optimal control (IOC) algorithm. The unique feature of this proposed PIOC algorithm is that it is simple and at the same time compensates for the time delay very effectively. Numerical examples of single degree of freedom structures are presented to compare the performance of PIOC and IOC systems for various time delay magnitudes. Results show that a time delay always causes degradation of control efficiency, but PIOC can greatly reduce this degradation compared to IOC. The effects of the structure's natural periods and the choice of control gains on the degradation induced by the time delay are also analyzed. Results show that shorter natural periods and larger control gains are both more sensitive and more serious to the degradation of control efficiency. Finally, a practical application of PIOC is performed on a six‐story moment‐resisting steel frame. It is demonstrated that PIOC contributes significantly to maintain stability in multiple degree of freedom structures, and at the same time PIOC has a satisfactory control performance. Copyright © 2003 John Wiley & Sons, Ltd.     

玄武岩盖层下石林的岩溶动力学特征

受玄武岩盖层的影响，石林地区的地下水在雨季和旱季对碳酸盐岩都具有侵蚀性，玄武岩盖层空气CO2呈现出低—高—低的双向变化梯度。溶蚀试验表明．地下0～0．6m，水平方向的溶蚀量大于垂直方向的溶蚀量，而随着深度的增加，垂直方向的溶蚀量大于水平方向。富含CO2的水通过具有最大渗透张量和较小主轴倾角的玄武岩裂隙下渗，对碳酸盐岩的溶蚀作用表现为一个脱钙、富铝铁、硅迁移的复杂过程，并在地下0～0．6m形成许多水平凹槽、穿洞等岩溶形态，而地表0．6m以下以垂向溶蚀为主，有利于石柱的形成与发育。     

A hybrid indirect boundary element—discrete wave number method applied to simulate the seismic response of stratified alluvial valleys

A hybrid indirect boundary element – discrete wavenumber method is presented and applied to model the ground motion on stratified alluvial valleys under incident plane SH waves from an elastic half-space. The method is based on the single-layer integral representation for diffracted waves. Refracted waves in the horizontally stratified region can be expressed as a linear superposition of solutions for a set of discrete wavenumbers. These solutions are obtained in terms of the Thomson–Haskell propagators formalism. Boundary conditions of continuity of displacements and tractions along the common boundary between the half-space and the stratified region lead to a system of equations for the sources strengths and the coefficients of the plane wave expansion. Although the regions share the boundary, the discretization schemes are different for both sides: for the exterior region, it is based on the numerical and analytical integration of exact Green's functions for displacements and tractions whereas for the layered part, a collocation approach is used. In order to validate this approach results are compared for well-known cases studied in the literature. A homogeneous trapezoidal valley and a parabolic stratified valley were studied and excellent agreement with previous computations was found. An example is given for a stratified inclusion model of an alluvial deposit with an irregular interface with the half-space. Results are displayed in both frequency and time domains. These results show the significant influence of lateral heterogeneity and the emergence of locally generated surface waves in the seismic response of alluvial valleys.     

A quantitative study of the energy release in the aftershocks of the Bhuj earthquake, 2001, India, using Lg phase

The devastating earthquake on 26 January 2001 at Bhuj, India, resulted in large-scale death and destruction of properties of several million US dollars. The moment magnitude of the earthquake was 7.7 and its maximum focal intensity exceeded X in MM scale. The rate of aftershocks of this earthquake, recorded at Gauribidanur seismic array station (GBA), shows a monotonic decay with time superposed with oscillations. For the Indian continent the Lg phase is a prominent arrival at regional distances. The estimate of Lg amplitude is obtained by optimally fitting the Lg wave train to a exponential decay curve. The logarithm of these amplitudes and logarithm of root mean square (rms) value of actual amplitudes of the Lg are calibrated with USGS m_b to create a local m_bLg magnitude scale. The energy released from these aftershocks is calculated from the rms value of Lg phase. The plot of cumulative energy release with time follows the power law of the form t^p, superposed with oscillations. The exponent of the power law, p, is estimated both by a time-window scanning method and by an interpolation method. The value of p is 0.434 for time-window scanning method and 0.432 for the interpolation method. The predominant periods found in the oscillatory part of the cumulative energy, obtained by differencing the observed from the power law fit, are 10.6, 7.9, 5.4, 4.6 and 3.5 h for time-window scanning method. The corresponding periods for interpolation method are 13.4, 11.5, 7.4, 4.2, 3.5, 2.6 and 2.4 h.     

A review of the physics and ecological implications of the thermal bar circulation

Following recent applications of numerical modelling and remote sensing to the thermal bar phenomenon, this paper seeks to review the current state of knowledge on the effect of its circulation on lacustrine plankton ecosystems. After summarising the literature on thermal bar hydrodynamics, a thorough review is made of all plankton observations taken in the presence of a thermal bar. Two distinct plankton growth regimes are found, one with production favoured throughout the inshore region and another with a maximum in plankton biomass near the position of the thermal bar. Possible explanations for the observed distributions are then discussed, with reference to numerical modelling studies, and the scope for future study of this interdisciplinary topic is outlined.