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.     

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.     

Seismic wave velocity and anisotropy of serpentinized peridotite in the Oman ophiolite

Shallow seismic measurements in harzburgite from the Oman ophiolite performed in a zone where the maximum horizontal anisotropy is expected (vertical foliation and horizontal lineation) point to a dominant dependence of seismic properties on fracturing.

Optical microscopy studies show that microcracks are guided by the serpentine (lizardite) penetrative network oriented subparallel to the harzburgite foliation and subperpendicular to the mineral lineation, and that serpentine (lizardite) vein filling has a maximum concentration of (001) planes parallel to the veins walls. The calculated elastic properties of the oriented alteration veins filled with serpentine in an anisotropic matrix formed by oriented crystals of olivine and orthopyroxene are compared with seismic velocities measured on hand specimens.

Laboratory ultrasonic data indicate that open microcracks are closed at 100 MPa pressure, e.g. (J. Geophys. Res. 65, (1960) 1083) and (Proc. ODP Sci. Results Leg 118, (1990) 227). Above this pressure, laboratory measurements and modeling show that P-compressional and S-shear wave velocities are mainly controlled by the mineral preferred orientation. Veins sealed with serpentine are effective in slightly lowering P and S velocities and increasing anisotropy. The penetrative lizardite network does not affect directly the geometry of seismic anisotropy, but contributes indirectly in the fact that this network controls the microcrack orientations.

Comparison between seismic measurements of peridotite and gabbro in the same conditions suggest that P- and S-waves anisotropies are a possible discriminating factor between the two lithologies in the suboceanic lithosphere.     

Architecture of fault zones determined from outcrop, cores, 3-D seismic tomography and geostatistical modeling: example from the Albalá Granitic Pluton, SW Iberian Variscan Massif

The 3-D seismic tomographic data are used together with field, core and well log structural information to determine the detailed 3-D architecture of fault zones in a granitic massif of volume 500×575×168 m at Mina Ratones area in the Albalá Granitic Pluton. To facilitate the integration of the different data, geostatistical simulation algorithms are applied to interpolate the relatively sparse structural (hard) control data conditioned to abundant but indirect 3-D (soft) seismic tomographic data. To effectively integrate geologic and tomographic data, 3-D migration of the velocity model from the time domain into the depth domain was essential. The resulting 3-D model constitutes an image of the fault zone architecture within the granitic massif that honours hard and soft data and provides an evaluation of the spatial variability of structural heterogeneities based on the computation of 3-D experimental variograms of Fracture Index (fault intensity) data. This probabilistic quantitative 3-D model of spatially heterogeneous fault zones is suitable for subsequent fluid flow simulations. The modeled image of the 3-D fault distribution is consistent with the fault architecture in the Mina Ratones area, which basically consists of two families of subvertical structures with NNE–SSW and ENE–WSW trends that displaces the surfaces of low-angle faults (North Fault) and follows their seismically detected staircase geometry. These brittle structures cut two subvertical dykes (27 and 27′ Dykes) with a NNE–SSW to N–S trend. The faults present high FI (FI>12) adjacent bands of irregular geometry in detail that intersect in space delimiting rhombohedral blocks of relatively less fractured granite (FI<6). Both structural domains likely correspond with the protolith and the damaged zone/fault core in the widely accepted model for fault zone architecture. Therefore, the construction of 3-D grids of the FI in granitic areas affected by brittle tectonics permits the quantitative structural characterization of the rock massif.     

Crustal structure of the continental margin of Korea in the East Sea (Japan Sea) from deep seismic sounding data: evidence for rifting affected by the hotter than normal mantle

Despite the various opening models of the southwestern part of the East Sea (Japan Sea) between the Korean Peninsula and the Japan Arc, the continental margin of the Korean Peninsula remains unknown in crustal structure. As a result, continental rifting and subsequent seafloor spreading processes to explain the opening of the East Sea have not been adequately addressed. We investigated crustal and sedimentary velocity structures across the Korean margin into the adjacent Ulleung Basin from multichannel seismic (MCS) reflection and ocean bottom seismometer (OBS) data. The Ulleung Basin shows crustal velocity structure typical of oceanic although its crustal thickness of about 10 km is greater than normal. The continental margin documents rapid transition from continental to oceanic crust, exhibiting a remarkable decrease in crustal thickness accompanied by shallowing of Moho over a distance of about 50 km. The crustal model of the margin is characterized by a high-velocity (up to 7.4 km/s) lower crustal (HVLC) layer that is thicker than 10 km under the slope base and pinches out seawards. The HVLC layer is interpreted as magmatic underplating emplaced during continental rifting in response to high upper mantle temperature. The acoustic basement of the slope base shows an igneous stratigraphy developed by massive volcanic eruption. These features suggest that the evolution of the Korean margin can be explained by the processes occurring at volcanic rifted margins. Global earthquake tomography supports our interpretation by defining the abnormally hot upper mantle across the Korean margin and in the Ulleung Basin.