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- Volume 47, Issue 4, 1999
Geophysical Prospecting - Volume 47, Issue 4, 1999
Volume 47, Issue 4, 1999
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Relationship between P‐ and S‐wave velocities and geological properties of near‐surface sediments of the continental slope of the Barents Sea
Authors Arthur Ayres and Friedrich TheilenSeismic velocities (Vp and Vs) of compressional (P‐) and shear (S‐) waves are important parameters for the characterization of marine sediments with respect to their sedimentological and geotechnical properties. P‐ and S‐wave velocity data of near‐surface marine sediments (upper 9 m) of the continental slope of the Barents Sea are analysed and correlated to sedimentological and geotechnical properties. The results show that the S‐wave velocity is much more sensitive to changes in lithology and mechanical properties than the P‐wave velocity, which is characterized by a narrow range of values. The correlation coefficients between S‐wave velocity and silt and clay content, wet bulk density, porosity, water content and shear strength are higher than 0.5 while the correlation coefficients of P‐wave velocity and the same parameters are always lower than 0.4. Although the relationship between Vs and clay content has been widely described, the data show that Vs is better correlated with silt content than with clay content for the sediments of the area investigated. However, they show different trends. While Vs increases with increasing clay content, it decreases with increasing silt content.
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Explicit expressions and numerical calculations for the Fréchet and second derivatives in 2.5D Helmholtz equation inversion
Authors Zhou Bing and GreenhalghIn order to perform resistivity imaging, seismic waveform tomography or sensitivity analysis of geophysical data, the Fréchet derivatives, and even the second derivatives of the data with respect to the model parameters, may be required. We develop a practical method to compute the relevant derivatives for 2.5D resistivity and 2.5D frequency‐domain acoustic velocity inversion. Both geophysical inversions entail the solution of a 2.5D Helmholtz equation. First, using differential calculus and the Green's functions of the 2.5D Helmholtz equation, we strictly formulate the explicit expressions for the Fréchet and second derivatives, then apply the finite‐element method to approximate the Green's functions of an arbitrary medium. Finally, we calculate the derivatives using the expressions and the numerical solutions of the Green's functions. Two model parametrization approaches, constant‐point and constant‐block, are suggested and the computational efficiencies are compared. Numerical examples of the derivatives for various electrode arrays in cross‐hole resistivity imaging and for cross‐hole seismic surveying are demonstrated. Two synthetic experiments of resistivity and acoustic velocity imaging are used to illustrate the method.
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Sharp boundary inversion of 2D magnetotelluric data
Authors Torquil Smith, Michael Hoversten, Erika Gasperikova and Frank MorrisonWe consider 2D earth models consisting of laterally variable layers. Boundaries between layers are described by their depths at a set of nodes and interpolated laterally between nodes. Conductivity within each layer is described by values at a set of nodes fixed within each layer, and is interpolated laterally within each layer. Within the set of possible models of this sort, we iteratively invert magnetotelluric data for models minimizing the lateral roughness of the layer boundaries, and the lateral roughness of conductivities within layers, for a given level of data misfit. This stabilizes the inverse problem and avoids superfluous detail. This approach allows the determination of boundary positions between geological units with sharp discontinuities in properties across boundaries, while sharing the stability features of recent smooth conductivity distribution inversions.
We compare sharp boundary inversion results with smooth conductivity distribution inversion results on a numerical example, and on inversion of field data from the Columbia River flood basalts of Washington State. In the synthetic example, where true positions and resistivities are known, sharp boundary inversion results determine both layer boundary locations and layer resistivities accurately. In inversion of Columbia flood basalt data, sharp boundary inversion recovers a model with substantially less internal variation within units, and less ambiguity in both the depth to base of the basalts and depth to resistive basement.
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Compressional‐ and shear‐wave velocities as a function of confining stress in dry sandstones
More LessA laboratory study was carried out to investigate the influence of confining stress on compressional‐ and shear‐wave velocities for a set of rock samples from gas‐producing sandstone reservoirs in the Cooper Basin, South Australia. The suite of samples consists of 22 consolidated sublitharenites with helium porosity ranging from 2.6% to 16.6%. We used a pulse‐echo technique to measure compressional‐ and shear‐wave velocities on dry samples (cylindrical 4.6 × 2 cm) at room temperature and at elevated confining stress (≤ 60 MPa). Compressional‐ and shear‐wave velocities in samples increase non‐linearly with confining stress. A regression equation of the form V = A − Be−DP gives a good fit to the measured velocities with improved prediction of velocities at high confining stresses compared with equations suggested by other studies. The predicted microcrack‐closure stresses of the samples show values ranging from 70 MPa to 95 MPa and insignificant correlation with porosity, permeability or clay content. There is a positive correlation between change in velocity with core porosity and permeability, but this association is weak and diminishes with increasing confining stress. Experimental results show that pore geometry, grain‐contact type, and distribution and location of clay particles may be more significant than total porosity and clay content in describing the stress sensitivity of sandstones at in situ reservoir effective stress. The stress dependence of Cooper Basin sandstones is very large compared with data from other studies. The implication of our study for hydrocarbon exploration is that where the in situ reservoir effective stress is much less than the microcrack‐closure stress of the reservoir rocks, the variation of reservoir effective stress could cause significant changes in velocity of the reservoir rocks. The velocity changes induced by effective stress in highly stress‐sensitive rocks can be detected at sonic‐log and probably surface‐seismic frequencies.
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Modelling the poroelasticity of rocks and ice
Authors Thomas Keller, Uwe Motschmann and Ludwig EngelhardFor many geophysical and astrophysical applications the relationship between physical bulk properties and porosity is needed. As part of the preparation for the ‘Rosetta’ comet rendezvous mission, a simple model for the porosity dependence of the elastic properties of granular media, i.e. the elastic moduli and the propagation velocities of elastic waves, has been developed based on textural properties and the contact stiffness of the constituent particles. It is shown that the derived relationships fit very well with sandstone data. The model is also consistent with data for snow and ice and is in agreement with the transformation mechanisms from snow to ice. A short review shows the relevance to another physical bulk property, the thermal conductivity.
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An efficient non‐linear least‐squares 1D inversion scheme for resistivity and IP sounding data
More LessNon‐linear least‐squares inversion operates iteratively by updating the model parameters in each step by a correction vector which is the solution of a set of normal equations. Inversion of geoelectrical data is an ill‐posed problem. This and the ensuing suboptimality restrict the initial model to being in the near vicinity of the true model. The problem may be reduced by introducing damping into the system of equations. It is shown that an appropriate choice of the damping parameter obtained adaptively and the use of a conjugate‐gradient algorithm to solve the normal equations make the 1D inversion scheme efficient and robust. The scheme uses an optimal damping parameter that is dependent on the noise in the data, in each iterative step. The changes in the damping and relative residual error with iteration number are illustrated. A comparison of its efficacy over the conventional Marquardt and simulated annealing methods, tested on Inman's model, is made. Inversion of induced polarization (IP) sounding is obtained by inverting twice (true and modified) DC apparent resistivity data. The inversion of IP data presented here is generic and can be applied to any of the IP observables, such as chargeability, frequency effect, phase, etc., as long as these observables are explicitly related to the DC apparent resistivity. The scheme is used successfully in inverting noise‐free and noisy synthetic data and field data taken from the published literature.
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Inversion of band‐limited TEM responses
Authors Flemming Effersø, Esben Auken and Kurt Ingvard SørensenIt is shown that the electromagnetic (EM) spectrum is characterized by strong amplitude‐modulated transmitters operating in the target bandwidth of transient electromagnetic (TEM) measurements. As these transmitters cause significant noise in TEM soundings, it is mandatory to band‐limit the input signals to improve the signal‐to‐noise ratio and thereby the depth of exploration. Band‐limitation will distort the TEM responses, which leads to erroneous inversion results if the applied low‐pass filters are not accounted for in the inversion scheme. We incorporate the low‐pass filters in the inversion scheme and test the inversion approach on theoretical and field data. Inversion of band‐limited theoretical responses results in recovery of erroneous resistivity models if the filters are not included in the inversion scheme. By contrast, inversion of band‐limited theoretical and field data, for which the applied low‐pass filters are included in the inversion scheme, leads to recovery of similar resistivity models, independent of the applied cut‐off frequencies.
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Seismic imaging of the shallow subsurface: shear‐wave case histories
More LessObtaining high‐resolution images of the geology and hydrogeology of the subsurface in the depth range from ground level to 50 m is one of the major challenges of modern geophysics. The methods which are commonly used (such as compressional‐wave surveys and ground‐penetrating radar) often suffer from adverse effects caused by the near‐surface conditions, changes in water saturation and various sources of noise. This paper demonstrates some of the advantages offered by the use of shear‐wave seismology and by the combination of shear‐ and compressional‐wave seismic methods in shallow subsurface investigations.
Multicomponent shallow seismic tests were carried out at four different sites to examine the effectiveness of different acquisition geometries under a variety of near‐surface geological conditions. Near‐surface conditions encountered at the sites included thick clays, clay/sand sequences overlying Chalk, mudstone overlying granodiorite bedrock and landfill material.
Under all conditions, shear‐wave data acquisition was found to have advantages over compressional‐wave acquisition for the investigation of the shallow subsurface. Shear head waves, being unaffected by water saturation, achieved penetration to greater depths at a site in Crewkerne, Dorset where compressional head‐wave penetration was limited to the near‐surface layers. Better vertical resolution was achieved at shallow depths using shear‐wave reflection energy at a landfill site. Shear‐wave reflections from shallow interfaces were in some cases less affected by noise compared with the equivalent compressional‐wave reflections. Combinations of shear‐ and compressional‐wave data recording allowed the measurement of a Poisson's ratio log and gave indications of seismic anisotropy at two sites where dipping clay layers were present.
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Measurement of magnetic properties of steel sheets
More LessMagnetic methods are used in detection of environmental, engineering and military objects fabricated of thin ferromagnetic sheets having volume susceptibilities higher than 100 SI units. Magnetic modelling of such objects would be advantageous, but it requires knowledge of the susceptibility and remanence values of sheet materials, which is scarce. We introduce a magnetometer method for the determination of susceptibility and remanence on thin steel samples. The area of the sample must be so large that its within‐sheet magnetization remains below the saturation state. The measurements are made in normal office surroundings in the Earth's magnetic field with an ordinary fluxgate magnetometer.
The square‐shaped sheet samples measured in this work have an edge length of 17.5 cm and a thickness in the range 0.5–1.0 mm. During the measuring procedure the sample is placed in four positions on a subvertical measurement board. For each position, the magnetic field in the dip direction of the board plane is measured on the opposite sides of the sample. The secondary field values are averaged for each sample position in order to reduce the effect of sample inhomogeneities. With these data, the susceptibility and remanence of the sample in its edge directions are then determined, based on a model curve which is calculated numerically using thin‐sheet integral equations.
The susceptibilities measured for different steel types (cold rolled and hot‐dip zinc‐coated steel sheets) varied in the range 200–500 SI units, and the remanence varied in the range 1000–20 000 A/m. No systematic differences were observed between the magnetic properties of various steel types. The repeatability of the susceptibility measurements was good (variations < 5%) but the remanence could be changed by 50% between repeated determinations.
The measured susceptibility range signifies that pieces of steel with a typical thickness of 0.5 mm remain below magnetic saturation when their edge dimension is larger than 5 cm. Therefore magnetic modelling of larger steel pieces must be made using the thin‐sheet theory with known magnetic properties, whereas smaller saturated pieces can be alternatively modelled as an equipotential system.
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Volumes & issues
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Volume 72 (2023 - 2024)
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Volume 71 (2022 - 2023)
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Volume 70 (2021 - 2022)
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Volume 69 (2021)
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Volume 68 (2020)
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Volume 67 (2019)
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Volume 66 (2018)
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Volume 65 (2017)
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Volume 64 (2015 - 2016)
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Volume 63 (2015)
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Volume 62 (2014)
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Volume 61 (2013)
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Volume 60 (2012)
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Volume 59 (2011)
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Volume 58 (2010)
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Volume 57 (2009)
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Volume 56 (2008)
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Volume 55 (2007)
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Volume 54 (2006)
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Volume 18 (1970 - 2006)
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Volume 53 (2005)
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Volume 52 (2004)
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Volume 51 (2003)
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Volume 50 (2002)
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Volume 49 (2001)
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Volume 48 (2000)
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Volume 47 (1999)
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Volume 46 (1998)
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Volume 45 (1997)
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Volume 44 (1996)
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Volume 43 (1995)
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Volume 42 (1994)
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Volume 41 (1993)
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Volume 40 (1992)
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Volume 39 (1991)
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Volume 38 (1990)
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Volume 4 (1956)
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Volume 2 (1954)
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