Effect of anisotropy of the earth on the impedance measurements

Summary Electromagnetic field response of a homogeneous uniaxially anisotropic conducting medium has been investigated in the presence of a vertical electric dipole placed at a heighth above the conducting surface. Expressions for the horizontal components of electric and magnetic fields and hence that of vertical impedance of the field, as a function of the distance of the place of observation from the source, have been derived. Numerical computations have been done and curves are given to illustrate the influence of anisotropy on the amplitude values of the impedance on the surface of the conducting medium.N.G.R.I. Contribution number 71–279.     

Fractal properties of medium and seismoelectric phenomena

Electrokinetic phenomena in a water-porous medium with a fractal structure above percolation threshold are theoretically investigated. Fracture zone with space-variable porosity is considered as a model of an earthquake hypocenter zone in which the electrokinetic current results from fluid filtration in a fractal pore network. A critical exponent of the streaming potential coefficient is found to depend on both the transport critical exponent and correlation length critical exponent. In this model, logarithmic dependence of electric field amplitude E on the earthquake magnitude M is derived which is compatible with the one observed by the VAN group. Without fractal properties, this form of dependence contradicts the empirical data. The electromagnetic field far from the hypocenter is calculated, which leads to the prediction of weak magnetic field variations. To explain the observed amplitude of VAN's Seismic Electric Signals (SES), the electric source must be at a distance of about 10 km from the registration point if the medium is homogeneous. Therefore, some conductive channel(s) are needed to explain the long distance selective SES transmission.     

Changes in the early part of the seismic coda due to localized scatterers: The estimation ofQ in a stope environment

A single scattering model was used to analyse the temporary changes in the mean density of scattered waves in a discrete random medium. The model of the mean energy density, originally proposed bySato (1977) for spherical radiation and isotropic scattering, has been modified and applied to a medium in which the scatterers are confined to a specified volume. The time variation of the early part of the mean energy density function for the different source durations was investigated. The dominant effect on the theoretical mean energy density is caused by the specified volume containing scatterers. The duration of the source pulse influences the early part of the coda fort/t ₀<1.2, wheret is the lapse time measured from the source origin time, andt ₀is arrival time of the body wave.The analysis of the coda signal of micro-events occurring immediately in front of the face enables us to estimate the size of the fracture zone induced by the stope. The model of the mean energy density of coda for a medium containing scatterers close to the seismic source was used to analyse a large number of events recorded close to an advancing mine face in a deep level gold mine in South Africa. The coda decay rate has two trends: the first, with a steep decay of coda, is produced by a larger deviation of rock parameters and/or larger size of the scatterers; the second trend, which decays more slowly, has the corresponding mean-free path ranging from 20 m to 200 m. The analysis indicates that the rock mass about 15–20 m from the stope contains a large proportion of fractured and blocked rock, which is the source of scattering. The scattering of theS-wave was much stronger and more stable, with the mean-free path varying from 11 m to 45 m. This is due to the shorter wavelength of theS wave in comparison with theP wave. The quality factor for theP coda wave varies from 30 to 100 in the fracture zone of stope and outside this zone it has a value of 300. The quality factor of theS wave varies from 20 to 78 in the equivalent volume. For rock surrounding the stope the ratioQ _sp ^–1 /Q _ss ^–1 varied from 0.31 to 0.69. This suggests that the radii of scatterers are smaller than 3.5 m.     

Elastic radiation from buried sources in a semi-infinite heterogeneous medium

Summary The wave equations of elasticity in the presence of body forces for a semi-infinite, isotropic, heterogeneous medium with exponentially varying material properties have been solved. Using double Fourier transform the equations are first transformed to linear second order differential equations. From the solution of these equations the displacements are obtained by the use of inversion theorem for double Fourier transform. The method followed resolves the disturbance into its constitutive parts—incident and reflectedP, SV andSH type waves. Surface displacements due to a single couple, double couple and various other sources have been calculated.     

Geometrical spreading factor of head waves in cased and open boreholes

Factors (coefficients) of geometrical spreading of compressional and shear head waves are calculated for an impulse multipole source of elastic oscillations in boreholes. It is shown that the length of the logging tool (i.e., the distance between the source and the nearest receiver) used for sonic measurements and the velocities of elastic waves in the medium both contribute to the factor of geometrical spreading. For a high-velocity formation (the shear wave velocity in the rock is higher than the compressional wave velocity in the fluid that fills the borehole) and a sufficiently long sonic tool with a monopole source, the coefficient of geometrical spreading is approximated by asymptotic formula 1/Z [Roever et al., 1974; Krauklis and Krauklis, 1976], where Z is the length of the tool; i.e., the amplitude of the compressional head wave decreases proportionally to the distance between the source and the receiver. In acoustically soft formations, this approximation is inapplicable even for long tools with length Z > 4 m. Waveforms in cased boreholes have a significant frequency dispersion even in case of good-quality cementing, and the factor of geometrical spreading there depends considerably on the length of the tool and the elastic properties of the rocks.     

ELECTROMAGNETIC FIELDS DUE TO A THIN RESISTIVE LAYER*

Using approximate boundary conditions, expressions for electromagnetic fields have been derived for a thin, highly resistive layer lying between two homogeneous layers excited by an electric dipole grounded on the surface of the earth. The variations of the fields with the parameter T/T₁ (ratio of the transverse resistance of the thin layer to the transverse resistance of the first layer) were studied in relation to frequency, time, the normalized separation source—receiver, and the angle between the source and the radius to the observation point. For a value of h₂/h₁ (ratio of thickness of second layer to the thickness of the first layer) approximately equal to 0.2, the general three-layer medium case gives the same results as this approach. It was found that the electric fields have a very strong dependence on the parameter T (transverse resistance) which characterizes the thin, highly resistive layer. However, the magnetic fields depend only very weakly on this parameter.     

Transport properties and microstructural characteristics of a thermally cracked mylonite

An experimental study was carried out on a granitic mylonite (La Bresse, France) to analyze the influence of pore microstructure on transport properties. Different crack networks were obtained by a controlled thermal treatment. Microstructures were analyzed by means of gas adsorption and mercury porosimetry. Transport properties have been investigated by measuring gas permeability and electrical conductivity. The dependence of permeability on confining pressure shows an exponential decrease, characteristic of a porosity made of cracks. Correlations between measured parameters have been analyzed by comparing them with relations deduced from theoretical models. Linking the formation factor to the porosity leads to a rather low tortuosity value (about 2.4), characterizing a medium with a well connected porosity. Correlation between permeabilityk and formation factorF leads to a power-law relationk F ^–n wheren2.9, which is consistent with a crack model describing the behavior of the thermally treated rock.     

On the disturbance due to a point source in an inhomogeneous medium

Summary The problem of a point source in an isotropic, inhomogeneous fluid medium is discussed. It is assumed that the density of the fluid is constant and the acoustic velocity varies with depth asc=c ₀(1 +m z) wherem is a constant andc ₀ is, the velocity at the level of the origin. An approximate expression for the field due to a point source in such a medium is obtained when the medium is infinite as well as when it is semi-infinite. It is found that the results obtained agree with the WKB solution of the problem.     

反卷积在人工震源数据处理中的应用

震源到接收台站之间的地层响应函数能够反映地下介质信息。对地震波传播过程中的卷积模型进行推导:记录信号是众多震源子波经过时移加权叠加的结果;通过反卷积方法可去除震源子波信息,提取震源到接收台站之间的地层响应函数;地层响应函数中第一个突跳值对应的时间即为P波走时。在河北赤城—张北地区进行人工震源实验,通过反卷积计算得到该地区地层响应函数剖面图,得出P波波速约6 km/s。利用人工震源系统还可以对地下介质波速变化进行长期动态监测,对地震预测具有一定意义。     

DETERMINATION OF ELECTRIC ROCK PARAMETERS FROM THE FIELD STRUCTURE OF A MAGNETIC DIPOLE*

In the theoretical part of the present paper, formulas have been analyzed for a magnetic dipole in a homogeneous and unbounded medium. The magnetic field is elliptically polarized in the region between the quasistatic zone and the far field. Since the position and the shape of the polarization ellipses depend on the complex wave number, k, it is possible to determine k by measuring the polarization ellipses. From k, the conductivity and the dielectric constant of the medium are easily calculated. The functions required for the measuring method have been computed and plotted in graphs. In the experimental part it was examined how far the theory may be applied to measurements of propagation through rock at frequencies ranging from 100-1000 kHz. These measurements showed that reasonably defined mean values of rock parameters can be given only if the deviations of the field from the theoretically expected field are not too high. These deviations have been named field distortions and have been examined by means of statistical methods (variance ratio tests). Gallery cavity and inhomogeneity or anisotropy of the medium account for these distortions.     

Empirical models for estimating liquefaction-induced lateral spread displacement

Existing empirical models for estimating liquefaction-induced lateral spread displacement (D_LL) have been derived from a dataset poorly distributed with respect to earthquake magnitude and source distance, and also produced from different tectonic source types and faulting mechanisms. Both the poor distribution and mixed tectonic source types and faulting mechanisms of the data have an adverse impact on the reliability of the empirical models. To overcome these problems in the development of empirical models, we replace the direct use of magnitude and source distance with pseudo-displacement derived from spectral acceleration attenuation models that are well supported by earthquake data, and use a modification factor to account for effects of the non-linear soil response. Attenuation models derived from very large and reasonably well-balanced datasets have been selected, one being a Japanese attenuation model and other being a combination of the Sadigh et al. model and the Youngs et al. model. These models are capable of accounting for the effects of earthquake tectonic source type and faulting mechanism. We determined the model coefficients by selecting the pseudo-displacements calculated for a number of spectral periods to achieve an unbiased distribution of residuals with respect to earthquake magnitude and source distance. Sensitivity analyses have been carried out based on the new and existing models, and show that the new model is more robust than the existing models. Comparison with a limited number of data from the 1997 Kocaeli, Turkey earthquake suggests our model provides comparable liquefaction-induced lateral displacement D_LL estimates.     

A single-station coda solution for source, attenuation and site factors

Based on the empirical formulation formed from coda observations, the digital waveforms from 33 local events with magnitude M _L ranging between 2.1 and 3.5, recorded at Changli station of Beijing Telemetered Seismographic Network from 1989 to 1991, are used to compute coda Q for the Changli region and the source factors of all earthquakes by single-station coda method. Furthermore, assuming a certain source model, we have obtained the station site frequency response and source spectra, as well as source parameters such as corner frequencies, seismic moments and stress drops and so on. Their variations with time are monitored before and after larger earthquakes. Because the coda method can more effectively reduce the influence of source radiation pattern and a particular propagation path than direct wave method, more data can be used and more accurate results can be obtained, which provided a possible approach to study the source properties and reveal the variation of source parameters before larger earthquakes. Contribution No. 97A0107, Institute of Geophysics, SSB, China.     

Joint elastic‐electrical effective medium models of reservoir sandstones

Improvements in the joint inversion of seismic and marine controlled source electromagnetic data sets will require better constrained models of the joint elastic‐electrical properties of reservoir rocks. Various effective medium models were compared to a novel laboratory data set of elastic velocity and electrical resistivity (obtained on 67 reservoir sandstone samples saturated with 35 g/l brine at a differential pressure of 8 MPa) with mixed results. Hence, we developed a new three‐phase effective medium model for sandstones with pore‐filling clay minerals based on the combined self‐consistent approximation and differential effective medium model. We found that using a critical porosity of 0.5 and an aspect ratio of 1 for all three components, the proposed model gave accurate model predictions of the observed magnitudes of P‐wave velocity and electrical resistivity and of the divergent trends of clean and clay‐rich sandstones at higher porosities. Using only a few well‐constrained input parameters, the new model offers a practical way to predict in situ porosity and clay content in brine saturated sandstones from co‐located P‐wave velocity and electrical resistivity data sets.     

ComprehensiveanalysesofseismicsourcelayerinXingtaiandTangshanseismicregionsandtheconditionsofmediaab

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AVO investigations of shallow marine sediments

Amplitude‐variation‐with‐offset (AVO) analysis is based on the Zoeppritz equations, which enable the computation of reflection and transmission coefficients as a function of offset or angle of incidence. High‐frequency (up to 700 Hz) AVO studies, presented here, have been used to determine the physical properties of sediments in a shallow marine environment (20 m water depth). The properties that can be constrained are P‐ and S‐wave velocities, bulk density and acoustic attenuation. The use of higher frequencies requires special analysis including careful geometry and source and receiver directivity corrections. In the past, marine sediments have been modelled as elastic materials. However, viscoelastic models which include absorption are more realistic. At angles of incidence greater than 40°, AVO functions derived from viscoelastic models differ from those with purely elastic properties in the absence of a critical angle of incidence. The influence of S‐wave velocity on the reflection coefficient is small (especially for low S‐wave velocities encountered at the sea‐floor). Thus, it is difficult to extract the S‐wave parameter from AVO trends. On the other hand, P‐wave velocity and density show a considerably stronger effect. Attenuation (described by the quality factor Q) influences the reflection coefficient but could not be determined uniquely from the AVO functions. In order to measure the reflection coefficient in a seismogram, the amplitudes of the direct wave and the sea‐floor reflection in a common‐midpoint (CMP) gather are determined and corrected for spherical divergence as well as source and streamer directivity. At CMP locations showing the different AVO characteristics of a mud and a boulder clay, the sediment physical properties are determined by using a sequential‐quadratic‐programming (SQP) inversion technique. The inverted sediment physical properties for the mud are: P‐wave velocity α=1450±25 m/s, S‐wave velocity β=90±35 m/s, density ρ=1220±45 kg/m³, quality factor for P‐wave Q_P=15±200, quality factor for S‐wave Q_S=10±30. The inverted sediment physical properties for the boulder clay are: α=1620±45 m/s,β=360±200 m/s,ρ=1380±85 kg/m³,Q_P=790±660,Q_S=25±10.     

Response spectral relationships for rock sites derived from the component attenuation model

The seismological model was developed initially from the fundamental relationship between earthquake ground motion properties and the seismic moment generated at the source of the earthquake. Following two decades of continuous seismological research in the United States, seismological models which realistically account for both the source and path effects on the seismic shear waves have been developed and their accuracy rigorously verified (particularly in the long and medium period ranges). An important finding from the seismological research by Atkinson and Boore and their co‐investigators is the similarity of the average frequency characteristics of seismic waves generated at the source between the seemingly very different seismic environments of Eastern and Western North America (ENA and WNA, respectively). A generic definition of the average source properties of earthquakes has therefore been postulated, referred to herein as the generic source model. Further, the generic ‘hard rock’ crustal model which is characteristic of ENA and the generic ‘rock’ crustal model characteristic of WNA have been developed to combine with the generic source model, hence enabling simulations to be made of the important path‐related modifications to ground motions arising from different types of crustal rock materials. It has been found that the anelastic contribution to whole path attenuation is consistent between the ENA and WNA models, for earthquake ground motions (response spectral velocities and displacements) in the near and medium fields, indicating that differences in the ENA and WNA motions arise principally from the other forms of path‐related modifications, namely the mid‐crust amplification and the combined effect of the upper‐crust amplification and attenuation, both of which are significant only for the generic WNA ‘rock’ earthquake ground motions. This paper aims to demonstrate the effective utilization of the latest seismological model, comprising the generic source and crustal models, to develop a response spectral attenuation model for direct engineering applications. The developed attenuation model also comprises a source factor and several crustal (wave‐path modification) component factors, and thus has also been termed herein the component attenuation model (CAM). Generic attenuation relationships in CAM, which embrace both ENA and WNA conditions, have been developed using stochastic simulations. The crustal classification of a region outside North America can be based upon regional seismological and geological information. CAM is particularly useful for areas where local strong motion data are lacking for satisfactory empirical modelling. In the companion paper entitled ‘response spectrum modelling for rock sites in low and moderate seismicity regions combining velocity, displacement and acceleration predictions’, the CAM procedure has been incorporated into a response spectrum model which can be used to effectively define the seismic hazard of bedrock sites in low and moderate seismicity regions. This paper and the companion paper constitute the basis of a long‐term objective of the authors, to develop and effectively utilize the seismological model for engineering applications worldwide.     

Source function of stress waves of a spherical explosive source

Summary The source functions of the stress wave patterns at an elastic source of these waves are analysed. The comparison of the properties of the functions with the stress wave records obtained earlier showed that their parameters do not satisfy, to a greater or lesser extent, the stress wave patterns in the neighbourhood of explosive sources. For this reason a new source function (1) was defined, which fully approximates the observed stress wave patterns in gravel sandy soil. The coefficientsP ₀, , , and were experimentally determined as functions of the distance from the source, its size and the radius of the elastic source in the medium considered. The properties of source function (1) are demonstrated on an example.Paper presented at the XIIIth General Assembly of the European Seismological Commission, Braov (Romania), 28 August to 6 September, 1972.     

Disturbance due to a point source in a layered half-space

Summary In this paper the displacement components due to a compressional point source in a layered half-space consisting of a liquid layer of finite thickness overlying a semi-infinite solid homogeneous medium have been deduced. Two different cases have been considered. In the first case the source is taken in the liquid layer and in the second case the source is taken in the solid layer. The displacement components in cylindrical coordinates have been obtained in closed form in detail at the interface for all values of distance from the source for the second case.     

The Ain Temouchent (Algeria) Earthquake of December 22<Superscript>nd</Superscript>, 1999

—On December 22^nd, 1999 an earthquake of Magnitude M_w : 5.7 occurred at Ain Temouchent (northwest Algeria). This moderate seismic event was located in a region characterized by a low seismic activity where few historical events have been observed. The earthquake, with a maximum intensity of VII (MSK scale), caused serious damages to the Ain Temouchent city and its surroundings. In the epicentral area, 25 people died and about 25,000 people were made homeless. Some minor breaks have been observed in several areas in the field. They were mainly related to minor collapses in the landscape or in volcanic cavities. The focal mechanism has been studied by using broadband data at regional and teleseismic distances, and different methods. The fault-plane solution has been estimated from first motions of P wave. Depth and source time function have been estimated from the modeling of body waveforms. Scalar seismic moment and source dimension have been obtained from spectral analysis. Results show thrust motion, with a horizontal pressure axis oriented in a NW-SE direction, a depth of 4 km and a simple source time function with time duration of 5 s. Scalar seismic moment estimated from waveform modeling is 4.7 × 10¹⁷ Nm, and spectral analysis gives a value of 1.7 × 10¹⁷ Nm and a source radius of 7.5 km.     

LAYERED PERMEABLE SYSTEMS1

Permeability is a second rank tensor relating flow rate to pressure gradient in a porous medium. If the permeability is a constant times the identity tensor the permeable medium is isotropic; otherwise it is anisotropic. A formalism is presented for the simple calculation of the permeability tensor of a heterogeneous layered system composed of interleaved thin layers of several permeable constituent porous media in the static limit. Corresponding to any cumulative thickness H of a constituent is an element consisting of scalar H and a matrix which is H times a hybrid matrix function of permeability. The calculation of the properties of a medium equivalent to the combination of permeable constituents may then be accomplished by simple addition of the corresponding scalar/matrix elements. Subtraction of an element removes a permeable constituent, providing the means to decompose a permeable medium into many possible sets of permeable constituents, all of which have the same flow properties. A set of layers of a constituent medium in the heterogeneous layered system with permeability of the order of 1/h as h→ 0, where h is that constituent's concentration, acts as a set of infinitely thin channels and is a model for a set of parallel cracks or fractures. Conversely, a set of layers of a given constituent with permeability of the order of h as h→ 0 acts as a set of parallel flow barriers and models a set of parallel, relatively impermeable, interfaces, such as shale stringers or some faults. Both sets of channels and sets of barriers are defined explicitly by scalar/matrix elements for which the scalar and three of the four sub-matrices vanish. Further, non-parallel sets of channels or barriers can be ‘added’ and 'subtracted’ from a background homogeneous anisotropic medium commutatively and associatively, but not non-parallel sets of channels and barriers reflecting the physical reality that fractures that penetrate barriers will give a different flow behaviour from barriers that block channels. This analysis of layered media, and the representations of the phenomena that can occur as the thickness of a constituent is allowed to approach zero, are applicable directly to layered heat conductors, layered electrostatic conductors and layered dielectrics.