Direct interpretation of self-potential anomalies produced by a vertical dipole

In the present paper a new method is proposed for the quantitative interpretation of self-potential anomalies which are produced by a vertical dipole. First the mathematical expression of the wavenumber spectrum of the self-potential anomaly is deduced. It is pointed out that at relatively high wavenumbers the behavior of the amplitude spectrum is controlled by the closer to the surface pole at depth h. On the other hand, the “width” of the amplitude spectrum depends on the depth h and the dipole length L.Making a proper mathematical transformation of the amplitude spectrum, and applying the least squares method, it is possible to calculate the depth to the upper pole. The dipole length may then be calculated, by solving numerically a characteristic algebraic equation, as long as the “width” of the amplitude spectrum has been previously defined.The proposed method is applied on a well known self-potential profile from Greece. The calculated parameters of the polarized body are in good agreement with real data. Experimentation with synthetic models in which random noise was introduced, showed that this method gives reliable results if the noise amplitude is not more than 20% of the signal amplitude. It is clearly more efficient than the methods which are based on the model of the point pole or the dipole with a small length. It can also give good results if the horizontal extensions of the polarized body are not more than a few tenths of the depth of the upper pole. If the polarized body is tilted, the depth of the upper pole can be calculated with satisfactory accuracy.The direct interpretation method which is proposed in the present paper, may be useful in mineral exploration, and particularly if the target of interest is the detection of massive sulfide mineralization.     

Moveout approximation for vertical seismic profile geometry in a 2D model with anisotropic layers

I introduce a new explicit form of vertical seismic profile (VSP) traveltime approximation for a 2D model with non‐horizontal boundaries and anisotropic layers. The goal of the new approximation is to dramatically decrease the cost of time calculations by reducing the number of calculated rays in a complex multi‐layered anisotropic model for VSP walkaway data with many sources. This traveltime approximation extends the generalized moveout approximation proposed by Fomel and Stovas. The new equation is designed for borehole seismic geometry where the receivers are placed in a well while the sources are on the surface. For this, the time‐offset function is presented as a sum of odd and even functions. Coefficients in this approximation are determined by calculating the traveltime and its first‐ and second‐order derivatives at five specific rays. Once these coefficients are determined, the traveltimes at other rays are calculated by this approximation. Testing this new approximation on a 2D anisotropic model with dipping boundaries shows its very high accuracy for offsets three times the reflector depths. The new approximation can be used for 2D anisotropic models with tilted symmetry axes for practical VSP geometry calculations. The new explicit approximation eliminates the need of massive ray tracing in a complicated velocity model for multi‐source VSP surveys. This method is designed not for NMO correction but for replacing conventional ray tracing for time calculations.     

On the interpretation of vertical gravity gradients produced by magmatic intrusions

A method for the computation and interpretation of gravity and height changes and vertical gravity gradients produced by magmatic intrusions in a layered elastic–gravitational medium is presented. The methodology assumes a planar medium geometry, which consists of welded layers overlying a half-space. The medium is elastic and gravitating. The intrusion is treated as a point source and can be located at any depth inside the medium. The theoretical elastic–gravitational model allows the computation of the so-called geometric and orthometric vertical displacements as well as gravity changes of different types. The corresponding vertical gravity gradients can also be computed. We present several examples of theoretical computations and study different types of these geometric and orthometric gravity gradients and the information we can get from the application of the methodology described. The results presented show that the use of these gradients is a useful tool to obtain information on the dynamics of the injection processes, including the detection of new magma recharge. We show that using the elastic–gravitational deformation model we can explain non-linear gravity–height relationships that appear in volcanic areas. We also present the application of the methodology to Mayon volcano, Philippines, delineating the intrusion of new magma, consistent with the produced eruptions after the observation period.     

Disturbance produced in a semi-infinite anisotropic elastic medium by an impulsive twist applied on the plane surface

Summary In this paper the displacement due to an impulsive twist produced by impulsive shearing stresses acting on a finite circular area on the plane surface of a semi-infinite solid of homogeneous anisotropic material has been found.Paper presented by Dr. A. K. Mitra of Jadavpur University.     

Horizontal soil-water intake through a thin zone of reduced permeability

One-dimensional, horizontal soil-water absorption through a thin zone of constant nonzero hydraulic resistance is examined theoretically and experimentally. Mathematically, this involves a numerical solution, as well as a similarity reduction of the problem for early to intermediate times. The flow equations are transformed by introducing a dimensionless parameter, which enables the solution for any value of thin-zone resistance to be obtained from the solution for a given known thin-zone resistance. At the inlet boundary between the thin zone and the soil column, the soil-water content increases with time to approach the saturated value. The cumulative absorption of water by the soil column increases more than proportionally with the square root of time for early and intermediate times, and approaches a square-root-of-time proportionality at large times. For both the soil-water content at the inlet boundary and the cumulative water absorption by the soil column, simple expressions arise from the similarity-reduction analysis, which is based on specific functional forms of the soil-water diffusivity and suction head. For early to intermediate times of flow, the similarity-reduction analysis describes adequately the calculated numerical-solution flow data for Yolo soil, as well as the measurements obtained experimentally on Salkum silty clay loam.     

各向异性半空间上方垂直磁偶极子电磁场的球面波展开式

文中推导出单轴各向异性媒质半空间上方垂直磁偶极源电磁场的精确解析表达式. 应用圆柱波函数的球面波展开式和超几何函数理论,场分量中的索末菲尔德型积分被表示成快速、绝对收敛的球面波函数系展开式;展开系数是以物性参数为复宗量的勒让德多项式. 该展开式数学物理意义明显,并且不受场点和源点的位置、媒质的物性参数和频率等条件的限制. 利用本文的结果可十分方便地计算和分析任意场点处的电磁场分布.     

Evidence from P-to-S mantle converted waves for a flat “660-km” discontinuity beneath Iceland

Iceland is the type example of a ridge-centered hotspot. It is controversial whether the seismic anomaly beneath it originates in the lower mantle or the upper mantle. Some recent studies reported that the 660-km discontinuity beneath central Iceland is shallow relative to peripheral regions and this was interpreted as an effect of elevated temperature at that depth. We investigate topography of the major upper mantle discontinuities by separating the effects of the topography and volumetric velocity heterogeneity in P receiver functions from 55 seismograph stations. Our analysis demonstrates that a significant (at least 10-km) shallowing of the 660-km discontinuity is only possible in the case of improbably low seismic velocities in the mantle transition zone beneath central Iceland. If, as in previous studies, lateral velocity variations in the mantle transition zone are neglected, the data require a depressed rather than an uplifted 660-km discontinuity. For a reasonable S-wave velocity anomaly in the mantle transition zone (around − 3%) no topography on the 660-km discontinuity is required. This can be explained by the lack of temperature anomaly or an effect of two phase transitions with opposite Clapeyron slopes.     

Experimental study of near-bed concentration and sediment vertical mixing parameter for vertical concentration distribution in the surf zone

Two formulae for the near-bed concentration(C_a) and the sediment vertical mixing parameter(m) are established based on a large scale wave flume experiment.The advantage of the new formulae is that the turbulent kinetic energy induced by wave breaking can be taken into account;the formula for C_a is in terms of the near-bed,time-averaged turbulent kinetic energy,and the formula for m is in terms of depth-and time-averaged turbulent kinetic energy.A new expression for suspended sediment load also is established by depth integration of the vertical distribution of the suspended sediment concentration obtained on basis of the new formulae.Equation validation is done by comparing the predicted C_a and m to measurements for different types of waves(regular wave,wave group,and irregular wave),and good agreement is found.The advantages of the proposed formulae over previous formulae also are discussed.     

Electromagnetic fields of a vertical magnetic dipole above a laterally inhomogeneous thin layer of conductive overburden

An analytical formulation is developed for the resultant electromagnetic field of an oscillating vertical magnetic dipole located over a thin conductive sheet of infinite extent. The sheet is characterized by a conductivity-thickness product or conductance d that may be a function of the horizontal coordinates. The system of integral equations arising in the general formulation is simplified greatly when azimuthal symmetry prevails. Numerical results for a Gaussian variation of d in the radial direction are presented for the case of a symmetrically located source. These results are for the fields at the level of the source dipole over the conductive sheet. It is shown that the quadrature response of the sheet is enhanced when there is rapid variation of the conductance. The null in the resultant wave tilt is also found to be shifted toward the direction of increasing conductance.     

Traveltime computation for 3D anisotropic media by a finite-difference perturbation method

The first-order perturbation theory is used for fast 3D computation of quasi-compressional (qP)-wave traveltimes in arbitrarily anisotropic media. For efficiency we implement the perturbation approach using a finite-difference (FD) eikonal solver. Traveltimes in the unperturbed reference medium are computed with an FD eikonal solver, while perturbed traveltimes are obtained by adding a traveltime correction to the traveltimes of the reference medium. The traveltime correction must be computed along the raypath in the reference medium. Since the raypath is not determined in FD eikonal solvers, we approximate rays by linear segments corresponding to the direction of the phase normal of plane wavefronts in each cell. An isotropic medium as a reference medium works well for weak anisotropy. Using a medium with ellipsoidal anisotropy as a background medium in the perturbation approach allows us to consider stronger anisotropy without losing computational speed. The traveltime computation in media with ellipsoidal anisotropy using an FD eikonal solver is fast and accurate. The relative error is below 0.5% for the models investigated in this study. Numerical examples show that the reference model with ellipsoidal anisotropy allows us to compute the traveltime for models with strong anisotropy with an improved accuracy compared with the isotropic reference medium.     

俯冲带板内地震竖向加速度谱阻尼修正系数模型研究

基于日本K-NET和KiK-net台网的4695条俯冲带板内地震记录,采用最小二乘法对阻尼修正系数(DMF)的几何均值进行关于阻尼比和谱周期的回归拟合,分场地类别建立了考虑阻尼比和谱周期的竖向加速度谱DMF模型.为探究震源、路径和场地效应对该模型残差分布的影响,采用随机效应模型将残差分离得到各类残差及相应的残差标准差,...     

Wave damping by a vertical porous structure placed near and away from a rigid vertical wall

Damping of water waves by a vertical porous structure placed at some distance from a vertical wall is investigated within the framework of linear water wave theory. The rectangular porous structure is placed on a small rectangular elevation. An incident wave of small amplitude propagates through the structure – some portion gets reflected back while some portion gets transmitted to a third region bounded vertically by a rigid wall which is considered to be at a distance near the porous structure, and also away from the wall at a large distance as a separate case. Boundary value problems are set up in all three regions and, by using the matching conditions along the vertical boundaries, a system of linear equations is deduced. The roots of the relevant dispersion relation are used in setting up the system of equations. The overall scattering phenomenon is studied with respect to different relevant parameters. The dependence of the coefficients on the thickness (width) of the porous structure is investigated for different numbers of modes and porosity. It is observed that, except for the case when the porous structure is thin, the reflection and transmission coefficients give rise to values as expected. In the case, when the rigid wall is nearer to the structure, the reflection coefficient decreases rapidly for a thin structure and converges for all numbers of evanescent modes afterwards. The transmission coefficient also decreases as the width increases, ultimately converging and vanishing for a wide structure. When the wall is at a large distance away from the structure, the behavior of both the reflection and transmission coefficients remain the same. For both cases of the wall being nearer and away from the structure, higher porosity gives rise to lower reflection coefficients and higher transmission coefficients. However, the transmission coefficients converge and vanish when the porous structure is very wide. We also discuss the energy loss against the width of the porous structure for different values of number of modes and porosity. Irrespective of the positioning of the rigid wall, we observe that for higher values of porosity, energy loss is more pronounced when the structure is not thin, whereas energy loss is same for all numbers of modes. All our observations are supported by graphs. Good agreement of our result with earlier results justifies our model.     

Scattering of elastic waves by a 3D anisotropic basin

Scattering of elastic waves by a three‐dimensional transversely isotropic basin of arbitrary shape embedded in a half‐space is considered using an indirect boundary integral equation approach. The unknown scattered waves are expressed in terms of point sources distributed on the so‐called auxiliary surfaces. The sources are expressed in terms of the full‐space Green's functions with their intensities determined from the requirement that the boundary and the continuity conditions are to be satisfied in the least‐squares sense. Steady‐state results were obtained for incident plane pseudo‐P‐, SH‐, SV‐, and Rayleigh waves. Using the Radon transform the Green's functions are obtained in the form of finite integrals over a unit sphere or a unit circle which can be numerically evaluated very efficiently. Detailed analysis of the method includes the discussion on the shape of the auxiliary surfaces and the distribution of the collocation points and sources. The convergence criteria is defined in terms of transparency tests, isotropic limit test, and minimization of a certain norm. The isotropic limit tests show excellent agreement with the isotropic results available in literature. For anisotropic materials the numerical results are given for a semispherical basin. The results show that presence of an anisotropic basin may result in significant amplification of surface motion atop the basin. While the amplitude of peak surface motion may be similar to the corresponding isotropic results, the difference in the displacement patterns may be quite different between the two. Therefore, this study clearly demonstrates that material anisotropy may be very important for accurate assessment of surface ground motion amplification atop basins. Copyright © 2000 John Wiley & Sons, Ltd.     

Any P-wave kinematic algorithm for vertical transversely isotropic media can be ADAPTed to moderately anisotropic media of arbitrary symmetry type

Most of P-wave anisotropic kinematic algorithms (modeling, processing, and inversion) have been developed for the case of Transverse Isotropy (TI). Does it mean that when dealing with more complex symmetry types (Arbitrarily tilted TI, orthorhombic, monoclinic or even triclinic), all these algorithms are irrelevant? In fact, not at all. It has recently been demonstrated that in 2D geometry any qP-wave TI kinematic algorithm can be simply generalized to the case of monoclinic symmetry using the so-called Azimuthally Dependent Anisotropy Parameter Transformation (ADAPT), assuming moderate anisotropy. The extension of the technique to the case of arbitrary anisotropy type (triclinic) is achieved in this paper. The method is successfully checked for seismic modeling in a full 2D model with layers of contrasted anisotropy types and with arbitrary vertical and horizontal velocity variations (non-constant gradient). Typically, the approximate travel times using ADAPT differ from the exact travel times by a few milliseconds for total travel times of the order of a few seconds. Applications to seismic processing are also described. The simplicity of the procedure and the generality of the applicability of the ADAPT recipe are striking and very convenient for practical applications. They certainly deserve further analysis.     

Some hydrodynamic problems for a nepheloid zone

Summary A layer of a few hundred meters thickness with suspended matter (a nepheloid zone) was discovered byEwing andThorndike [4]³⁾ near the bottom on the continental slope of the North Atlantic. A downward pressure gradient is produced in this layer due to increment of water density with suspensoid. When only the Coriolis force balances with this pressure gradient, a bottom nepheloid current flows southwestward parallel to the depth contours with a velocity of about 10 (cm/sec) for a slope of one degree. The pressure gradient for fluid with locally variable density above a sloping bottom is treated and an extra term due to density gradient along the slope is derived. The vertical profiles of the nepheloid current with an effect on the vertical eddy viscosity are computed. Two kinds of vertical distributions of eddy viscosity are determined from the observed nepheloid distributions and used in the calculations: constant but different values at two layers and those increasing with height. The effect of the change of density along the bottom is treated by introducing dimensionless variables. Rossby number of the nepheloid current becomes about 10^–2 indicating inertia terms to be negligible. Rossby number of turbidity currents ranges from 2 (in a decaying area) to 5 (developing area), suggesting that inertia terms are more important than Coriolis terms. The trajectories of turbidity currents are computed from motion of a mass of mud under the Coriolis force and friction, and the results are applied to those inferred byHand andEmery [6] in the San Diego Through off California.LGO Contribution Number 925.     

Evidences for a low-velocity core-mantle transition zone

Using the spectral ratios $\text{P}\text{PcP}\text{,}\text{ScS}{}_{\mathrm{n+1}}\text{ScS}{}_{\mathrm{n}}\text{,}\text{sScS}{}_{\mathrm{n+1}}\text{sScS}{}_{\mathrm{n}}\text{and}\text{SKS}\text{ScS}$, models for the core-mantle boundary are found. The models have close similarity with each other, implying an irregular surface with lateral variation in the core-mantle properties. The models are characterized by two to four low-velocity, high-density layers imbedded between the mantle and the core half space. The velocities of the imbedded layers decrease towards the core boundary with a lower bound of 9.3 km/sec for the compressional wave and 3.5 km/sec for the shear wave. The models fitted to the empirical data support the hypothesis of a finite rigid outer core with a higher bound for the shear velocity of 1.4 km/sec. Based on this finite rigidity in the outer core and a layered core-mantle transition zone, the value of Q for the whole mantle is 2,000. For the outer core Q ranges from 100–1,000 , which may indicate that it is chemically zoned.     

Forecasting the energy produced by a windmill on a yearly basis

The objective of this article is to study as extensively as possible the uncertainties affecting the annual energy produced by a windmill. In the literature, the general approach is to estimate the mean annual energy from a transformation of a Weibull distribution law. Then the issue is reduced to estimating the coefficients of this distribution. This is obtained by classical statistical methods. Therefore, the uncertainties are mostly limited to those resulting from the statistical procedures. But in fact, the real uncertainty of the random variable which represents the annual energy cannot been reduced to the uncertainty on its mean and to the uncertainties induced from the estimation procedure. We propose here a model, which takes advantage of the fact that the annual energy production is the sum of many random variables representing the 10?min energy production during the year. Under some assumptions, we make use of the central limit theorem and show that an intrinsic uncertainties of wind power, usually not considered, carries an important risk. We also explain an observation coming from practice that the forecasted annual production is always overestimated, which creates a risk of reducing the profitability of the operation.     

Transmission and reflection of Rayleigh waves at a thin low velocity vertical layer: A laboratory and theoretical study

A three-dimensional ultrasonic modelling was used to study the Rayleigh waves reflected from a thin low velocity vertical layer and those transmitted through the same zone. The reflection and transmission coefficients of the Rayleigh waves have been calculated by an approximate method based on the Green function technique. Nonrigid contact boundary conditions were used for the low velocity layer modelling. A rather good correspondence between the theoretical and experimental absolute values of the reflection and the transmission coefficients was obtained. Some discrepancies between experimental and theoretical results, in particular with regard to phase shifts, may be explained by a certain inadequacy of the theoretical model to the low velocity layer investigated by the ultrasonic modelling.     

Elastic wave scattering by inhomogeneous and anisotropic bodies in a half space

Scattering of elastic waves by inhomogeneous and anisotropic bodies in a half space is considered. The integral equation method is formulated by using the fundamental solution of a homogeneous isotropic body in elastostatics and regarding the resulting inhomogeneous terms as equivalent body forces. Numerical examples are presented for the wave scattering by inhomogeneous and/or anisotropic alluvial valleys and for the dynamic analysis of an inhomogeneous dam. The effect of inhomogeneities and anisotropy on the dynamic behaviour of alluvial valley and dam is discussed.     

Impact of floodwaters on vertical water fluxes in the deep vadose zone of an alluvial aquifer in a semi-arid region

The spatial and temporal variation of moisture distribution, overall water balance and quantity of infiltrated water in the vadose zone of the Sidi Bouzid Plain (Tunisia) during successive flooding events is quantified in this study. The variation in water content in response to environmental factors such as evaporation and water root uptake is also highlighted. One-dimensional flow simulations in the deep vadose zone were conducted at three spreading perimeters located near Wadi El Fekka. The hydraulic boundary conditions of a time-dependent water blade applied to the soil surface were determined from measured flood hydrographs. For the chosen wet year, the successive flooding events contributed to a significant artificial recharge of the natural groundwater. Although the soil hydraulic parameters did not vary strongly in space, flow simulations showed significant differences in the overall water balance of approximately 9–16% for the various spreading perimeters.