Application of Global Particle Swarm Optimization for Inversion of Residual Gravity Anomalies Over Geological Bodies with Idealized Geometries

A global particle swarm optimization (GPSO) technique is developed and applied to the inversion of residual gravity anomalies caused by buried bodies with simple geometry (spheres, horizontal, and vertical cylinders). Inversion parameters, such as density contrast of geometries, radius of body, depth of body, location of anomaly, and shape factor, were optimized. The GPSO algorithm was tested on noise-free synthetic data, synthetic data with 10% Gaussian noise, and five field examples from different parts of the world. The present study shows that the GPSO method is able to determine all the model parameters accurately even when shape factor is allowed to change in the optimization problem. However, the shape was fixed a priori in order to obtain the most consistent appraisal of various model parameters. For synthetic data without noise or with 10% Gaussian noise, estimates of different parameters were very close to the actual model parameters. For the field examples, the inversion results showed excellent agreement with results from previous studies that used other inverse techniques. The computation time for the GPSO procedure is very short (less than 1 s) for a swarm size of less than 50. The advantage of the GPSO method is that it is extremely fast and does not require assumptions about the shape of the source of the residual gravity anomaly.     

Bimodal electromagnetic induction in non-uniform thin sheets with an application to the northern Pyrenean induction anomaly

In order to handle the distortion of large-scale induced electric currents by local conductivity anomalies, the problem of electromagnetic induction in non-uniform thin sheets has been reformulated in terms of an integral equation over the anomalous domain. This formulation considers in the layered substratum in addition to toroidal currents also the poloidal current mode (vertical current loops), at the expense that two scalar functions have to be determined. Simple formulas for the required kernels are derived. The algorithm is applied to model the gross features of the northern Pyrenean induction anomaly. It is suggested that this pronounced anomaly results from a conductive channel between the Atlantic Ocean and the Mediterranean Sea.     

Uplift by thermal expansion of the lithosphere

Summary. If one can measure the anomalous horizontal magnetic field associated with a (locally bounded) two-dimensional conductivity anomaly, the transfer function which results from correlating the vertical with the anomalous horizontal magnetic field directly indicates the depth to an equivalent line-current. A. numerical model can be used to illustrate this. If three-dimensional effects (including current channelling) produce the current anomaly, interpretation in terms of conductive structure would be less clear. It has been claimed (Babour & Mosnier etc.) that such three-dimensional effects are experimentally observed in the highly coherent transfer functions determined from differential geomagnetic sounding experiments. These effects are, specifically, the 'linear polarization' of the anomalous fields, and the invariance of the phase of the measured anomalous field across the anomaly. It is suggested in this present paper that both these effects can be explained in terms of simple local induction models.
If the embedded two-dimensional anomaly is sufficiently close to the Earth's surface, the transfer function (between the vertical and the total horizontal field) contains more information than is usually interpreted. With this in mind, the magnetovariational data collected by Rooney & Hutton in the Kenyan Rift is re-examined.     

Sudden Local Conductivity Changes in the Ionosphere

Summary. An attempt is made to describe the transient magnetic change caused by a sudden local change of conductivity in the ionosphere. In a rough illustrative model, electric current is taken to be flowing uniformly in a thin plane rigid sheet of uniform isotropic integrated conductivity, I/ϱO e.m.u. A particular type of perturbing current system is defined, and the type of conductivity anomaly which could produce it is derived. It is shown that the problem is equivalent to that of the free decay of the perturbing current system. For a very small change of conductivity, the current system is found to spread radially at a uniform rate, while decaying. The case of a large conductivity anomaly is analysed by a numerical method. It is concluded that effects at a distance would be similar to those produced by a very small change, and that near the anomaly there would be as well, a local decaying current vortex system. It is found in particular, that at a large distance L cm, the magnetic change would commence immediately and reach an extremum after time of order L × 10⁻⁶ s.     

Simulated envelopes of non-isotropically scattered body waves as compared to observed ones: another manifestation of fractal heterogeneity

Envelopes of scalar waves are simulated at various distances from an instant point source embedded in a random uniformly scattering medium by means of direct Monte-Carlo modelling of wave-energy transport. Three types of scattering radiation pattern ('indicatrix') are studied, for media specified by (1) a Gaussian autocorrelation function of inhomogeneities, (2) a power-law ('fractal', k -^α) inhomogeneity spectrum and (3) the mix of case (1) and the isotropic indicatrix (very small + large inhomogeneities). We look for a model that can qualitatively reproduce the two most characteristic features of real S-wave envelopes of near earthquakes, namely (1) the broadening of the 'direct' wave group with distance and (2) the monotonously decaying shape of the coda envelope that does not deviate strongly from that expected in the isotropic scattering case. Both properties are observed for any band over a wide frequency range (1-40 Hz). The well-studied isotropic scattering model realistically predicts the appearance of codas but fails to predict pulse broadening. The model of large-scale inhomogeneity realistically predicts the mode of pulse broadening but fails to predict codas. We have found that, for a particular frequency band, within each class of inhomogeneity studied, both requirements can be qualitatively satisfied by a certain choice of parameters. In the Gaussian-ACF case, however, this match can be obtained only for a narrow frequency range. In contrast, the fractal case (with a value of exponent a of about 3.5-4) reproduces qualitatively the observed wide-band behaviour, and we consider it a reasonable representation of the gross properties of the earth medium.     

Sequential integrated inversion of refraction and wide-angle reflection traveltimes and gravity data for two-dimensional velocity structures

A new algorithm is presented for the integrated 2-D inversion of seismic traveltime and gravity data. The algorithm adopts the 'maximum likelihood' regularization scheme. We construct a 'probability density function' which includes three kinds of information: information derived from gravity measurements; information derived from the seismic traveltime inversion procedure applied to the model; and information on the physical correlation among the density and the velocity parameters. We assume a linear relation between density and velocity, which can be node-dependent; that is, we can choose different relationships for different parts of the velocity–density grid. In addition, our procedure allows us to consider a covariance matrix related to the error propagation in linking density to velocity. We use seismic data to estimate starting velocity values and the position of boundary nodes. Subsequently, the sequential integrated inversion (SII) optimizes the layer velocities and densities for our models. The procedure is applicable, as an additional step, to any type of seismic tomographic inversion.
We illustrate the method by comparing the velocity models recovered from a standard seismic traveltime inversion with those retrieved using our algorithm. The inversion of synthetic data calculated for a 2-D isotropic, laterally inhomogeneous model shows the stability and accuracy of this procedure, demonstrates the improvements to the recovery of true velocity anomalies, and proves that this technique can efficiently overcome some of the limitations of both gravity and seismic traveltime inversions, when they are used independently.
An interpretation of field data from the 1994 Vesuvius test experiment is also presented. At depths down to 4.5 km, the model retrieved after a SII shows a more detailed structure than the model obtained from an interpretation of seismic traveltime only, and yields additional information for a further study of the area.     

Exact synthetic seismograms for an inhomogeneity in a layered elastic half-space

Summary. The propagation of a pulsed elastic wave in the following geometry is considered. An elastic half-space has a surface layer of a different material and the layer furthermore contains a bounded 3-D inhomogeneity. The exciting source is an explosion, modelled as an isotropic pressure point source with Gaussian behaviour in time.
The time-harmonic problem is solved using the null field approach (the T matrix method), and a frequency integral then gives the time-domain response. The main tools of the null field approach are integral representations containing the free space Green's dyadic, expansions in plane and spherical vector wave functions, and transformations between plane and spherical vector wave functions. It should be noted that the null field approach gives the solution to the full elastodynamic equations with, in principle, an arbitrarily high accuracy. Thus no ray approximations or the like are used. The main numerical limitation is that only low and intermediate frequencies, in the sense that the diameter of the inhomogeneity can only be a few wavelengths, can be considered.
The numerical examples show synthetic seismograms consisting of data from 15 observation points at increasing distances from the source. The normal component of the velocity field is computed and the anomalous field due to the inhomogeneity is sometimes shown separately. The shape of the inhomogeneity, the location and depth of the source, and the material parameters are all varied to illustrate the relative importance of the various parameters. Several specific wave types can be identified in the seismograms: Rayleigh waves, direct and reflected P -waves, and head waves.     

New advances in three-dimensional controlled-source electromagnetic inversion

New techniques for improving both the computational and imaging performance of the three-dimensional (3-D) electromagnetic inverse problem are presented. A non-linear conjugate gradient algorithm is the framework of the inversion scheme. Full wave equation modelling for controlled sources is utilized for data simulation along with an efficient gradient computation approach for the model update. Improving the modelling efficiency of the 3-D finite difference (FD) method involves the separation of the potentially large modelling mesh, defining the set of model parameters, from the computational FD meshes used for field simulation. Grid spacings and thus overall grid sizes can be reduced and optimized according to source frequencies and source–receiver offsets of a given input data set. Further computational efficiency is obtained by combining different levels of parallelization. While the parallel scheme allows for an arbitrarily large number of parallel tasks, the relative amount of message passing is kept constant. Image enhancement is achieved by model parameter transformation functions, which enforce bounded conductivity parameters and thus prevent parameter overshoots. Further, a remedy for treating distorted data within the inversion process is presented. Data distortions simulated here include positioning errors and a highly conductive overburden, hiding the desired target signal. The methods are demonstrated using both synthetic and field data.     

Use of Intelligent Methods to Design Effective Pattern Parameters of Mine Blasting to Minimize Flyrock Distance

Flyrock is one of the most important environmental issues in mine blasting, which can affect equipment, people and could cause fatal accidents. Therefore, minimization of this environmental issue of blasting must be considered as the ultimate objective of many rock removal projects. This paper describes a new minimization procedure of flyrock using intelligent approaches, i.e., artificial neural network (ANN) and particle swarm optimization (PSO) algorithms. The most effective factors of flyrock were used as model inputs while the output of the system was set as flyrock distance. In the initial stage, an ANN model was constructed and proposed with high degree of accuracy. Then, two different strategies according to ideal and engineering condition designs were considered and implemented using PSO algorithm. The two main parameters of PSO algorithm for optimal design were obtained as 50 for number of particle and 1000 for number of iteration. Flyrock values were reduced in ideal condition to 34 m; while in engineering condition, this value was reduced to 109 m. In addition, an appropriate blasting pattern was proposed. It can be concluded that using the proposed techniques and patterns, flyrock risks in the studied mine can be significantly minimized and controlled.

     

Modelling of solar quiet magnetic field variations near a conductivity anomaly

Summary. A simplified model of the solar quiet-time ionospheric current system is used to calculate the induced currents in a model earth. The conductivity is assumed to be constant below a depth of about 400 km and zero above that depth. The current induced in the north—south conductivity anomaly under the Rocky Mountains is then estimated from the time-varying potential difference between points at 30 and 45° latitude at the surface of the conducting sphere. The purpose of these calculations is to investigate whether variations in the latitude of the northern hemisphere current system vortex will substantially alter the relationship between the observed magnetic field components at the Earth's surface and the local magnetic field gradient caused by the conductivity anomaly. We find that a 10° shift in the latitude of the ionospheric current focus causes a change of 6 per cent or less in the transfer function from the field components to the gradient in the total field. Thus such latitude shifts cannot explain much of the magnetic field gradient variation at periods near 24 hr that has been observed near Boulder, Colorado.     

A Bouguer anomaly map of India and its relation to broad tectonic elements of the sub-continent

Summary. A new Bouguer anomaly map of India and its generalized interpretation is presented in this paper. Bouguer anomalies in India show good correlation with the geology and tectonics. Isostatic anomalies in India are primarily geologic anomalies caused by intracrustal inhomogeneities. For example, the negative isostatic anomalies in southern India arise from large thicknesses of granitic bodies in the upper crust and the positive anomaly over the Himalaya may be attributed to a possible thickening of the basalt layer in the lower crust. The gravity data suggest that an overall isostatic equilibrium generally prevails in India and the Himalayan region. Crustal thickness estimates from DSS data in India are comparable to the values obtained from gravity data based on the Ahy's concept of isostatic compensation.     

GIS techniques for regional-scale landslide susceptibility assessment: the Sicily (Italy) case study

This study describes the assessment of landslide susceptibility in Sicily (Italy) at a 1:100,000 scale using a multivariate logistic regression model. The model was implemented in a GIS environment by using the ArcSDM (Arc Spatial Data Modeller) module, modified to develop spatial prediction through regional data sets. A newly developed algorithm was used to automatically extract the detachment area from mapped landslide polygons. The following factors were selected as independent variables of the logistic regression model: slope gradient, lithology, land cover, a curve number derived index and a pluviometric anomaly index. The above-described configuration has been verified to be the best one among others employing from three to eight factors. All the regression coefficients and parameters were calculated using selected landslide training data sets. The results of the analysis were validated using an independent landslide data set. On an average, 82% of the area affected by instability and 79% of the not affected area were correctly classified by the model, which proved to be a useful tool for planners and decision-makers.     

Subspace inversion of electromagnetic data: application to mid-ocean-ridge exploration

Controlled-source electromagnetic (CSEM) surveys have the ability to provide tomo-graphic images of electrical conductivity within the Earth. the interpretation of such data sets has long been hampered by inadequate modelling and inversion techniques. In this paper, a subspace inversion technique is described that allows electric dipole-dipole data to be inverted for a 2-D electrical conductivity model more efficiently than with existing techniques. the subspace technique is validated by comparison with conventional inversion methods and by inverting data collected over the East Pacific Rise in 1989. A model study indicates that, with adequate data, a variety of possible mid-ocean-ridge conductivity models could be distinguished on the basis of a CSEM survey.     

Electrical conductivity anomalies and their relationship with the tectonics of South Australia

Summary. Geomagnetic variation studies have been conducted in the Gawler Craton and Adelaide Geosyncline of South Australia. The magnetometer stations extend from the coast up to the southern edge of the 1970 array of Gough, McElhinny & Lilley. The coast effect is the dominant feature of the data but use is made of the hypothetical event technique to identify two zones of telluric current concentration. Both of them appear to be associated with linear zones of enhanced electrical conductivity within the crust. The Southern Eyre Peninsula anomaly lies within the Gawler Craton and may identify a major fracture or shear in the upper crust. The conductivity anomaly within the Adelaide Geosyncline appears to be the continuation of the Flinders anomaly discovered by the 1970 array study. It correlates well with the arcuate fold pattern of the Southern Flinders Zone of the Geosyncline and with the local pattern of seismicity. In both anomalies the enhanced conductivity is probably caused by saline waters within fractured crustal rocks.     

Electromagnetic response of an arbitrarily shaped three-dimensional conductor in a layered earth—numerical results

Summary. In an earlier work, mathematical formulation on computing the electromagnetic response of an arbitrarily shaped three-dimensional inhomogeneity in a layered earth had been worked out using an integral equation technique. The method has been used to show its efficacy by computing numerical results. Introducing suitable changes of variables the secondary contributions to Green's dyadic are put in the form of convolution integrals and are computed using a digital linear filtering scheme. The matrix equation is solved for the unknown electric fields in the inhomogeneity. The scattered fields are then calculated at the surface of the Earth using the appropriate Green's dyadic. The performance of the computations has been shown by comparing the numerical results with those obtained by analogue modelling as well as by other numerical schemes. The use of digital linear filtering saves an enormous amount of computer time.
The effects of varying excitation-frequency, conductivity of the host medium and that of the overburden have been studied in detail for a horizontal loop system traversing over a two-layered earth with a prismatic inhomogeneity situated in the lower conducting half space.     

Three-dimensional gravity inversion for Moho depth at rifted continental margins incorporating a lithosphere thermal gravity anomaly correction

This paper describes a method for determining Moho depth, lithosphere thinning factor (γ= 1 − 1/β) and the location of the ocean–continent transition at rifted continental margins using 3-D gravity inversion which includes a correction for the large negative lithosphere thermal gravity anomaly within continental margin lithosphere. The lateral density changes caused by the elevated geotherm in thinned continental margin and adjacent ocean basin lithosphere produce a significant lithosphere thermal gravity anomaly which may be in excess of −100 mGal, and for which a correction must be made in order to determine Moho depth accurately from gravity inversion. We describe a method of iteratively calculating the lithosphere thermal gravity anomaly using a lithosphere thermal model to give the present-day temperature field from which we calculate the lithosphere thermal density and gravity anomalies. For continental margin lithosphere, the lithosphere thermal perturbation is calculated from the lithosphere thinning factor (γ= 1 − 1/β) obtained from crustal thinning determined by gravity inversion and breakup age for thermal re-equilibration time. For oceanic lithosphere, the lithosphere thermal model used to predict the lithosphere thermal gravity anomaly may be conditioned using ocean isochrons from plate reconstruction models to provide the age and location of oceanic lithosphere. A correction is made for crustal melt addition due to decompression melting during continental breakup and seafloor spreading. We investigate the sensitivity of the lithosphere thermal gravity anomaly and the predicted Moho depth from gravity inversion at continental rifted margins to the methods used to calculate and condition the lithosphere thermal model using both synthetic models and examples from the North Atlantic.     

中国西北空中可降水量的年内非均匀性特征

利用NCAR/NCEP资料,通过引进表征时间分配特征的参数集中度和集中期对西北上空大气可降水量年内非均匀性特征进行分析,结果表明:一致性异常分布是西北上空大气可降水量集中度和集中期的最主要的空间分布特征;西北地区上空大气可降水量集中度和集中期近45年来主要表现为2~4年、6~8年的高频振荡;西北上空大气可降水量集中度异常强弱年其水汽输送特征存在显著差异,在集中度异常强年,西北东南部西南季风水汽输送较常年偏强,其余区域西风带水汽输送较常年偏强,由于充足的水汽供应使得整个西北地区上空大气可降水量与常年相比偏多;反之亦然。     

Finite-difference modelling of magnetotelluric fields in two-dimensional anisotropic media

An algorithm for the numerical modelling of magnetotelluric fields in 2-D generally anisotropic block structures is presented. Electrical properties of the individual homogeneous blocks are described by an arbitrary symmetric and positive-definite conductivity tensor. The problem leads to a coupled system of partial differential equations for the strike-parallel components of the electromagnetic field. E _x, and H _x These equations are numerically approximated by the finite-difference (FD) method, making use of the integro-interpolation approach. As the magnetic component H _x, is constant in the non-conductive air, only equations for the electric mode are approximated within the air layer. The system of linear difference equations, resulting from the FD approximation, can be arranged in such a way that its matrix is symmetric and band-limited, and can be solved, for not too large models, by Gaussian elimination. The algorithm is applied to model situations which demonstrate some non-trivial phenomena caused by electrical anisotropy. In particular, the effect of 2-D anisotropy on the relation between magnetotelluric impedances and induction arrows is studied in detail.     

GIS技术支持下的洪水模型建模

在复杂区域建立洪水模型时,计算网格的手工生成方法容易出错甚至不可行,自动生成算法则可大大节省计算网格生成的工作量。洪水模型中的计算网格与GIS栅格数据及不规则三角网空间数据结构非常相似,因此,GIS中成熟的网格自动生成算法可用于生成洪水模型计算网格。文章详细讨论了GIS支持下的洪水模型自动建立步骤,并以黄河下游花园口～夹河滩河段为例,利用地形图、土地利用图、水利工程设施分布、水文站点图等资料,通过自动生成网格及其空间拓扑关系,建立了洪水过程数值模拟模型,并详细解释了计算网格数据格式。     

Geomagnetic induction in a heterogeneous sphere: fully three-dimensional test computations and the response of a realistic distribution of oceans and continents

Long-period geomagnetic data can resolve large-scale 3-D mantle electrical conductivity heterogeneities which are indicators of physiochemical variations found in the Earth's dynamic mantle. A prerequisite for mapping such heterogeneity is the ability to model accurately electromagnetic induction in a heterogeneous sphere. A previously developed finite element method solution to the geomagnetic induction problem is validated against an analytic solution for a fully 3-D geometry: an off-axis spherical inclusion embedded in a uniform sphere. Geomagnetic induction is then modelled in a uniform spherical mantle overlain by a realistic distribution of oceanic and continental conductances. Our results indicate that the contrast in electrical conductivity between oceans and continents is not primarily responsible for the observed geographic variability of long-period geomagnetic data. In the absence of persistent high-wavenumber magnetospheric disturbances, this argues strongly for the existence of large-scale, high-contrast electrical conductivity heterogeneities in the mid-mantle. Lastly, for several periods the geomagnetic anomaly associated with a mid-mantle spherical inclusion is calculated. A high-contrast inclusion can be readily detected beneath the outer shell of oceans and continents. A comparison between observed and computed c responses suggests that the mid-mantle contains more than one order of magnitude of lateral variability in electrical conductivity, while the upper mantle contains at least two orders of magnitude of lateral variability in electrical conductivity.