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1.
We have developed an automatic method to determine the depth of a buried sphere from numerical second horizontal derivative anomalies obtained from total field magnetic data. The method is based on using a relationship between the depth and a combination of observations at symmetric points with respect to the coordinate of the projection of the center of the source in the plane of the measurement points with a free parameter (graticule spacing). The problem of depth determination has been transformed into the problem of finding a solution of a nonlinear equation of f(z) = 0. Procedures are also formulated to determine the magnetic moment and the effective angle of magnetization. The method is applied to synthetic examples with and without random errors and tested on a field example from Senegal. In all cases, the depth solutions are in good agreement with the actual ones.  相似文献   

2.
We have developed a least‐squares minimization approach to depth determination using numerical second horizontal derivative anomalies obtained from magnetic data with filters of successive window lengths (graticule spacings). The problem of depth determination from second‐derivative magnetic anomalies has been transformed into finding a solution to a non‐linear equation of the form, f(z) = 0. Formulae have been derived for a sphere, a horizontal cylinder, a dike and a geological contact. Procedures are also formulated to estimate the magnetic angle and the amplitude coefficient. We have also developed a simple method to define simultaneously the shape (shape factor) and the depth of a buried structure from magnetic data. The method is based on computing the variance of depths determined from all second‐derivative anomaly profiles using the above method. The variance is considered a criterion for determining the correct shape and depth of the buried structure. When the correct shape factor is used, the variance of depths is less than the variances computed using incorrect shape factors. The method is applied to synthetic data with and without random errors, complicated regionals, and interference from neighbouring magnetic rocks. Finally, the method is tested on a field example from India. In all the cases examined, the depth and the shape parameters are found to be in good agreement with the actual parameters.  相似文献   

3.
We have developed a new numerical method to determine the shape (shape factor), depth, polarization angle, and electric dipole moment of a buried structure from residual self-potential (SP) anomalies. The method is based on defining the anomaly value at the origin and four characteristic points and their corresponding distances on the anomaly profile. The problem of shape determination from residual SP anomaly has been transformed into the problem of finding a solution to a nonlinear equation of the form q = f (q). Knowing the shape, the depth, polarization angle and the electric dipole moment are determined individually using three linear equations. Formulas have been derived for spheres and cylinders. By using all possible combinations of the four characteristic points and their corresponding distances, a procedure is developed for automated determination of the best-fit-model parameters of the buried structure from SP anomalies. The method was applied to synthetic data with 5% random errors and tested on a field example from Colorado. In both cases, the model parameters obtained by the present method, particularly the shape and depth of the buried structures are found in good agreement with the actual ones. The present method has the capability of avoiding highly noisy data points and enforcing the incorporation of points of the least random errors to enhance the interpretation results.  相似文献   

4.
—We have developed a least-squares minimization approach to depth determination from magnetic data. By defining the anomaly value T(0) at the origin and the anomaly value T(N) at any other distance (N) on the profile, the problem of depth determination from magnetic data has been transformed into finding a solution to a nonlinear equation of the form f(z)=0. Formulas have been derived for a sphere, horizontal cylinder, dike, and for a geologic contact. Procedures are also formulated to estimate the effective magnetization intensity and the effective magnetization inclination. A scheme for analyzing the magnetic data has been formulated for determining the model parameters of the causative sources. The method is applied to synthetic data with and without random errors. Finally, the method is applied to two field examples from Canada and Arizona. In all cases examined, the estimated depths are found to be in goodagreement with actual values.  相似文献   

5.
The method of downward continuation is well known to those working in gravity, magnetic, SP and low-frequency electromagnetic exploration. It is demonstrated that the method of continuation can also be usefully employed in the interpretation of induced polarization gradient profiling using point electrodes to determine target depth. The apparent resistance Ra and chargeability Ma measurements obtained with point electrode excitation of the ground have been used to compute the values of (Ra)l and (Ma)l that would be obtained with a linear array. Continuation of the apparent polarizability profile thus obtained with the linear array gives a value for the depth of the target which agrees closely with that obtained by the continuation of the SP profile. On the other hand, continuation of the profile of the secondary transient signal (VS)L alone, yields a depth of the target which is in agreement with the borehole information. However, it is seen that the secondary transient voltage profiling response splits into two anomalies which fall on either side of the SP and/or (Ma)l anomaly centre, and does not coincide with that of the latter.  相似文献   

6.
A boundary integral scheme based on boundary-integral discrete-wave-number approach has been developed to compute the seismic response of two-dimensional irregular-shaped basins with horizontal soil layers. Each layer exhibits a linear gradient of shear wave velocity with depth. The approach combines the boundary-integral representation of the seismic wave field outside the basin with plane wave representation of the seismic wave field inside the basin. The propagation throughout the layers is performed by matrix propagators in which the effect of the vertical variation of the velocity is incorporated by using confluent hyper-geometric functions of the Whittaker type. Our method is tested against otherwell-accepted solutions for the case of a circular basin with excellent agreement. Test of the ground response for a semi-circular basin with radius a shows that stable solutions are obtained if the chosen model parameters satisfy following conditions: (1) the distance from the sources to the interface is greater than 0·1a; (2) the distance between the sources is smaller than a quarter of the incident wavelength; and (3) the discrete wave-number step is smaller than 2π/4a. The computation of ground response of basins with a sharp interface and several horizontal deposits leads to the following main results: (1) the amplification of a basin with velocity gradients is larger than that of a basin with homogeneous layers; (2) the frequencies of the second- and third-order harmonics for a basin with velocity gradients are lower than those of a basin with homogeneous layers; and (3) the response amplitude of the basin with velocity gradients attenuates more slowly in time domain than when layers are homogeneous. Since these results have been obtained for realistic values of basin geometrical and mechanical consideration, they should find some interest in earthquake engineering or seismic microzonation studies. © 1998 John Wiley & Sons, Ltd.  相似文献   

7.
A new method is proposed for the quantitative interpretation of SP field data produced by a polarized ore body and simulated by an inclined sheet. The theoretical concept is based on the study of the amplitude Spectrum. It is shown that the SP amplitude Spectrum is not continuous at zero frequency; this leads to the dip angle determination of the inclined sheet. It is also shown that the SP amplitude spectrum is practically nullified at a characteristic amortization frequency that depends on the depth of the polarized body. The maximum amplitude Spectrum value of the SP gradient is used to estimate the depth to the bottom of the polarized body. Thus, the geometrical parameters h and H, the depths to the top and bottom, respectively, as well as the dip angle of the inclined sheet, can be satisfactorily determined. Some problems may arise in the determination of these parameters, affecting their accuracy, whenever unwanted frequency noise is present.  相似文献   

8.
A new best estimate methodology is proposed and oriented towards the determination of parameters related to a magnetic field anomaly produced by a simple geometric-shaped model or body such as a thin dike and horizontal cylinder. This approach is mainly based on solving a system of algebraic linear equations for estimating the three model parameters, e.g., the depth to the top (center) of the body (z), the index parameter or the effective magnetization angle (θ) and the amplitude coefficient or the effective magnetization intensity (k). The utility and validity of this method is demonstrated by analyzing two synthetic magnetic anomalies, using simulated data generated from a known model with different random errors components and a known statistical distribution. This approach was also examined and applied to two real field magnetic anomalies from the United States and Brazil. The agreement between the results obtained by the proposed method and those obtained by other interpretation methods is good and comparable. Moreover, the depth obtained by such an approach is found to be in high accordance with that obtained from drilling information. The advantages of such a proposed method over other existing interpretative techniques are clarified, where it can be generalized to be automatically applicable for interpreting other geological structures described by mathematical formulations.  相似文献   

9.
We have developed three different least-squares approaches to determine successively: the depth, magnetic angle, and amplitude coefficient of a buried sphere from a total magnetic anomaly. By defining the anomaly value at the origin and the nearest zero-anomaly distance from the origin on the profile, the problem of depth determination is transformed into the problem of finding a solution of a nonlinear equation of the form f(z)=0. Knowing the depth and applying the least-squares method, the magnetic angle and amplitude coefficient are determined using two simple linear equations. In this way, the depth, magnetic angle, and amplitude coefficient are determined individually from all observed total magnetic data. The method is applied to synthetic examples with and without random errors and tested on a field example from Senegal, West Africa. In all cases, the depth solutions are in good agreement with the actual ones.  相似文献   

10.
The ‘depth from extreme points’ method is an important tool to estimate the depth of sources of gravity and magnetic data. In order to interpret gravity gradient tensor data conveniently, formulas for the tensor data form regarding depth from the extreme points method were calculated in this paper. Then, all of the gradient tensor components were directly used to interpret the causative source. Beyond the gzz component, also the gxx and gyy components can be used to obtain depth information. In addition, the total horizontal derivative of the depth from extreme points of the gradient tensor can be used to describe the edge information of geologic sources. In this paper, we investigated the consistency of the homogeneity degree calculated by using the different components, which leads to the calculated depth being confirmed. Therefore, a more integrated interpretation can be obtained by using the gradient tensor components. Different synthetic models were used with and without noise to test the new approach, showing stability, accuracy and speed. The proposed method proved to be a useful tool for gradient tensor data interpretation. Finally, the proposed method was applied to full tensor gradient data acquired over the Vinton Salt Dome, Louisiana, USA, and the results are in agreement with those obtained in previous research studies.  相似文献   

11.
An interpretative method based on a nonlinearly mathematical optimization concept has been developed in this paper, in order to interpret self-potential anomalies (SP) due to horizontal cylinder, vertical cylinder, sphere and sheet-like structures. This interpretative method comprises three main steps. The first step is to formulate mathematically a nonlinearly constrained minimization problem (NCMP) to describe the geophysical problem related to the studied structure. The second one is to suggest an interior penalty function in order to convert the nonlinearly constrained minimization problem (NCMP) into a nonlinearly unconstrained minimization one (NUMP). The third step is to solve the converted nonlinearly unconstrained minimization problem (NUMP) by the well-known Hooke and Jeeves direct search algorithm in order to estimate the geophysical parameters of the studied structure, i.e., depth, polarization angle, electric dipole moment (magnitude of polarization) and geometric shape factor. The Hooke and Jeeves direct search algorithm is purposely chosen for being robust and its application to SP data allows a rapid convergence towards the optimal estimate of parameters. This interpretative method was first tested on theoretical synthetic models with different random noise, where a very close agreement was obtained between assumed and evaluated parameters.The validity of the proposed interpretative method is also tested on practical field examples taken from Turkey, India and Germany, where available SP data existed and was previously analyzed by different interpretative methods. The agreement between the results obtained by the developed method and those obtained by other published methods is good.Acknowledgment Authors would like to thank Dr. I. Othman Director General of the Atomic Energy Commission of Syria for his interest and continuous encouragement to achieve this work. Special thanks to the reviewers for their constructive suggestions aimed at enhancing the quality of this paper.  相似文献   

12.
The gravity gradient tensor (GGT) is deduced from products of second-order derivatives of the gravitational potential. A new method based on the invariants of the GGT has been proposed in this research to interpret gravity data due to sphere, infinite horizontal cylinder and semi-infinite vertical cylinder. The method estimates the depth of these simple causative sources from the multiplication of the maximum of the gravity vertical component by the maximum value of the invariants I 1 to I 2 ratio. To show the reliability and correctness of the estimated depths on 3-D models, the method has been tested using theoretical data with and without random noise. In addition, I have applied the method to a field-data example in Texas, USA and the depth obtained by the present method is compared with those published in the literature.  相似文献   

13.
A simple and fast determination of the limiting depth to the sources may represent a significant help to the data interpretation. To this end we explore the possibility of determining those source parameters shared by all the classes of models fitting the data. One approach is to determine the maximum depth-to-source compatible with the measured data, by using for example the well-known Bott–Smith rules. These rules involve only the knowledge of the field and its horizontal gradient maxima, and are independent from the density contrast.Thanks to the direct relationship between structural index and depth to sources we work out a simple and fast strategy to obtain the maximum depth by using the semi-automated methods, such as Euler deconvolution or depth-from-extreme-points method (DEXP).The proposed method consists in estimating the maximum depth as the one obtained for the highest allowable value of the structural index (Nmax). Nmax may be easily determined, since it depends only on the dimensionality of the problem (2D/3D) and on the nature of the analyzed field (e.g., gravity field or magnetic field). We tested our approach on synthetic models against the results obtained by the classical Bott–Smith formulas and the results are in fact very similar, confirming the validity of this method. However, while Bott–Smith formulas are restricted to the gravity field only, our method is applicable also to the magnetic field and to any derivative of the gravity and magnetic field. Our method yields a useful criterion to assess the source model based on the (∂f/∂x)max/fmax ratio.The usefulness of the method in real cases is demonstrated for a salt wall in the Mississippi basin, where the estimation of the maximum depth agrees with the seismic information.  相似文献   

14.
Broadband (100–4000 Hz) cross‐hole seismic data have been acquired at a borehole test site where extensive hydrological investigations have previously been performed, including in situ estimates of permeability. The rock type is homogeneous chalk and fractures and bedding planes have been identified from well logs. High values of seismic attenuation, Q= 22 ≤ 27 ≤ 33, were observed over a 10 m depth interval where fracture permeability values of 20–50 darcy had been recorded. An attempt has been made to separate the attenuation due to scattering and intrinsic mechanisms. The estimated values of intrinsic attenuation, Q= 31 ≤ 43 ≤ 71, have been reproduced using a number of current theories of seismic‐wave propagation and fluid‐flow‐induced seismic attenuation in cracked and fractured media. A model that considers wavelength‐scale pressure gradients is the preferred attenuation mechanism. Model parameters were obtained from the hydro‐geological and seismic data. However, we conclude that it is not possible to use seismic Q to measure rock permeability remotely, principally because of the inherent uncertainties arising from model parameterisations.  相似文献   

15.
A new approach is proposed in order to interpret field self-potential (SP) anomalies related to simple geometric-shaped models such as sphere, horizontal cylinder, and vertical cylinder. This approach is mainly based on solving a set of algebraic linear equations, and directed towards the best estimate of the three model parameters, e.g., electric dipole moment, depth, and polarization angle. Its utility and validity are demonstrated through studying and analyzing synthetic self-potential anomalies obtained by using simulated data generated from a known model and a statistical distribution with different random errors components. Being theoretically tested and proven, this approach has been consequently applied on two real field self-potential anomalies taken from Colorado and Turkey. A comparable and acceptable agreement is obtained between the results derived by the new proposed method and those deduced by other interpretation methods. Moreover, the depth obtained by such an approach is found to be very close to that obtained by drilling information.  相似文献   

16.
Tilted transversely isotropic formations cause serious imaging distortions in active tectonic areas (e.g., fold‐and‐thrust belts) and in subsalt exploration. Here, we introduce a methodology for P‐wave prestack depth imaging in tilted transversely isotropic media that properly accounts for the tilt of the symmetry axis as well as for spatial velocity variations. For purposes of migration velocity analysis, the model is divided into blocks with constant values of the anisotropy parameters ε and δ and linearly varying symmetry‐direction velocity VP0 controlled by the vertical (kz) and lateral (kx) gradients. Since determination of tilt from P‐wave data is generally unstable, the symmetry axis is kept orthogonal to the reflectors in all trial velocity models. It is also assumed that the velocity VP0 is either known at the top of each block or remains continuous in the vertical direction. The velocity analysis algorithm estimates the velocity gradients kz and kx and the anisotropy parameters ε and δ in the layer‐stripping mode using a generalized version of the method introduced by Sarkar and Tsvankin for factorized transverse isotropy with a vertical symmetry axis. Synthetic tests for several models typical in exploration (a syncline, uptilted shale layers near a salt dome and a bending shale layer) confirm that if the symmetry‐axis direction is fixed and VP0 is known, the parameters kz, kx, ε and δ can be resolved from reflection data. It should be emphasized that estimation of ε in tilted transversely isotropic media requires using nonhyperbolic moveout for long offsets reaching at least twice the reflector depth. We also demonstrate that application of processing algorithms designed for a vertical symmetry axis to data from tilted transversely isotropic media may lead to significant misfocusing of reflectors and errors in parameter estimation, even when the tilt is moderate (30°). The ability of our velocity analysis algorithm to separate the anisotropy parameters from the velocity gradients can be also used in lithology discrimination and geologic interpretation of seismic data in complex areas.  相似文献   

17.
Orientations of the principal axes of the tectonic stress field reconstructed from seismological data on focal mechanisms of earthquakes and strain fields determined from GPS measurements in China are compared. The data of GPS measurements used in the paper were obtained by the Crustal Movement Observation Network of China (about 1000 stations) in the period of 1998–2004. On the basis of information on the recent horizontal crustal motions, the strain field is calculated for the study territory by the finite element method. Calculations of the strain tensor using GPS data were carried out with a step of 1° in latitude and longitude. A catalog of earthquake focal mechanisms was used for the reconstruction of tectonic stress field components. Focal mechanisms of earthquakes were calculated with the use of seismological data on signs of first arrivals from the bulletin of the International Seismological Center. To estimate characteristics of the regional stress field, an approach based on the kinematic method proposed by O.I. Gushchenko was applied. The tectonic stress field was reconstructed in depth intervals of 0 < H < 35 km and 35 km < H < 70 km from data on focal mechanisms of earthquakes over the periods of 1998–2004 and 1985–2004. Comparison of directions of the principal strain axes at the surface (according to GPS measurements) and directions of the principal stress axes (reconstructed from focal mechanisms of earthquakes) showed their good convergence. Seismotectonic strains and GPS measurements coincide within a larger part of the territory. The coincidence is best in a depth interval of 0 < H < 35 km. Maximum misfit values are confined to areas of high 3-D gradients of strain axis directions and are possibly related to the structural heterogeneity of the region, zones with strains of the same type along both horizontal axes (compression or extension along all directions), or areas of small absolute values of recent horizontal movements. Areas with invariable directions of the stress axes are recognizable regardless of the depth of initial data. Good reproducibility of results obtained by two different methods made it possible to check the method of stress field reconstruction using data on focal mechanisms of earthquakes.  相似文献   

18.
A method for three-dimensional (3D) ray tomography that uses the data on the travel time residuals of body waves is suggested. The underlying assumption of the method is smoothness of horizontal velocity variations. The region under study is divided into layers, and the velocity correction in each layer is assumed to only depend on the horizontal coordinates. The starting velocity model is specified as a function of depth. The numerical implementation of the method is noticeably simpler if the velocity-depth distribution is described by a linear function. The solution is determined by minimizing the functional that contains the sum of the integrals of the square gradients of the velocity corrections. The procedure is reduced to solving the two-dimensional (2D) problem in a way similar to the way previously developed for surface wave tomography (Ditmar and Yanovskaya, 1989). The obtained solution is smoothed, and the degree of smoothing is estimated jointly with the reconstruction of the solution. This approach does not require adaptive parameterization of the medium, i.e., division of the region into the blocks each of which is intersected by a sufficiently large number of rays. The efficiency of the method is demonstrated by the example of synthetic data and on the data on real traveltime residuals of the P waves in the Black Sea basin.  相似文献   

19.
—We have developed a least-squares minimization approach to determine the shape (shape-factor) of a buried polarized body from a residual self-potential anomaly profile. By defining the zero anomaly distance and the anomaly value at the origin on the profile, the problem of the shape-factor determination is transformed into the problem of finding a solution of a nonlinear equation of the form f(q) = 0. Procedures are also formulated to estimate the depth of polarization angle, and the electric dipole moment. The method is applied to synthetic data with and without random noise. The obtained shape-factor agrees very well with the model shape-factor when using synthetic data. After adding ± 2 percent random error in the synthetic data, the shape factor obtained is within ± 4 percent. Finally the validity of the method is tested on a field example from the Ergani copper district, Turkey.  相似文献   

20.
Study on in-situ stress measurement around coastal marginal land in Fujian   总被引：1，自引：1，他引：1  
Introduction The southeast coastal margin of Chinese mainland is important to understand the mutual movement, matter exchange and energy transfer between ocean and land lithospheres, as well as their effects. The coastal area in Fujian Province is advanced in economy development but it has frequent earthquakes, or even strong earthquakes. Therefore, the current study on in-situ stress state measurement is of great significance for studying continental dynamics, marginal sea dy- namics, seismo…  相似文献   

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