Spatial sampling design and covariance-robust minimax prediction based on convex design ideas

This paper presents new ideas on sampling design and minimax prediction in a geostatistical model setting. Both presented methodologies are based on regression design ideas. For this reason the appendix of this paper gives an introduction to optimum Bayesian experimental design theory for linear regression models with uncorrelated errors. The presented methodologies and algorithms are then applied to the spatial setting of correlated random fields. To be specific, in Sect. 1 we will approximate an isotropic random field by means of a regression model with a large number of regression functions with random amplitudes, similarly to Fedorov and Flanagan (J Combat Inf Syst Sci: 23, 1997). These authors make use of the Karhunen Loeve approximation of the isotropic random field. We use the so-called polar spectral approximation instead; i.e. we approximate the isotropic random field by means of a regression model with sine-cosine-Bessel surface harmonics with random amplitudes and then, in accordance with Fedorov and Flanagan (J Combat Inf Syst Sci: 23, 1997), apply standard Bayesian experimental design algorithms to the resulting Bayesian regression model. Section 2 deals with minimax prediction when the covariance function is known to vary in some set of a priori plausible covariance functions. Using a minimax theorem due to Sion (Pac J Math 8:171–176, 1958) we are able to formulate the minimax problem as being equivalent to an optimum experimental design problem, too. This makes the whole experimental design apparatus available for finding minimax kriging predictors. Furthermore some hints are given, how the approach to spatial sampling design with one a priori fixed covariance function may be extended by means of minimax kriging to a whole set of a priori plausible covariance functions such that the resulting designs are robust. The theoretical developments are illustrated with two examples taken from radiological monitoring and soil science.     

History of the Method for Sourcewise Approximations of Geopotential Fields

Izvestiya, Physics of the Solid Earth - Abstract—This paper presents the history of the method of approximating discretely specified values of gravitational and magnetic fields by sourcewise...     

Weakly nonlinear shallow water magnetohydrodynamic waves

We consider an electrically conducting rotating fluid governed by the shallow water magnetohydrodynamic equations with no diffusion. We use an a priori asymptotic technique (the method of geometric optics or ray method) to study weakly nonlinear hydromagnetic waves. These waves are intermediate in length in the following sense: they are much longer than the fluid depth but much shorter than the radius of the earth. The time scale for the waves is much longer than that of the free surface oscillations and the approximation varies on an even longer timescale. The waves we are considering are studied in the beta plane approximation for an ambient magnetic field parallel to the equator which varies in the direction perpendicular to the equator. The leading order approximation gives a dispersion relation for the waves, which are generally found to be confined to bands about the equator as well as in bands at higher and lower latitudes. At the next order of approximation, a conservation law is found for the wave amplitude. We also obtain an equation governing the behavior of the leading order mean azimuthal velocity which is forced to grow linearly with time.     

Electromagnetic fields generated by finite‐length wire sources: comparison with point dipole solutions

In present‐day land and marine controlled‐source electromagnetic (CSEM) surveys, electromagnetic fields are commonly generated using wires that are hundreds of metres long. Nevertheless, simulations of CSEM data often approximate these sources as point dipoles. Although this is justified for sufficiently large source‐receiver distances, many real surveys include frequencies and distances at which the dipole approximation is inaccurate. For 1D layered media, electromagnetic (EM) fields for point dipole sources can be computed using well‐known quasi‐analytical solutions and fields for sources of finite length can be synthesized by superposing point dipole fields. However, the calculation of numerous point dipole fields is computationally expensive, requiring a large number of numerical integral evaluations. We combine a more efficient representation of finite‐length sources in terms of components related to the wire and its end points with very general expressions for EM fields in 1D layered media. We thus obtain a formulation that requires fewer numerical integrations than the superposition of dipole fields, permits source and receiver placement at any depth within the layer stack and can also easily be integrated into 3D modelling algorithms. Complex source geometries, such as wires bent due to surface obstructions, can be simulated by segmenting the wire and computing the responses for each segment separately. We first describe our finite‐length wire expressions and then present 1D and 3D examples of EM fields due to finite‐length sources for typical land and marine survey geometries and discuss differences to point dipole fields.     

跨孔地震层析成像的级联方法

对厚度小于1/4波长的超薄波速干扰体进行高分辨率成像,作者曾采用走时反演和波场反演相结合的方法,体现了由低分辨率向高分辨率逐步逼近的思想.级联算法是这种思想的进一步发展,我们将具有不同分辨率的算法串联起来,以达到高分辨率成像的目的.本文介绍一种三级串联的算法,并进行了算法分析,数值计算的例子说明这种级联算法分辨率高、稳定性好,只需要地震资料而不要求其它先验信息,因此能较好地满足实际应用的要求.     

井地电法的准解析近似三维反演研究

研究复杂地电模型上的井地电法三维反演一直是一个具有挑战性的课题。本文在准解析近似和重加权正则化的共轭梯度法的基础上,用visualFortran6.5开发了井地电法三维准解析近似反演程序。反演过程中的正演和Frechet导数矩阵计算都应用准解析近似大大提高了计算的速度。通过理论模型的合成数据反演试算,说明基于准解析近似法和加权正则化的共轭梯度法的井地电法三维反演程序有着计算速度快,反演精度高等特点。     

海底电性源频率域CSEM勘探建模及水深影响分析

为了探索我国海域油气和水合物等高阻目标体CSEM勘探的可行性和方法技术,本文研究了在海水中水平电性源激励下有限水深海洋地电模型的频率域电磁响应,为进一步的1D和3D仿真计算奠定了理论基础.在推导电磁响应公式时,首先给出了各层介质的Lorentz势,然后根据Coulomb势与Lorentz势的关系,得到了各层介质的Coulomb势.各层介质中的电磁场均可以由Lorentz势或者Coulomb势计算得到,但在有限元计算时Coulomb势具有优势.长导线源的电磁场和势函数可以由电偶源的电磁场和势函数沿导线长度积分得到.文中具体给出了海水中水平电偶源和长导线源在海水层的电磁场公式,并根据该公式计算了不同水深环境下海底表面的电磁场分布,分析了海水深度对海底油气储层电磁异常的影响.结果表明,随着水深减小,异常幅度和形态特征发生明显变化.当水深很浅时(如50 m),只有同线方向的E_x和E_z两个电场分量存在明显异常.最后,以两个已知海底油田为例,计算了不同水深环境下可观测到的电场异常,展示了电性源频率域CSEM在海底勘探中(包括浅海环境)的良好应用前景.对于该方法实用化过程中还需进一步解决的问题,文中结尾部分也进行了初步探讨.     

SITE EVALUATION AND VOLCANIC HAZARD ASSESSMENT FOR THE NUCLEAR POWER PLANTS OF CHINA

Starting from the 1980's of last century, China has launched the national plan of constructing nuclear power plants along the coastline region in eastern China. Currently, in some of these candidate sites, nuclear facilities have been installed and are in operation, but some other nuclear power plants are still under construction or in site evaluation. In 2012 the Atomic Energy Commission issued the specific guide for volcanic hazards in site evaluation for nuclear installations(IAEA Safety Standards Series No. SSG-21), which was prepared under the IAEA's program for safety standards. It supplements and provides recommendations for meeting the requirements for nuclear installations established in the safety requirements publication on site evaluation for nuclear installations in relation to volcanic hazards. To satisfy the safety standards for volcanic hazard, we follow the IAEA SSG-21 guidelines and develop a simple and practical diffusion program in order to evaluate the potential volcanic hazard caused by tephra fallout from the explosive eruptions. In this practice, we carried out a case study of the active volcanoes in north Hainan Province so as to conduct the probabilistic analysis of the potential volcanic hazard in the surrounding region. The Quaternary volcanism in north Hainan Island, so-called Qiongbei volcanic field is characterized by multi periodic activity, in which the most recent eruption is dated at about 4 000a BP. According to IAEA SSG-21, a capable volcano is one for which both 1)a future eruption or related volcanic event is credible; and 2)such an event has the potential to produce phenomena that may affect a site. Therefore, the Qiongbei volcanic field is capable of producing hazardous phenomena that may reach the potential nuclear power plants around. The input parameters for the simulation of tephra fallout from the future eruption of the Qiongbei volcanic field, such as the size, density and shape of the tephra, the bulk volume and column height, the diffusion parameter P(z), wind direction and intensity, were obtained by field investigation and laboratory analysis. We carried out more than 10000 tephra fallout simulations using a statistical dataset of wind profiles which are obtained from China Meteorological Data Sharing Service System(CMDSSS). Tephra fallout hazard probability maps were constructed for tephra thickness threshold of 1cm. Our results show that the tephra produced by the future large-scale explosive eruption from the Qiongbei volcanic field can affect the area in a range about 250km away from the eruption center. In summary, the current key technical parameters related to volcanic activity and potential hazards in IAEA/SSG-21 guidelines, such as 10Ma volcanic life cycle and 1×10^-7 volcanic disaster screening probability threshold, etc. are based on the volcanic activity characteristics in the volcanic island arc system. In consideration of the relatively low level of volcanic activity compared with volcanic island arc system due to the different tectonic background of volcanism in mainland China, the time scale of volcanic disaster assessment in IAEA SSG-21 guideline is relatively high for volcanoes in mainland China. We suggest that the study of "conceptual model" of volcanic activity should be strengthened in future work to prove that there is no credible potential for future eruptions, so that these volcanoes should be screened out at early stage instead of further evaluation by probabilistic model.     

基于逆算子估计的AVO反演方法研究

传统反演算法以优化算法为主,而基于逆算子估计的AVO反演算法则利用了直接求逆的思路.算法的关键在于寻找存在逆函数的子域,进而可以在子域内直接求逆,这种解决反问题的思路不同于一般的优化类算法所采用的直接搜索解的方式,具有更高的效率.AVO反演利用了振幅随着偏移距的变化特征,反演的精度受到地震资料质量的影响,通过加入L1范数约束以及合理的初始模型有助于提高反演的稳定性以及准确度.模型测算和实际应用表明,基于逆算子估计的AVO反演方法具有较高的精确程度和可靠性.     

The Uncertainty of 2D Models Along Wide Angle Seismic Profiles

The estimation of uncertainty for any geophysical model is important for determining how reliable the model is. It is especially important for subjective trial and error modelling techniques like forward ray-tracing modelling of wide-angle seismic data when the final result is very dependent on the interpreter’s knowledge of the area and experience. In this kind of modelling, it is common to encounter over interpretation of the seismic data without checking the uncertainty of the result, especially in the deep parts that are not constrained with other a priori knowledge. In this paper, we propose a method of estimating the uncertainty of the final models based on a one dimensional method of small error propagation generalized for 2D profiles. With a simple approximation, we estimate the uncertainty for published interpretative models of selected profiles from seismic experiments in the Central Europe. We conclude that for typical wide angle seismic profiles we can reliably interpret four layered models of the Earth’s crust based on traveltimes fitting. We also show how the number of layers influence obtained uncertainties. Estimated uncertainties for both the velocity fields and the boundaries between layers are important for future tectonic and geodynamic interpretation of those profiles.     

Effects of crustal conductivity heterogeneities on the electromagnetic field

Examples of observed and computed effects of crustal conductivity heterogeneities are described. The physical processes responsible for these effects are discussed with special reference to their characteristic dimensions. Simple criteria allowing the recognition of the physical phenomena which govern the circulation of Earth currents are given.These criteria are taken into account in a study of the electromagnetic fields relating to three typical effects of crustal conductivity heterogeneïties. This study suggest that we should begin by interpreting data in frequency ranges for which the static distortion approximation of currents hold. The rough but correct model thus obtained can then be used as starting model in the interpretation of the whole data set, involving numerical modelling.IPGP Contribution NS N^o 1003.     

Extraoptimal a posteriori estimates of the solution accuracy in the ill-posed problems of the continuation of potential geophysical fields

A new scheme is proposed for a posteriori estimation of the accuracy of the approximate solutions to the linear ill-posed problems of the continuation of potential geophysical fields. When special methods are applied for the solution of the ill-posed problems of interest, namely, the algorithms of extraoptimal regularization, these a posteriori estimates have the optimal (in the order of magnitude) accuracy. The proposed theory is illustrated by numerical experiments.     

GNSS掩星中大气水汽的非线性反演

研究利用无线电掩星探测数据反演大气水汽参数,文中使用一维非线性方法,反演对流层水汽压廓线.首先,定义了一维目标函数,并以几何光学假设为前提,反演出电波弯曲角;将电波弯曲角作为掩星探测量,大气模式输出的温、湿参量作为初始场,代入目标函数,对目标函数求最优反演出水汽压廓线.文中给出了部分反演结果,经讨论分析认为:非线性方法反演水汽压对初始场的精度依赖较小,能够同时反演出大气温度\水汽压廓线及相应的误差分析,对数值天气预报的应用及数据同化研究具有重要意义.     

Analytical modeling of wave fields at extremely long distances and experimental research of water waves

The analytical algorithm developed in this work is intended for modeling wave fields at extremely long distances; it has no limitations on accuracy, media models, and observation databases and makes it possible to calculate the dynamics of individual waves (primary waves, ghost waves, etc). Comparison with experimental marine data is performed with a program developed for the calculation of wave fields. The modeling performed shows that the incorporation of absorption in the Earth ensures a good agreement between the model and the observed wave fields. The formula for the ratio between waves of different multiplicities corroborated by experimental and mathematical modeling data is obtained to a first approximation for large source-receiver separation. An analytical modeling of full wave fields has been performed, some types of waves are analyzed, and the physics of multiple waves in a layer of water is studied numerically     

Penetration of Nonstationary Ionospheric Electric Fields into Lower Atmospheric Layers in the Global Electric Circuit Model

The problem of the penetration of nonstationary ionospheric electric fields into the lower atmospheric layers is considered based on the model of the global electric circuit in the Earth’s atmosphere. For the equation of the electric field potential, a solution that takes into account exponential variation in the electrical conductivity with height has been obtained. Analysis of the solution made it possible to reveal three cases of the dependence of the solution on height. The first case (the case of high frequencies) corresponds to the Coulomb approximation, when the electrical conductivity of the atmosphere can be neglected. In the case of low frequencies (when the frequency of changes in the ionosphere potential is less than the quantity reciprocal to the time of electric relaxation of the atmosphere), a quasi-stationary regime, in which the variation in the electric potential of the atmosphere is determined by the electric conduction currents, occurs. In the third case, due to the increase in the electrical conductivity of the atmosphere, two spherical regions appear: with the Coulomb approximation in the lower region and conduction currents in the upper one. For these three cases, formulas for estimating the electric field strength near the Earth’s surface have been obtained.     

Semi-analytical evaluation of integral forms associated with Lamb's problem

The present work gives solutions of integrals resulting from Lamb's problem solution by an accurate and efficient approximation procedure. The formulation of the solutions requires the study of Green's function of Lamb problem solution. Unfortunately, this problem is associated to great mathematical difficulties and needs the evaluation of some complex integrals. We handled these integrals by an appropriate strategy based on decoupling their effects mathematically and solved by using the least squares method. The present solutions can be applied to study the dynamical interaction between soil and structures, to be used to determine the transient wave fields caused by a seismic source, and also to assess numerical computations with a different numerical methods program.     

Use of Green’s function for determining the disturbing potential of an ellipsoidal Earth

A spherical approximation makes the basis for a majority of formulas in physical geodesy. However, the present-day accuracy in determining the disturbing potential requires an ellipsoidal approximation. The paper deals with constructing Green’s function for an ellipsoidal Earth by an ellipsoidal harmonic expansion and using it for determining the disturbing potential. From the result obtained the part that corresponds to the spherical approximation has been extracted. Green’s function is known to depend just on the geometry of the surface where boundary values are given. Thus, it can be calculated irrespective of the gravity data completeness. No changes of gravity data have an effect on Green’s function and they can be easily taken into account if the function has already been constructed. Such a method, therefore, can be useful in determining the disturbing potential of an ellipsoidal Earth.     

Towards an accurate real-time locator of infrasonic sources

Infrasonic signals propagate from an atmospheric source via media with stochastic and fast space-varying conditions. Hence, their travel time, the amplitude at sensor recordings and even manifestation in the so-called “shadow zones” are random. Therefore, the traditional least-squares technique for locating infrasonic sources is often not effective, and the problem for the best solution must be formulated in probabilistic terms. Recently, a series of papers has been published about Bayesian Infrasonic Source Localization (BISL) method based on the computation of the posterior probability density function (PPDF) of the source location, as a convolution of a priori probability distribution function (APDF) of the propagation model parameters with likelihood function (LF) of observations. The present study is devoted to the further development of BISL for higher accuracy and stability of the source location results and decreasing of computational load. We critically analyse previous algorithms and propose several new ones. First of all, we describe the general PPDF formulation and demonstrate that this relatively slow algorithm might be among the most accurate algorithms, provided the adequate APDF and LF are used. Then, we suggest using summation instead of integration in a general PPDF calculation for increased robustness, but this leads us to the 3D space-time optimization problem. Two different forms of APDF approximation are considered and applied for the PPDF calculation in our study. One of them is previously suggested, but not yet properly used is the so-called “celerity-range histograms” (CRHs). Another is the outcome from previous findings of linear mean travel time for the four first infrasonic phases in the overlapping consecutive distance ranges. This stochastic model is extended here to the regional distance of 1000 km, and the APDF introduced is the probabilistic form of the junction between this travel time model and range-dependent probability distributions of the phase arrival time picks. To illustrate the improvements in both computation time and location accuracy achieved, we compare location results for the new algorithms, previously published BISL-type algorithms and the least-squares location technique. This comparison is provided via a case study of different typical spatial data distributions and statistical experiment using the database of 36 ground-truth explosions from the Utah Test and Training Range (UTTR) recorded during the US summer season at USArray transportable seismic stations when they were near the site between 2006 and 2008.     

基于GPU并行的重力、重力梯度三维正演快速计算及反演策略

利用NVIDIA CUDA编程平台,实现了基于GPU并行的重力、重力梯度三维快速正演计算方法.采用当前在重力数据约束反演或联合反演中流行的物性模型(密度大小不同、规则排列的长方体单元)作为地下剖分单元,对任意三维复杂模型体均可用很多物性模型进行组合近似,利用解析方法计算出所有物性模型在计算点的异常值并累加求和,得到整个模型体在某一计算点引起的重力(或重力梯度)值.针对精细的复杂模型体产生的问题,采用GPU并行计算技术,主要包括线程有效索引与优化的并行归约技术进行高效计算.在显卡型号为NVIDIA Quadro 2000相对于单线程CPU程序,重力和重力梯度U_xx、U_xy正演计算可以分别达到60与50倍的加速.本文还讨论了GPU并行计算在两种反演方法中的策略,为快速三维反演技术提供了借鉴.     

Anisotropy parameter inversion in vertical axis of symmetry media using diffractions

Diffractions play a vital role in seismic processing as they can be utilized for high‐resolution imaging applications and analysis of subsurface medium properties like velocity. They are particularly valuable for anisotropic media as they inherently possess a wide range of dips necessary to resolve the angular dependence of velocity. However, until recently, the focus of diffraction imaging or inversion algorithms have been only on the isotropic approximation of the subsurface. Using diffracted waves, we develop a framework to invert for the effective η model. This effective model is obtained through scanning over possible effective η values and selecting the one that best fits the observed moveout curve for each diffractor location. The obtained effective η model is then converted to an interval η model using a Dix‐type inversion formula. The inversion methodology holds the potential to reconstruct the true η model with sufficiently high accuracy and resolution properties. However, it relies on an accurate estimation of diffractor locations, which in turn requires good knowledge of the background velocity model. We test the effectiveness and applicability of our method on the vertical transverse isotropic Marmousi model. The inversion results yield a reasonable match even for the complex Marmousi model.