On Gravity Inversion for Point Mass Anomalies by Means of the Truncated Geoid

The physical meaning of the truncated geoid, which is defined by the convolution of gravity anomalies with the Stokes function on a spherical cap of specified radius, has been studied by the authors. They investigated its relation to the density distribution, generating the surface gravity, and its potential use in inversion. Some progress results for simulated studies on point mass anomalies are presented. The behavior of the truncated geoid is controlled by the radius of the integration domain, hereinafter referred to as the truncation parameter, which is treated as a free parameter. The change of the truncated geoid in response to the change of the truncation parameter was studied in the context of the simulated mass distributions. By means of such computer simulations we have managed to demonstrate the clear sensitivity of the truncated geoid to the depths, in addition to the horizontal positions, of point mass anomalies generating the synthetic surface gravity. The objective of this paper is to illustrate, with the help of computer simulation as the method of our study, the contribution of the truncated geoid to the solution of the gravimetric inverse problem. Further work towards employing the truncated geoid in gravity exploration is being conducted.     

井下倾斜仪的定向反演问题

倾斜观测已在地球物理领域以及地震部门获得广泛应用。有时,由于种种原因井下倾斜仪难以定向,这会对倾斜观测资料的解释带来困难,本文阐明一种利用潮汐信号进行井下倾斜仪定向反演的方法。     

反演模型分辨率的估算方法

反演问题的时空间分辨率或称时空分辨长度是评估模型精细程度的重要参数,决定了该模型应用的范围和价值,但是分辨长度估算却是比反演更复杂和麻烦的数学问题。除了层析成像中广泛利用理论模型恢复试验定性提取空间分辨长度外,通过求解分辨率矩阵可定量获得分辨长度。通过矩阵操作给出的分辨率矩阵包括三类:直接分辨率矩阵、正则化分辨率矩阵和混合分辨率矩阵。这三类矩阵包含了反演本身不同侧面的信息,因此在一个反演应用中,同时提供这三类分辨率矩阵可更全面地评估反演模型分辨率分布。最近An(2012)提出了从大量随机理论模型及其解中统计出分辨率矩阵的方法。这种分辨率矩阵是从模拟真实反演实验的输入和输出模型中通过反演得到的,因此这种分辨率矩阵更能反映整个反演所涉及到的更多因素和过程;同时由于这种分辨率矩阵计算过程无需进行矩阵操作且不依赖于具体正演和反演方法,因此可以被应用于更普遍的反演问题。实际应用证明统计分辨率分析方法适用于对二维和三维层析成像反演模型进行分辨率分析。     

On the inverse dynamo problem in a simplified mean-field model

Inverse dynamo theory seeks to gain information about the motion of a liquid conductor from measurements of the magnetic field in the surrounding vacuum. We consider here a highly simplified model problem, namely a steady α²-dynamo in plane geometry with an α-field varying only in the z-direction normal to the conductor–vacuum interface. Based on perturbation theory about constant-α solutions, we find as many integral conditions on α(z) as modes are present in the vacuum field. This result is corroborated by the complete solution of a special case.     

免疫粒子群优化在波阻抗反演中的应用

针对标准粒子群优化（PSO）算法易出现早熟而陷入局部最优以及进化后期收敛速度慢等缺陷,引入免疫系统的免疫记忆和抗体浓度选择机制,构造了基于免疫机制的粒子群优化（IPSO）算法,并将其应用到波阻抗反演问题中。免疫记忆能够保留高适应度个体,抗体浓度选择机制进一步保证了粒子的多样性,从而能较好地避免早熟收敛,提高算法的全局搜索能力。对理论模型试算表明,IPSO算法在进行波阻抗反演时不仅收敛速度快,而且具有较高的精确度和抗噪性能。     

Seismic frame design via inverse mode design of frame-ground systems

A two-step stiffness design procedure is developed for a moment-resisting planar frame supported by a prescribed two-dimensional finite-element ground-pile system. In the first step, a hybrid inverse eigenmode problem is formulated and its solution is derived in an analytical form. A difficulty resulting from the existence of multiple interface nodes is overcome by incorporating a deformation constraint into a set of linear equations for finding the lowest-mode displacements at the interface nodes and in the ground. In the second step, the fundamental natural frequency of the combined system and the lowest mode-strain ratios in the frame specified in the first step are regarded as the parameters for adjusting the mean peak seismic member-end strains to their specified values. If the fundamental natural frequency of the frame with a fixed-base happens to be close to that of the ground, a difficulty arises in the two-step stiffness design procedure because of an irregular response amplification and of the non-predominance of the lowest-mode components. A new practical design procedure of rapid convergence is proposed such that an initial design is found for a stiff ground and that a sequence of stiffness designs is generated with respect to a ground stiffness parameter without any differential coefficient of series expansion. The accuracy of the model utilized in this paper and the validity of the present stiffness design procedure are verified through time-history response analysis.     

用GPS资料反演区域断层运动的若干问题

本文介绍了用GPS资料反演断层运动中存在的一些问题。GPS资料区域构造信息的提取是反演中非常重要的环节,结合一定区域反演时选择符合断层运动的位错模型是必要的,断层运动参数的选取问题,最后是反演的算法问题。     

Multi-parameter reflection waveform inversion for acoustic transversely isotropic media with a vertical symmetry axis

Full waveform inversion in transversely isotropic media with a vertical symmetry axis provides an opportunity to better match the data at the near and far offsets. However, multi-parameter full waveform inversion, in general, suffers from serious cycle-skipping and trade-off problems. Reflection waveform inversion can help us recover a background model by projecting the residuals of the reflected wavefield along the reflection wavepath. Thus, we extend reflection waveform inversion to acoustic transversely isotropic media with a vertical symmetry axis utilizing the proper parameterization for reduced parameter trade-off. From a radiation patterns analysis, an acoustic transversely isotropic media with a vertical symmetry axis is better described by a combination of the normal-moveout velocity and the anisotropic parameters η and δ for reflection waveform inversion applications. We design a three-stage inversion strategy to construct the optimal resulting model. In the first stage, we only invert for the background by matching the simulated reflected wavefield from the perturbations of and δ with the observed reflected wavefield. In the second stage, the background and η are optimized simultaneously and the far-offset reflected wavefield mainly contribute to their updates. We perform Born modelling to compute the reflected wavefield for the two stages of reflection waveform inversion. In the third stage, we perform full waveform inversion for the acoustic transversely isotropic media with a vertical symmetry axis to delineate the high-wavenumber structures. For this stage, the medium is described by a combination of the horizontal velocity , η and ε instead of , η and δ. The acoustic multi-parameter full waveform inversion utilizes the diving waves to improve the background as well as utilizes reflection for high-resolution information. Finally, we test our inversion algorithm on the modified Sigsbee 2A model (a salt free part) and a two-dimensional line from a three-dimensional ocean bottom cable dataset. The results demonstrate that the proposed reflection waveform inversion approach can recover the background model for acoustic transversely isotropic media with a vertical symmetry axis starting from an isotropic model. This recovered background model can mitigate the cycle skipping of full waveform inversion and help the inversion recover higher resolution structures.     

Some Applied Aspects of the Study of Trends in the Upper and Middle Atmosphere

Geomagnetism and Aeronomy - It is shown that that there are currently trends in the parameters of the middle and upper atmosphere and ionosphere that are already leading or may lead in the near...     

Conditionality of inverse solutions to discretised integral equations in geoid modelling from local gravity data

The eigenvalue decomposition technique is used for analysis of conditionality of two alternative solutions for a determination of the geoid from local gravity data. The first solution is based on the standard two-step approach utilising the inverse of the Abel-Poisson integral equation (downward continuation) and consequently the Stokes/Hotine integration (gravity inversion). The second solution is based on a single integral that combines the downward continuation and the gravity inversion in one integral equation. Extreme eigenvalues and corresponding condition numbers of matrix operators are investigated to compare the stability of inverse problems of the above-mentioned computational models. To preserve a dominantly diagonal structure of the matrices for inverse solutions, the horizontal positions of the parameterised solution on the geoid and of data points are identical. The numerical experiments using real data reveal that the direct gravity inversion is numerically more stable than the downward continuation procedure in the two-step approach.     

Mechanical problems in geodynamics and work done in China

The subject of geodynamics concerns the dynamics of the global motion of the earth, of the motion in the earth's interior and its interaction with surface features, together with mechanical processes in the deformation and rupture of geological structures. A brief historical review is given from Sir I. Newton, Maclauwin, Jacobi, Poincaré, Poisson, Lamé, Darwin, Rayleigh, and Love, who dealt with the homogeneous sphere, to Leibenson, Takeuchi, and Meinesz, concentrating on layered spheres, and after the advent of plate tectonics, on the use of numerical simulation, to the analyses of tectonic features, earthquake mechanism, the application of nonlinear dynamics. By discussing the forward and inverse mechanical problems, and the questions facing the inverse problems of searching for the structural parameters, driving forces, etc. are raised in more detail. Thereafter, some works accomplished in China on the global and regional stress fields analyses; tectonic features' analyses, mantle flow studies; experimental studies of rocks and their constitutive relations are presented. Finally, the interdisciplinary nature of the subject is emphasized, and the main mechanical problems that need special attention are then proposed.     

Investigation of the electrical conductivity beneath China using geomagnetic spatial gradient method

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Variational coupling of Plinian column models and data: Application to El Chichón volcano

Many efforts have been done in the modelling of Plinian columns. However, until now, the inverse problem of the reconstruction of a Plinian event from observed data has been only roughly tackled. This paper discusses the efficient variational data assimilation (VDA) that manages the optimization iterate sequence by means of gradient computations. Theoretical developments of VDA are presented for both the Woods equations and a generic system allowing for the modelling of the Navier–Stokes equations. Two- and three-dimensional unsteady Plinian models being based on the latters, VDA could be clearly performed on their differentiable subset of equations.     

Ellipsoidal Stokes Boundary-Value Problem with Ellipsoidal Corrections in the Boundary Condition

We would like to solve the Stokes boundary-value problem taking into consideration the ellipsoidal corrections in the boundary condition in ellipsoidal coordinates The original problem, i.e., the ellipsoidal Stokes boundary-value problem has been solved by Martinec and Grafarend (1997) We use the same philosophy expressed by Martinec (1998) to solve the spherical Stokes boundary-value problem with ellipsoidal corrections in the boundary condition We wish to show the magnitude of the integration kernel describing the effect of the ellipsoidal corrections in the boundary condition in a cap around the computational point.     

On the Problem of Sample Preservation by Freezing

During routine analysis of running water samples differences of the analytical results of water‐soluble anions were observed between analysis carried out immediately after sampling and after storage of the cooled/frozen sample. This phenomenon was investigated for some years with the “model ion” chloride. A high number of samples (ca. 210) were analysed over three years with different analytical methods, and by alteration of the sample containers the discrete physical influence of the wall effect of the sample vessel could be worked out definitely. No significant differences occur with the mean value of the year but the single values have high differences in the positive or negative direction. Assuming a similar behaviour of other water constituents when preserved by freezing the analytical values had to be looked at very critically.     

Maximum Entropy Density Determination for the Earth and Terrestrial Planets

The maximum entropy principle of the information theory gives rise to a general regularization strategy for ill-posed inverse problems. The methods based on this principle have become standard in various branches of engineering sciences. Of course, ill-posed problems frequently appear in Earth sciences, too. Nonetheless, the concept of maximum entropy is not very popular here. Therefore, we review the basic approaches employing the principle of maximum entropy in one way or another. We can distinguish at least three different approaches, partly yielding coincident results. One possible area of application is the determination of Earth and planetary models, although the paper cannot treat this in its practical complexity. Most of the discussion is restricted to the determination of the Earth's mass density function from various sources of data. Three sample problems are solved using the principle of maximum entropy: a spherical and an ellipsoidal problem related to the Earth and an ellipsoidal problem related to Mars. This illustrates the numerical procedure, which is non-trivial in many cases. It also shows some results, partly compared to standard solutions. The pros and cons of the approaches are discussed.     

Some Aspects of Energy Balance and Tsunami Generation by Earthquakes and Landslides

— Tsunamis are generated by displacement or motion of large volumes of water. While there are several documented cases of tsunami generation by volcanic eruptions and landslides, most observed tsunamis are attributed to earthquakes. Kinematic models of tsunami generation by earthquakes — where specified fault size and slip determine seafloor and sea-surface vertical motion — quantitatively explain far-field tsunami wave records. On the other hand, submarine landslides in subduction zones and other tectonic settings can generate large tsunamis that are hazardous along near-source coasts. Furthermore, the ongoing exploration of the oceans has found evidence for large paleo-landslides in many places, not just subduction zones. Thus, we want to know the relative contribution of faulting and landslides to tsunami generation. For earthquakes, only a small fraction of the minimum earthquake energy (less than 1% for typical parameter choices for shallow underthrusting earthquakes) can be converted into tsunami wave energy; yet, this is enough energy to generate terrible tsunamis. For submarine landslides, tsunami wave generation and landslide motion interact in a dynamic coupling. The dynamic problem of a 2-D translational slider block on a constant-angle slope can be solved using a Green's function approach for the wave transients. The key result is that the largest waves are generated when the ratio of initial water depth above the block to downslope vertical drop of the block H ₀ /W sin δ is less than 1. The conversion factor of gravitational energy into tsunami wave energy varies from 0% for a slow-velocity slide in deep water, to about 50% for a fast-velocity slide in shallow water and a motion abruptly truncated. To compare maximum tsunami wave amplitudes in the source region, great earthquakes produce amplitudes of a few meters at a wavelength fixed by the fault width of 100 km or so. For submarine landslides, tsunami wave heights — as measured by b, block height — are small for most of the parameter regime. However, for low initial dynamic friction and values of H ₀ /W sin δ less than 1, tsunami wave heights in the downslope and upslope directions reach b and b/4, respectively.Wavelengths of these large waves scale with block width. For significant submarine slides, the value of b can range from meters up to the kilometer scale. Thus, the extreme case of efficient tsunami generation by landslides produces dramatic hazards scenarios.