2-D Versus 3-D Magnetotelluric Data Interpretation

In recent years, the number of publications dealing with the mathematical and physical 3-D aspects of the magnetotelluric method has increased drastically. However, field experiments on a grid are often impractical and surveys are frequently restricted to single or widely separated profiles. So, in many cases we find ourselves with the following question: is the applicability of the 2-D hypothesis valid to extract geoelectric and geological information from real 3-D environments? The aim of this paper is to explore a few instructive but general situations to understand the basics of a 2-D interpretation of 3-D magnetotelluric data and to determine which data subset (TE-mode or TM-mode) is best for obtaining the electrical conductivity distribution of the subsurface using 2-D techniques. A review of the mathematical and physical fundamentals of the electromagnetic fields generated by a simple 3-D structure allows us to prioritise the choice of modes in a 2-D interpretation of responses influenced by 3-D structures. This analysis is corroborated by numerical results from synthetic models and by real data acquired by other authors. One important result of this analysis is that the mode most unaffected by 3-D effects depends on the position of the 3-D structure with respect to the regional 2-D strike direction. When the 3-D body is normal to the regional strike, the TE-mode is affected mainly by galvanic effects, while the TM-mode is affected by galvanic and inductive effects. In this case, a 2-D interpretation of the TM-mode is prone to error. When the 3-D body is parallel to the regional 2-D strike the TE-mode is affected by galvanic and inductive effects and the TM-mode is affected mainly by galvanic effects, making it more suitable for 2-D interpretation. In general, a wise 2-D interpretation of 3-D magnetotelluric data can be a guide to a reasonable geological interpretation.     

Parallel 3-D Simulation of a Fault Gouge Using the Lattice Solid Model

Despite the insight gained from 2-D particle models, and given that the dynamics of crustal faults occur in 3-D space, the question remains, how do the 3-D fault gouge dynamics differ from those in 2-D? Traditionally, 2-D modeling has been preferred over 3-D simulations because of the computational cost of solving 3-D problems. However, modern high performance computing architectures, combined with a parallel implementation of the Lattice Solid Model (LSM), provide the opportunity to explore 3-D fault micro-mechanics and to advance understanding of effective constitutive relations of fault gouge layers. In this paper, macroscopic friction values from 2-D and 3-D LSM simulations, performed on an SGI Altix 3700 super-cluster, are compared. Two rectangular elastic blocks of bonded particles, with a rough fault plane and separated by a region of randomly sized non-bonded gouge particles, are sheared in opposite directions by normally-loaded driving plates. The results demonstrate that the gouge particles in the 3-D models undergo significant out-of-plane motion during shear. The 3-D models also exhibit a higher mean macroscopic friction than the 2-D models for varying values of interparticle friction. 2-D LSM gouge models have previously been shown to exhibit accelerating energy release in simulated earthquake cycles, supporting the Critical Point hypothesis. The 3-D models are shown to also display accelerating energy release, and good fits of power law time-to-failure functions to the cumulative energy release are obtained.     

一种反演不均匀介质大地电磁测深资料的方法

通过反演受近地表不均匀介质影响的大地电磁测深资料的新方法,可获得较准确的一维地电断面参数、不均匀体埋藏深度及其电性特征。本方法计算速度快,单测ρxy,ρyx可独立反演并相互验证结果的准确性     

井间电磁场的一维、二维联合反演方法

提出了针对轴对称二维井间模型的一维、二维联合反演方法.该方法基于纵向成层背景地层的Green函数,以一维反演结果作为联合反演的迭代初始值,同时反演一维背景地层和二维异常剖面的电导率.采用递推技术计算Green函数的系数,可以很方便地同时得到Green函数对空间坐标的积分和对背景层电导率的微分,大大加快了计算雅可比矩阵〖WTHX〗M〖WTBZ〗的速度并使计算方便、准确.反演实例说明了该方法的有效性.反演实例还显示,背景层电导率较二维成像剖面的电导率收敛速度要快,测量数据的精度对二维剖面电导率成像质量的影响大于对背景层电导率分布的影响.     

Real-time 3-D space numerical shake prediction for earthquake early warning

In earthquake early warning systems, real-time shake prediction through wave propagation simulation is a promising approach. Compared with traditional methods, it does not suffer from the inaccurate estimation of source parameters. For computation efficiency, wave direction is assumed to propagate on the 2-D surface of the earth in these methods. In fact, since the seismic wave propagates in the 3-D sphere of the earth, the 2-D space modeling of wave direction results in inaccurate wave estimation. In this paper, we propose a 3-D space numerical shake prediction method, which simulates the wave propagation in 3-D space using radiative transfer theory, and incorporate data assimilation technique to estimate the distribution of wave energy. 2011 Tohoku earthquake is studied as an example to show the validity of the proposed model. 2-D space model and 3-D space model are compared in this article, and the prediction results show that numerical shake prediction based on 3-D space model can estimate the real-time ground motion precisely, and overprediction is alleviated when using 3-D space model.     

Numerical modeling of 3-D terrain effect on MT field

Using the boundary element method, the numerical modeling problem of three-dimensional terrain effect on magnetotelluric (MT) field is solved. This modeling technique can be run on PC in the case of adopting special net division. The result of modeling test for 2-D terrain by this modeling technique is basically coincident with that by 2-D modeling technique, but there is a great difference between the results of 3-D and 2-D modeling for 3-D terrain. Project supported by the National Natural Science Foundation of China.     

单源单缆方式采集的天然气水合物三维地震数据处理技术

作为潜在的能源储备,天然气水合物的重要性持续上升.针对天然气水合物的地震勘探也逐步由二维方式向三维方式转变.本文以单源单缆方式采集的天然气水合物三维地震数据为基础,探讨了地震数据成像的关键技术,在获得准确的三维地震成像数据体的同时,还得到三维地层速度数据体.三维地震数据更有利于描述含天然气水合物地层的地震反射特征,并刻画可能含天然气水合物地层的分布,从而拓宽对天然气水合物储层的认识.     

二维层状介质点电源边界单元解

本文用付氏变换将点源二维地电断面的三维边值问题变成二维边值问题,然后讨论了边界元法在解决层状介质中存在二维柱体时点源场视电阻率计算问题中的应用。由于选取的基本解避免了对水平层状界面的积分计算,从而大大减少了边界剖分节点数。在计算中设法略去了对边界上位场法向导数的求解,使未知量大为减少,从而便利了求解二维边值问题,并由付氏反变换求得三维空间中的位。本方法所需计算机内存少,原始数据的输入简单,且有较高的计算精度。     

1-D and 2-D analyses of weak motion data in Fraser Delta from 1966 Duvall earthquake

The 1996 Duvall earthquake in Washington State triggered ground motion stations in the Fraser Delta, British Columbia, located on varying depths of Holocene and Pleistocene soils to a maximum depth of 800 m and one station on bedrock. Recorded ground motions were used to examine the applicability of 1-D and 2-D site response analyses for amplification studies in the Delta. 1-D response analysis gave a good indication of the period of peak response. Response spectra computed by 1-D analysis did not compare well with recorded spectra except at very deep sites. The use of 2-D analyses to include buried topography generally improved the predictions of site response spectra at the shallow sites. However, for the shallow earth sites, the recorded motions showed a strong spectral response at short periods in the range of 0.1–0.25 s. Neither 1-D nor 2-D analysis predicted this response.     

A quasi three-dimensional model for flow and transport in unsaturated and saturated zones: 1. Implementation of the quasi two-dimensional case

A quasi three-dimensional (QUASI 3-D) model is presented for simulating the subsurface water flow and solute transport in the unsaturated and in the saturated zones of soil. The model is based on the assumptions of vertical flow in the unsaturated zone and essentially horizontal groundwater flow. The 1-D Richards equation for the unsaturated zone is coupled at the phreatic surface with the 2-D flow equation for the saturated zone. The latter was obtained by averaging 3-D flow equation in the saturated zone over the aquifer thickness. Unlike the Boussinesq equation for a leaky-phreatic aquifer, the developed model does not contain a storage term with specific yield and a source term for natural replenishment. Instead it includes a water flux term at the phreatic surface through which the Richards equation is linked with the groundwater flow equation. The vertical water flux in the saturated zone is evaluated on the basis of the fluid mass balance equation while the horizontal fluxes, in that equation, are prescribed by Darcy law. A 3-D transport equation is used to simulate the solute migration. A numerical algorithm to solve the problem for the general quasi 3-D case was developed. The developed methodology was exemplified for the quasi 2-D cross-sectional case (QUASI2D). Simulations for three synthetic problems demonstrate good agreement between the results obtained by QUASI2D and two fully 2-D flow and transport codes (SUTRA and 2DSOIL). Yet, simulations with the QUASI2D code were several times faster than those by the SUTRA and the 2DSOIL codes.     

三维地震勘探数据处理的问题及其解决方法

三维地震勘探在十年内取得了显著的地质效果和经济效益。三维地震数据处理技术也得到了迅速的发展。但是,与二维相比,三维地震数据处理技术有许多不完善之处。本文对其中几个主要问题进行分析并提出解决方法。这些问题是三维叠加速度分析、三维静校正和叠前三维偏移等处理方法。     

三维F－K域DMO方法及应用效果

在常速情况下，从三维时距方程出发，通过倾角代换，将三维倾角时差分裂为两个正交方向上的二维倾角时差，然后在这两个正交方向上分别做一次二维倾角时差校正，便可达到三维倾角时差校正的目的．应用实例表明这种三维ＤＭＯ分裂方法是切实有效的．     

三维F－K域DMO方法及应用效果

在常速情况下，从三维时距方程出发，通过倾角代换，将三维倾角时差分裂为两个正交方向上的二维倾角时差，然后在这两个正交方向上分别做一次二维倾角时差校正，便可达到三维倾角时差校正的目的．应用实例表明这种三维ＤＭＯ分裂方法是切实有效的．     

三维F－K域DMO方法及应用效果

在常速情况下,从三维时距方程出发,通过倾角代换,将三维倾角时差分裂为两个正交方向上的二维倾角时差,然后在这两个正交方向上分别做一次二维倾角时差校正,便可达到三维倾角时差校正的目的．应用实例表明这种三维ＤＭＯ分裂方法是切实有效的．     

Multidimensional GPR array processing using Kirchhoff migration

We compare the ability of several practical ground-penetrating radar (GPR) array processing methods to improve signal-to-noise ratio (SNR), increase depth of signal penetration, and suppress out-of-plane arrivals for data with SNR of roughly 1. The methods include two-dimensional (2-D) monostatic, three-dimensional (3-D) monostatic, and 3-D bistatic Kirchhoff migration. The migration algorithm is modified to include the radiation pattern for interfacial dipoles. Results are discussed for synthetic and field data. The synthetic data model includes spatially coherent noise sources that yield nonstationary signal statistics like those observed in high noise GPR settings. Array results from the model data clearly indicate that resolution and noise suppression performance increases as array dimensionality increases. Using 50-MHz array data collected on a temperate glacier (Gulkana Glacier, AK), we compare 2-D and 3-D monostatic migration results. The data have low SNR and contain reflections from a complex, steeply dipping bed. We demonstrate that the glacier bed can only be accurately localized with the 3-D array. In addition, we show that the 3-D array increases SNR (relative to a 2-D array) by a factor of three.     

大地电磁二维层状模型参数化反演

本文针对目前二维反演存在求解参数过多和求其偏导数困难的两个问题，在近年来关于连续介质二维大地电磁测深资料快速反演的理论基础上，对二维层状模型反演的目标函数，进行线性近似，采用加权法来近似计算二维模型参数的偏导数。从而实现比较快速的二维层状模型的参数化反演。理论模型的反演试验表明，反演迭代可以较快地以足够的精度拟合视电阻率和相位资料，并收敛接近理论模型。     

汶川地震发震构造带过WSFD-2钻井深反射地震数据3-D处理技术研究

2008年5月12日汶川发生里氏8.0级地震的发震机制与龙门山断裂带的构造特征紧密相关,应用反射地震探测方法精细探测发震构造内部的结构特征,对研究汶川地震的发震机理有重要意义.5.12地震后在地表错断最剧烈的区域之一虹口乡白庙村穿过发震构造和深钻科研井WSFD-1和WSFD-2布置了兼顾浅中深层信息的反射地震探测剖面,该区域断裂带硬岩出露,地形地貌复杂多变,起伏剧烈,只能采取弯线地震测线布设方式采集二维反射地震数据,而且弯曲度大,造成CDP点分散严重.区域内构造复杂,褶皱逆推构造发育,地层和构造倾角大,采用常规二维地震数据处理方法进行叠加处理时,易将不同地层的反射信息叠加到同一反射层.弯线叠加剖面上侧面波,混波干扰严重,会显著地降低原本低信噪比数据的分辨率,或剖面可靠性低,容易在二维剖面中造成解释陷阱.本文利用弯线地震采集的三维特性,用拟三维地震叠加技术处理汶川地震科学钻井附近横跨北川—映秀断裂带的二维弯线地震数据,弥补常规二维弯线地震数据处理技术的不足,将不同地层的反射信息分离归位到不同的三维叠加剖面上,解决二维弯线地震数据处理时混波干扰严重的难题.通过理论分析和实验选取合适的共中心点面元,获得了高分辨率的三维叠加剖面.相比于二维弯线叠加剖面,三维叠加剖面切片成像更真实,剔除了不同地层反射信息混叠的影响,能得到更准确的断点信息,并可以获得沿断层走向横向的信息,显著提高了构造解释的可靠性和精度.应用拟三维地震数据处理方法处理龙门山断裂带的二维弯线地震数据,获取高分辨率的构造信息,有利于断裂带内汶川地震发震机制和龙门山隆起机制的解释.

     

1-D and 2-D spatial frequency analysis of self-potential field anomalies,produced by a polarized sphere

This paper gives analytical expressions for the 1-D and 2-D frequency spectra of the self-potential field produced by a polarized sphere. In 1-D, the amplitude spectrum of the potential field leads to a criterion for determination of the depthh to the centre of the sphere. The polarization angle of the buried sphere can be calculated from the maximum point of the amplitude spectrum of the electric field. In 2-D, the depth to the centre of the polarized sphere can be calculated if the polarization is vertical.     

利用混合法构建三维数字岩心(英文)

在弹性波有三维数字岩心描述了岩石的微观孔隙结构。X射线CT扫描是获取三维数字岩心最准确和直接的方法,但实验成本高。本文结合沉积过程模拟和模拟退火算法,提出了重建三维数字岩心的混合法,基于岩石二维图像重建三维数字岩心。利用岩石颗粒沉积算法构建初始数字岩心,作为模拟退火算法的初始状态。运用模拟退火算法调整岩石颗粒和孔隙的相对位置,使三维数字岩心与岩心二维图像具有相似的自相关函数,从而建立三维数字岩心。与传统模拟退火算法相比,该方法计算时间明显减小。运用局部孔隙度理论定量比较了重建数字岩心和岩心X射线微CT图像,两种数字岩心具有相似的均质性和孔隙连通性。利用有限元方法和格子玻尔兹曼方法分别模拟了重建三维数字岩心的地层因素和渗透率,数值模拟结果与实验结果相符。相比传统模拟退火算法,混合法重建数字岩心的传导特性更接近真实岩心的传导特性。     

Global SH-wavefield calculation for a two-dimensional whole-Earth model with the parallel hybrid PSM/FDM algorithm

We present a parallel hybrid algorithm based on pseudospectral method (PSM) and finite difference method (FDM) for two-dimensional (2-D) global SH-wavefield simulation. The whole-Earth model is taken as a cross section of spherical Earth, and corresponding wave equations are defined in 2-D cylindrical coordinates. Spatial derivatives in the wave equations are approximated with efficient and high accuracy PSM in the lateral and high-order FDM in the radial direction on staggered grids. This algorithm allows us to divide the whole-Earth into sub-domains in radial direction and implement efficient parallel computing on PC cluster, while retains high accuracy and efficiency of PSM in lateral direction. A transformation of moment tensor between 3-D spherical Earth and our 2-D model was proposed to give corresponding moment tensor components used in 2-D modeling. Comparison of modeling results with those obtained by direct solution method shows very good accuracy of our algorithm. We also demonstrate its feasibility with a lateral heterogeneous whole-Earth model with localized velocity perturbation.