Fast imaging and inversion of on and off shore electromagnetic data

We consider thin layer algorithms for inversion of electromagnetic data acquired on large experimental grids. These algorithms do not involve targeted search of the model parameters. Instead, they determine an integrated characteristic of the model, i.e. heterogeneous conductance or transverse resistance, using a filtration technique developed for thin layer models, which adequately represent the geo-electric situation by a sequence of laterally homogeneous and heterogeneous layers. The corresponding filter reflects impedance/admittance relations between different components of the electromagnetic field in the stratified part of the model. Convolution of such filters with the data obtained from experimental measurements represents the most time consuming part of the computation. The convolution is carried out using a high performance algorithm, which makes the process of inversion extremely fast. The choice of a particular inversion algorithm is dictated by the specific geo-electric situation in the area of interest and the electromagnetic data subject to interpretation. Typically, most computations can be carried out in up to several minutes using a regular desktop or laptop PC.We restrict our consideration to two simplest algorithms for determination of the conductance of heterogeneous conductive layers (S-algorithm) and the transverse resistance of heterogeneous resistive layer (T-algorithm). The algorithms can be useful for interpretation of data acquired in on- and off-shore conditions with natural and controlled sources. Inversion can be jointly carried out for data sets collected for different source locations, at different frequencies, etc. Likewise, the algorithms can be used for interpreting the data collected using a moving source.Performance of the algorithms is demonstrated on a set of test inversions of numerically simulated data sets. The first group of the examples is typical for environmental applications. It is studied using the S-algorithm applied to natural and controlled source measurements for shallow and deep targets. The T-algorithm is applied for delineation of a gas hydrate type of reservoir using the data numerically simulated for such a problem.In geo-electrical situations that can be addressed using thin layer models, results of inversion hardly require any further elaboration. For instance, this happens when parameters of the heterogeneous layer satisfy thin layer conditions and its thickness can be determined from seismic measurements. When this is not the case, the model found by a thin layer inversion usually reveals correct location of the anomalous body and provides reasonable estimate of its integrated electric properties. In such situations the algorithm works as an imaging technique, which together with seismic information on the layer boundaries provides a justified initial model for a full scale 3D inversion and hopefully allows for avoiding pitfalls associated with a straightforward application of more traditional 3D inversion algorithms.     

An efficient regularized inversion approach for self-potential data interpretation of ore exploration using a mix of logarithmic and non-logarithmic model parameters

A very fast and efficient approach to self-potential (SP) data inversion for ore exploration has been developed. This approach is based on Tikhonov regularization and the conjugate gradient method, and simultaneously inverts for the depth (z), electric dipole moment (k), and angle of polarization (θ) of a buried anomalous body from SP data measured along a profile. This inversion algorithm works iteratively, and solves for z and k in the logarithmic-space (log(z) and log(k)), and solves for θ in the linear-space (non-logarithmic). It is found that the original inversion formulation that uses the model parameters themselves (z, k and θ) is unstable and divergent. It is also found that the inversion formulation that uses the logarithm of the model parameters (log(z), log(k) and log(θ)) is unstable and divergent. Rather, the new inversion scheme that is based on the aforementioned mixed log-linear combination of the model parameters (log(z), log(k), and θ) overcomes and eliminates the mentioned instability and divergence problems. The sensitivity analysis and numerical experiments investigated have indicated that the new approach has a far better and far more optimized minimization search direction. This proposed technique fits the observed data by some geometrically simple body in the restricted class of vertical cylinder, horizontal cylinder, and sphere models. The applicability of the algorithm has been demonstrated on various reliable synthetic data sets with and without noise. The algorithm has been carefully and successfully applied to six real data examples, with ore bodies buried in different complex geologic settings and at various depths in the subsurface. The method is shown to be highly applicable for mineral exploration, and is of particular value in cases where the SP observed data is due to ore body embedded in the subsurface. On average, it took about 40 s of computation (not CPU) time on a 1 GHz PC.     

Graph theory and digitization of geological maps

A method is presented which describes rational digitization and efficient treatment of a geologic map. An oriented graph, S,the arcs of which are associated with stratigraphic boundaries and imply a difference in the topological nature of the map if it includes faults, is used. From S,we deduce other graphs: a dendrogram which is used to structure the data and a graph which summarizes the geologic properties of the map. This structure is useful for graphic reconstitutions on a plotter or screen, and for quantitative correlation and calculation of dips, surfaces, and volumes.     

基于非结构三角网格的海洋CSEM和MT二维联合反演研究

采用非结构三角形网格结合快速Occam算法对海洋可控源电磁(CSEM)与大地电磁(MT)数据进行二维联合反演试验研究.非结构三角形网格能够准确地模拟起伏地形和复杂地质构造,对反演目标区域采用精细网格剖分,其他区域采用粗网格剖分,在满足精度的前提下减少了不必要的计算量.将CSEM与MT数据加入到同一反演数据集中,通过对联...     

Three-dimensional finite element modelling of stress relaxation tests in anisotropic clayey medium: direct problem and back analysis

This paper deals with a new strategy for initial stress identification by stress relaxation methods, coupled with finite element calculation, and applied to the overcoring test. The back-analysis of such a test uses an inversion method which consists in the minimisation, with a gradient-based algorithm, of a cost functional of least-squares type, which quantizes the difference between measured and computed strains. The computed strains are assessed by three-dimensional finite element modellings of the overcoring test. The inversion methodology is applied to a recent in situ overcoring test performed at Mont Terri laboratory, Switzerland. The inversion gave good results and allows us to validate the inversion methodology. The constitutive law considered for this application is transverse isotropic elasticity but the inversion method developed is applicable to most constitutive laws and every kind of in situ test.     

绕射波信息提取与成像技术研究——以某盆地海相碳酸盐岩为例

绕射波是提高地震分辨率或超分辨率的重要信息载体,绕射波的提取与成像技术是地震勘探提取小尺度异常体的有效途径.基于传统的反射成像的处理过程没有充分地利用到绕射信息,特别是一些常规处理方法通常对绕射信息有着压制作用.为了进一步提高地震资料中绕射波的使用效率,重点研究了在成像道集上采用预测反演算法对绕射波进行提取与成像,并以...     

Multiple response surfaces for slope reliability analysis

This paper develops a multiple response surfaces approach to approximate the limit state function for slope failure by second‐order polynomial functions, to incorporate the variation of the most probable slip surfaces, and to evaluate the slope failure probability p_f. The proposed methodology was illustrated through a cohesive soil slope example. It is shown that the p_f values estimated from multiple response surfaces agree well with those p_f values that have been obtained by searching a large number of potential slip surfaces in each Monte Carlo simulation (MCS) sample. The variation of number of the most probable slip surfaces is studied at different scale of fluctuation (λ) values. It is found that when full correlation assumed for each of random fields (i.e., spatial variability is ignored), the number of the most probable slip surfaces is equal to the number of random fields (in this study, it is 3). When the spatial variability grows significantly, the number of the most probable slip surfaces or number of multiple response surfaces firstly increases evidently to a higher value and then varies slightly. In addition, the contribution of a specific most probable slip surface varies dramatically at different spatial variability level, and therefore, the variation of the most probable slip surfaces should be accounted for in the reliability analysis. The multiple response surfaces approach developed in this paper provides a limit equilibrium method and MCS‐based means to incorporate such a variation of the most probable slip surfaces in slope reliability analysis. Copyright © 2014 John Wiley & Sons, Ltd.     

Reliability of selected procedures of stress inversion and data separation for inhomogeneous populations of calcite twins and striated faults: insights from numerical experiments

In the course of numerical experiments selected algorithms for stress tensor inversion and separation of heterogeneous populations of calcite twins and striated faults were tested. Artificial data sets were created in a manner simulating natural processes. They were composed of data, dynamically compatible with one or two stress tensors and chaotic “noise” imitating natural imperfections. For calcite twins the classical inversion procedure is considered valid, with restrictions regarding a high proportion of chaotic data, when shape ratio of the stress tensor Φ is poorly constrained. The algorithm of Etchecopar (1984 fide Tourneret and Laurent in Tectonophysics 180:287–302, 1990) devised originally for calcite twins has been modified and applied to fault/slip data, facilitating a rejection of incompatible outliers. Two main classes of data separation procedures were tested: separation contemporary with inversion and separation prior to inversion, utilising hierarchical clustering. The separation contemporary with inversion performs moderately but often fails with complex calcite twin sets. The performance of hierarchical clustering is high, but only with a σ ₁ orientation as a similarity criterion—the new strategy introduced in this contribution. For fault/slip data the hierarchical clustering with the right-dihedra construction as the similarity criterion (Nemcok et al. 1999) is satisfactory. Additionally, a new approach is proposed for fault/slip data, utilising principles of the classical algorithm for heterogeneous populations of calcite twins. Validated algorithms for striated faults were successfully applied to a natural data set from the Holy Cross Mts (central Poland).     

Spatial variation of aftershock activity across the rupture zone of the 17 August 1999 Izmit earthquake, Turkey

We examined the spatial variation in the aftershock activity from the 17 August 1999 Izmit, Turkey earthquake. We found that this aftershock sequence is non-uniform both in space and time, aspects that need to be taken into account in any further statistical analysis. Other aspects of this aftershock sequence are similar to other aftershock sequences, namely low b-values and a high degree of spatial variation. We have detected three zones of relatively high b-values, two of which coincide with asperities revealed by previous slip inversion studies. The third zone with an anomalous b-value is located beyond the fault rupture and indicates a weakened fractured zone in the Yalova-Tuzla area. This b-value analysis provided no evidence for any significant difference that may exist between the two sides of the mainshock fault plane.     

The spatial extent of chemical equilibrium in some high-grade metamorphic rocks from the grenville of southeastern Ontario

Many of the recent studies of chemical equilibrium in metamorphic rocks may have been hampered by sampling which did not reflect single regions or domains of local equilibration. This paper records results of tests performed to determine the specific volume of rock in chemical equilibrium with respect to a certain phase, under a particular set of conditions. Two samples of high-grade metamorphic gneisses from the Grenville Series of southeastern Ontario were selected for intensive study. The garnets of one specimen, possessing a biotite-garnet-cordierite assemblage, underwent in situ laser microprobe spectrochemical determinations for Fe, Mg, Mn and Ca. Conclusions are thus possible as to the volumes over which free diffusion and chemical equilibrium took place. These volumes were found to be on the order of only a few cubic centimeters and their shapes are strongly controlled by rock structures such as foliation and lineation. A higher-grade pyroxene granulite was also investigated with respect to garnet and biotite equilibrium. Somewhat larger volumes of equilibration were noted in this rock.     

Distribution and mode of occurrence of zinc and lead in glacial soils

The distribution and mode of occurrence of zinc and lead have been examined in glacial soils developed over a complex Precambrian marble-paragneiss terrain in the Adirondack Mountains of New York. Based on distribution within the soil profiles, zinc is enriched in the B₁ horizon of soils sampled over marble and lead is generally enriched in the A horizon, particularly in soils developed over paragneiss. Contrast is calculated using

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, where is the mean of n_A anomalous and n_B background samples, and S_p is the pooled standard deviation) for zinc, lead and cold-extractable heavy metals in soils sampled over marble and paragneiss. The t-values indicate that the B₁, soil horizon is the most suitable for sampling on a regular basis, even though lead is most concentrated in the A horizon.The distribution of zinc and lead among exchangeable, organic, iron-manganese oxide, clay, silt and sand fractions of B₁ horizons from two anomalous and one background soil indicates that both zinc and lead are tied up principally in iron and manganese oxides. The anomalous samples exhibit zinc enrichment in the Fe-oxide digestion and high Mn/Fe ratios for the Mn-oxide digestion (as well as the total analysis). In terms of total contribution to the sample, significant proportions of zinc in the clastic fraction can be attributed to zinc substitution into clays plus the ineffective removal of Fe-oxides by the ammonium oxalate extraction procedure. Lead, on the other hand, occurs in significant concentrations in clay, silt and sand as well as Fe- and Mn-oxides, probably as a trace constituent in feldspars or adsorbed onto clay surfaces.     

Stable methods of interpretation of gravimetric data

A method for interpretation of potential geophysical fields, based on a stable inversion algorithm, is proposed. The stability of the algorithm is provided by an original choice of the zero approximation model and stepwise solution of the inverse problem by a correctness set. The three-dimensional density distribution of local structures as grid functions is reconstructed by layer-wise anomalies of a spilt field. Examples of interpretation of the practical gravimetric data illustrating the efficiency of the method are given.

     

基于探地雷达的路基地下异常体全波形反演

路面塌陷及地下空洞隐患往往较为隐蔽且事发突然,造成了人们生命和财产的巨大损失,对于道路塌陷及地下空洞隐患的检测分析显得至关重要。探地雷达(Groud Penetrating Radar, GPR)因其具有精度高、效率快、连续无损、实时成像等优点,是目前城市道路塌陷隐患探测的主要方法。针对GPR传统目标函数全波形反演(Full Waveform Inversion, FWI)中激励源子波估计不准确而导致反演准确性和可靠性降低的问题,提出了一种褶积型目标函数FWI算法。对于路面塌陷及地下空洞2种情况,通过建立合成数据模型,与传统目标函数FWI的反演结果进行对比,说明了褶积型目标函数FWI算法在激励源子波估计不准确的情况下依然可以得到良好的反演结果,验证了该算法的有效性;最后将该算法用于2组不同灾害类型的GPR实测数据中,分析反演得到的地下介质相对介电常数分布情况,验证了褶积型目标函数FWI算法对于实测数据的实用性,从而为路基地下异常体探测提供理论依据。      

The Hilina Pali palaeomagnetic excursion and possible self‐reversal in the loess from western Ukraine

A loess‐palaeosol succession from the last glacial cycle was palaeomagnetically studied in the Rivne abandoned brickyard (western Ukraine). Two samples of undisturbed loess from the same depth of parallel sections display steep negative inclinations. These reversed directions in the loess dated at c. 18 ka may possibly be correlated with the Hilina Pali palaeomagnetic excursion. This is the first occurrence of the Hilina Pali in a loess sediment. Unfortunately, the loess with negative inclination does not form any continuous layer that could be suitable for studies of detailed features of geomagnetic field inversion. Another six samples from an illuvial horizon of the Holocene soil also showed negative inclinations and strongly deviated declinations. This part of the section does not represent, however, any palaeomagnetic excursion. The anomalous magnetization in maghemite‐ and titanomagnetite‐rich sediment results most probably from self‐reversal remagnetization. A new insight into palaeomagnetic excursions noted in loess, especially in its parts affected by pedogenic processes, is recommended.     

Orthogonal polynomial trend surfaces for irregularly spaced data

The advantages of using orthogonal rather than nonorthogonal polynomials for trend-surface analysis are discussed briefly. A method for calculating orthogonal polynomial trend surfaces of any degree on the basis of irregularly spaced data is described. The method is illustrated with subsurface data for the elevation on top of the Devonian Dundee Limestone, Michigan.     

Comparative study between filtering and inversion of VLF-EM profile data

This paper discusses the practical use of filtering and inversion in VLF-EM data processing and interpretation. The advantages and disadvantages of both mentioned techniques were outlined to avoid the misleading interpretation of such data in some case studies. Much concern is taken to show the interval distance effect upon the correct depth identification of the anomalous body by either inversion or filtering. The methodology of the study is going through proposing an initial model, generating the synthetic VLF-EM data of the model by means of forward modeling, filtering (Karous–Hjelt filter) and inversion (Inv2DVLF software) of the synthetic data and comparing between the results of both methods and the initial model. The study reached to (1) Karous–Hjelt filter provides misleading depths for his limited depth of resolution and cannot provide estimates of deep targets if the profile is too small, whereas inversion provides exact results, particularly in case of shallow anomalous target; (2) crossover between in-phase and out-of-phase data could resulted from a small shallow conductive target or a large deep one; (3) selection of a reasonable environmental resistivity has an important impact on the inversion process; and (4) the numerical reflection resulted during VLF-EM data inversion could lead to an erroneous interpretation.     

Mean Traveltime Curves Analysis: A Method to Improve Understanding of Data Behaviour in 2-D Transmission Tomography at the Pre-Inversion Stage

Transmission tomography methods show a great sensibility to data variability, which eventually includes data errors, often present in field experiments. Local optimization methods, traditionally used to solve this inverse problem, are very sensitive to these difficulties, failing to converge properly in the presence of spurious data. Regularization methods partially cope with these weaknesses, damping the instabilities.A complementary approach, adopted here, is to perform a structured analysis of data variability before the inversion, oriented to discriminate the contribution of errors from that of true geological heterogeneities. The key concept of mean traveltime curves ( and ) is introduced and described. Their analytical equations are deduced for isotropic homogeneous media and any recording geometry. Empirical mean traveltime curves can be inferred based solely on traveltime data, using the corresponding discrete estimators. The methodology proposed here proceeds through a user-defined subdivision of the domain of interest into isotropic homogeneous areas. Least squares velocity estimations and associated data misfits are used to scrutinize the behaviour of the implied source-receiver sets and of the ray-swept part of the geologic medium. Data are considered suspicious if zonal estimated velocities are non-consistent with a priori information. Also, independent fitting of both empirical curves helps to classify the genesis of the residuals: some situations are illustrated.Finally, we show the application of this technique to a data set from the Grimsel test site in Switzerland. Using this methodology, we detect some anomalous gathers, which may be responsible for the large range of velocities found in the initial imaging with this data set. Also, we give some indications of the possible sources of these anomalies. This approach offers a quick data variability analysis in the pre-processing stage, which, even if no data editing algorithms are finally used, always improves the understanding of the data structure.     

定回线源瞬变电磁三维异常特征反演

分析了实现定回线源瞬变电磁三维异常特征反演的可行性,简要地介绍了改进的广义逆反演方法基本原理,给出了定回线源瞬变电磁三维异常特征反演的流程。对正演模拟数据进行反演的实例表明,定回线源瞬变电磁三维异常特征反演已得到初步实现。