近地表密度估计的重力贝叶斯分析方法及在云南地区的应用

基于布格重力异常相对于地形起伏光滑分布的约束条件,从一维自由空气重力异常数据出发,采用贝叶斯方法估算近地表岩石密度,同时采用三次B样条函数拟合布格重力异常,获取光滑分布的布格重力异常.数据拟合和光滑约束之间的权重采用Akaike贝叶斯准则(ABIC准则)自动确定.均匀剖分模型和不均匀剖分模型数据试验都验证了该方法的有效性.相关参数评价表明,足够多的样条系数可以提高估计结果的准确性,样条系数的个数接近测点数时可获得较稳定的估计结果.增大异常的噪声水平时,ABIC准则可有效地自动增大先验光滑约束的权重.云南地区两条重力剖面应用结果表明,剖面沿线的近地表密度值起伏变化明显(达2.45~2.8g·cm^-3),前寒武纪和古生代地层密度相对较高(主要为2.53~2.75g·cm^-3),而中生代密度较低(2.45~2.73g·cm^-3);本文估计的近地表密度结果与区域物性资料及地表地质特征较吻合;估计的剖面布格重力异常具有光滑性;红河断裂两侧近地表密度差异较大,可达0.4g·cm^-3.本文获得的两条剖面近地表密度结构和布格重力异常为该区深部结构与构造研究提供更可靠的重力基础数据.     

ESTIMATION OF THE DEGREE OF POLYNOMIAL FITTED TO GRAVITY ANOMALIES AND ITS APPLICATION1

A method for estimating the degree of polynomial fitted to gravity anomalies to evaluate the regional anomaly is presented. The anomaly can be fitted by polynomials of different degrees with the least-squares method and the optimum degree of the polynomial evaluating this anomaly can be estimated from the point of discontinuity of the gradient on a graph of variance against the polynomial degree. The Bouguer gravity is initially separated by upward continuation to a proper height and then the degree of regional polynomial to fit the Bouguer anomaly can be estimated. Theoretical and field examples show the effectiveness of the method.     

Crustal Structure of the Flood Basalt Province of Ethiopia from Constrained 3-D Gravity Inversion

The Oligocene Afar mantle plume resulted in the eruption of a large volume of basaltic magma, including major sequences of rhyolitic ignimbrites, in a short span of time across Ethiopia. In order to assess the impact of these magmatic processes on the crust and to investigate the general crustal configuration beneath the Ethiopian plateau, northern part of the Main Ethiopian Rift and the Afar depression, analysis and modeling of the gravity field have been conducted. The Bouguer gravity map is dominated by long-wavelength anomalies that primarily arise from the isostatic compensation of the topography. Consequently, anomalies within the crust/upper mantle are masked and quantitative interpretation becomes difficult. The long-wavelength anomalies are approximated using admittance technique and subsequently removed from the Bouguer anomalies to obtain the residual isostatic anomalies. The residual map contains both short- and intermediate-wavelength anomalies related to geologic and tectonic features. The long-wavelength regional isostatic field is used to map the crust-mantle interface and the results are in good agreement with those determined by other geophysical methods. Seismic constrained gravity inversion was performed on the isostatic residual field and series of three-dimensional models have been constructed for the structures of the crust and upper mantle beneath the uplifted and rifted flood basalt province of northern Ethiopia. The inversion results have shown that the NW plateau has thick crust that rests on normal lithospheric mantle. Afar, On the other hand, is marked by thin stretched crust resting on a low-density upper mantle indicating a hotter thermal regime and partial melt. No lithospheric mantle is observed beneath Afar. The models further indicate the presence of an extensive sub-crustal thick (~12 km on average) and high-density (~3.06 gm/cc) mafic accreted igneous layer of fractionated cumulate (magmatic underplating) beneath the NW plateau. The study suggests that the underplate was fundamental to the accretion process and may have played a role in compensating most of the plateau uplift and in localizing stresses.     

Shortcomings in the determination of regional fields by polynomial fitting: A simple solution

The procedure of polynomial fitting by least-squares technique to obtain the regional field from potential field data is commonly used in processing geophysical data. However, it has been found that the unguarded use of this procedure with measured field data may lead to erroneous regional fields. This is due to the fact that the least-squares technique pre-supposes a random variation of the residual or anomaly field. This condition is rarely fulfilled in measured field data where there is the common occurrence of ‘deviatory field points’ in the residual field data. In this paper, a procedure to overcome the problem using robust statistics is described with the straight-forward Downhill Simplex method used to obtain the optimum coefficients for the polynomial. The method is illustrated with aeromagnetic field data from the Mamfe basin of Nigeria and Cameroon. The result shows that the trend of the regional field obtained from robust statistics is consistent with the trend in the aeromagnetic field obtained by using the method of cross-correlation trend analysis.     

Gravimetric study of a potential mineral deposit in the Itapororoca region, Brazil

A semi-detailed gravity survey was carried out over an area of 650 km² localized in the Eo-Neoproterozoic coastal zone of Paraiba State where 548 new gravity stations were added to the existing database. Gravity measurements were made with a LaCoste and Romberg model G meter with a precision of 0.04 mGal. The altitude was determined by barometric levelling with a fixed base achieving a 1.2 m measure of uncertainty, corresponding to an overall accuracy of 0.24 mGal for the Bouguer anomaly. The residual Bouguer map for a 7th degree regional polynomial showed a circumscribed negative anomaly coincident with a localized aero-magnetic anomaly and with hydro-thermally altered outcrops, near the city of Itapororoca. The 3D gravity modelling, constrained by geologic mapping was interpreted as a low density, fractured and/or altered material with a most probable volume of approximately 23 km³, extending to about 8,500 m depth. This result is in accordance with a volcanic body associated with hydrothermal processes accompanied by surface mineralization evidence, which may be of interest to the mining industry.     

Sea gravity data in the Gulf of Naples. A contribution to delineating the structural pattern of the Phlegraean Volcanic District

Bathymetric and gravity surveys were carried out from 1988 to 1994, in the Gulf of Naples (Southern Italy) to offshore extend the already existing Bouguer anomaly map. In order to improve the knowledge of the structural setting beneath the active Neapolitan volcanoes (Vesuvio, Campi Flegrei and Ischia), 862 stations were surveyed within the isobath of 400 m; at the same time, and about 2000 on-land gravity values were also collected. A new Bouguer anomaly map spanning the whole volcanic region was drawn from the final data set. Gravity anomalies were referred to the new absolute gravity station in Naples and computed according to 1980 Geodetic Reference System. Finally, a density value of 2200 kg/m³ was used in the computation of the Bouguer and terrain effects. We carried out the inversion of the gravity anomalies adopting a 2.5-D modelling along selected profiles crossing the investigated area. The interpretative models were constrained to data obtained from deep wells and other geophysical investigations.     

基于软约束模式的波阻抗反演

通过在目标函数中增加先验知识约束,我们可以解决波阻抗反演的病态问题及带限问题.基于马尔柯夫随机域（MRF）的邻域系统及势函数构建一种软性约束模式,将井眼约束信息外推到井间,避免过往强制约束的不足.马尔柯夫随机域的一阶邻域偏好于常数值区域,而模型中常梯度值区域和常曲率值区域分别需要用到二阶和三阶邻域,综合使用三种类型的邻域可以改善反演效果.通过理论模型试算和实际资料处理,证明了本文提出的约束模式具有非强制性约束特点,实用性强.     

格莱尼改正及其在地球物理数据处理中的意义

格莱尼改正是重力改正的一种,是对球面半径约166.7 km以外地形和均衡造成的重力综合效应的改正,改正后所得格莱尼异常可对应研究区范围内地壳结构特征,具有重要的研究意义.但近年来国内的重力研究中,对格莱尼改正的认识和重要性还不是十分透彻,特别是在大区域研究中,忽略这一远区重力效应可能会对研究结果的解释造成误导.针对这一问题,本文介绍了格莱尼改正的含义、由来与研究历史,指出了在大区域研究中需要考虑格莱尼效应的重要性,以“扇形球壳块”法为例给出了格莱尼改正的计算原理,列举了格莱尼异常在地球物理中的常见应用,并通过重力改正与莫霍面深度反演实例,通过对反演结果的控制点检测与精度评价,指出格莱尼异常反演所得莫霍面埋深更接近地震方法结果,从而表明了格莱尼改正在地球物理研究中的不可忽视性,并指出完全布格改正与格莱尼改正在计算方法上可实现统一.     

3D upper crustal density structure of the Deccan Syneclise,Central India

A constrained 3D density model of the upper crust along a part of the Deccan Syneclise is carried out based on the complete Bouguer anomaly data. Spectral analysis of the complete Bouguer gravity anomaly map of the study region suggests two major sources: short wavelength anomalies (<100 km) caused primarily due to the density inhomogeneities at shallow crustal level and long wavelength anomalies (>100 km) produced due to the sources deeper than the upper crust. A residual map of the short wavelength anomalies is prepared from the complete Bouguer anomaly using Butterworth high‐pass filter (100 km cut‐off wavelength). Utilizing the constraints from deep resistivity sounding, magnetotellurics and deep seismic sounding studies, 2.5D density models have been generated along 39 profiles of this region. The mismatch between the calculated response of the a priori 2.5D model with the residual (short wavelength) gravity anomalies is minimized by introducing high‐density intrusive bodies (≥2.81 g/cm³) in the basement. With these 2.5D density models, the initial geometry of our 3D density model, which includes alluvium, Deccan trap, Mesozoic sediment and high‐density intrusive bodies in the basement up to a depth of 7 km (upper crust), is generated. In the final 3D model, Deccan trap extends from 200 m to nearly 1700 m below the 90–150 m thick Quaternary sediment. Further down, the sub‐trappean Mesozoic sediment is present at a depth range of 600–3000 m followed by the basement. The derived 3D density model also indicates six intrusive bodies of density 2.83 g/cm³ in the basement at an average depth of about 4–7 km that best fits the residual gravity anomaly of the study area.     

基于一种改进凸集投影方法的地震数据同时插值和去噪

基于稀疏反演的地震插值方法是一种重要的插值方法,然而大多数这类方法只针对无噪声数据或者高信噪比数据插值.实际上,地震数据含有各种噪声,使得插值问题变得更加困难.凸集投影方法是一种高效的插值算法,但是对于含噪声数据的插值效果不理想,针对含噪声数据提出的加权凸集投影方法能够实现同时插值和去噪,但是除了最小阈值需要认真选取外,增加一个权重因子来实现去噪功能.本文由迭代阈值算法推导出加权凸集投影方法,证明其是解无约束优化问题的一种方法,加权因子可以看作拟合误差项的系数.本文还提出了一种改进的凸集投影方法,与原始凸集投影方法相比该方法不需要增加任何计算量,只要通过阈值的选择来进行插值和去噪.数值模拟证明了该算法的计算效率,并且对含噪声数据能够实现较好的插值效果;先插值后去噪的结果证明了同时去噪和插值算法的可靠性和稳定性.     

黄海及邻区莫霍面起伏特征

针对地壳构造形成的动力学机制,在广泛收集区域地质、地质构造和地球物理等资料的基础上,着重对重力数据进行了数字化、坐标、重力公式、投影方式和比例尺的统一化处理,进而进行了网格化处理.为将区域异常和局部异常分离开来,以便以对深部构造的系统研究,笔者选取趋势分析法分别对研究区内预处理后的布格重力异常数据(Δg)进行了三维多项式迭代拟合计算,得到了区域布格重力异常二阶、五阶、十阶趋势分析结果.继而,利用二级近似公式迭代法对布格重力异常五阶趋势分析区域异常数据进行了三维运算处理,得到了黄海及周边地区的莫霍面埋深值.分析了黄海及邻区莫霍面起伏特征,并进行了深部构造区划,探讨了深部断裂构造与莫霍面起伏间的成因联系,为深部构造和活动断裂演化的地球动力学研究提供了依据.     

Exponential data fitting applied to infiltration, hydrograph separation, and variogram fitting

Most lumped rainfall-runoff models separate the interflow and groundwater components from the measured runoff hydrograph in an attempt to model these as hydrologic reservoir units. Similarly, rainfall losses due to infiltration as well as other abstractions are separated from the measured rainfall hyetograph, which are then used as inputs to the various hydrologic reservoir units. This data pre-processing is necessary in order to use the linear unit hydrograph theory, as well as for maintaining a hydrologic budget between the surface and subsurface flow processes. Since infiltration determines the shape of the runoff hydrograph, it must be estimated as accurately as possible. When measured infiltration data is available, Horton’s exponential infiltration model is preferable due to its simplicity. However, estimating the parameters from Horton’s model constitutes a nonlinear least squares fitting problem. Hence, an iterative procedure that requires initialization is subject to convergence. In a similar context, the separation of direct runoff, interflow, and baseflow from the total hydrograph is typically done in an ad hoc manner. However, many practitioners use exponential models in a rather “layer peeling” fashion to perform this separation. In essence, this also constitutes an exponential data fitting problem. Likewise, certain variogram functions can be fitted using exponential data fitting techniques. In this paper we show that fitting a Hortonian model to experimental data, as well as performing hydrograph separation, and total hydrograph and variogram fitting can all be formulated as a system identification problem using Hankel-based realization algorithms. The main advantage is that the parameters can be estimated in a noniterative fashion, using robust numerical linear algebra techniques. As such, the system identification algorithms overcome the problem of convergence inherent in iterative techniques. In addition, the algorithms are robust to noise in the data since they optimally separate the signal and noise subspaces from the observed noisy data. The algorithms are tested with real data from field experiments performed in Surinam, as well as with real hydrograph data from a watershed in Louisiana. The system identification techniques presented herein can also be used with any other type of exponential data such as exponential decays from nuclear experiments, tracer studies, and compartmental analysis studies.     

Main crustal discontinuities of Morocco derived from gravity data

Sharp linear gradients in maps of potential field data are generally assumed to result from sharp discontinuities or boundaries between rocks having different densities or magnetic susceptibilities and are usually associated with faults or other geological contacts. The computation of the horizontal gradients of the gravity field permits us to localize the limits of such blocks and then the fault locations. The horizontal derivative maxima of the Bouguer anomaly and its upward continuation at several heights show lineaments that could reflect the layout of faults and/or contacts and their dip directions. The application of this method to the Bouguer anomaly map of Morocco (with 19,571 points, using an average crustal density ρ = 2.67 g/cm³) allowed us to perform a multiscale analysis of the gravimetric lineaments of the country. The obtained structural map is consistent with several faults already identified in previous studies, and highlights five new major subsurface faults systems with location and dip: the Saghro fault system; Bou-Arfa Midelt fault system; Sidi Slimane Mezquitem fault; Ksar El Kebir–Chefchaouen fault and the Rifan West Mediterranean fault. In addition, this study suggests a new shape and localization for the Agadir-Oujda trans-Moroccan major fault with a NE-SW direction and 900 km length, subdividing Morocco into two main domains. The results of this study contribute to the improvement of the regional structural map of the north western part of Africa, which is situated within the convergence zone between Africa and Eurasia.     

A REGIONAL GRAVITY STUDY OF THE NORTHERN NORTH SEA (56–62° N)*

A Bouguer gravity anomaly map is presented of the North Sea and adjacent land areas in Norway and Denmark, covering an area situated between 56° and 62°N, 1°W and 10°E. The gravity data from the UK sector of the North Sea, the land and offshore areas of Denmark, and the land areas of Norway have been published before. However, the gravity data from the Norwegian sector of the North Sea are new. A large number (about 60) of individual gravity features can be defined in the mapped area. Most of those situated in the UK sector of the North Sea and on land in Norway have been discussed earlier; however, most of the anomalies found elsewhere which are qualitatively interpreted here have not been discussed before. An interpreted Bouguer anomaly map is presented which identifies all these features. The majority of the gravity anomalies encountered in the mapped area can be shown to be associated with one of the following geological features: (i) basement highs, (ii) large bodies of heavy basic or ultrabasic rock in the crystalline basement, (iii) large igneous intrusions within the sedimentary column and thick accumulations of volcanic rocks or their associated eruption centers, (iv) major basement faults. Large-scale geological structures such as the Central, Viking and Sogn Grabens and the East Shetland, Stord, Forth Approaches and Norwegian-Danish Basins are essentially in isostatic equilibrium and are only locally marked by relatively weak gravity minima. A residual gravity anomaly map has been produced by subtracting from the observed Bouguer anomalies the estimated gravity effect of an assumed thinned crust. This residual gravity anomaly map shows a number of features of the Bouguer anomaly field with greater clarity.     

On Two-Dimensional Modeling Of Magnetotelluric Field Data

In this paper, some recent topics on the modeling of magnetotelluric data are introduced. The focus is on the handling of real field data for two-dimensional resistivity modeling. First, the removal of the effects of near surface heterogeneity is reviewed. It covers telluric distortions (phase mixing and static shift) and magnetic distortions using conventional Groom-Bailey type 3D/2D model (three-dimensional local anomaly underlain by regional two-dimensional structure). The extension of a 3D/2D distortion model for multi-site, multi-frequency is a new development. Magnetic distortion seems to be less significant for land observations, but significant for sea floor data, where the regional magnetic field is weak due to seawater. In special cases involving for example, distortion due to topography and bathymetry, explicit removal is possible. There are some schemes proposed for a 3D/3D model (three-dimensional local anomaly underlain by regional three-dimensional structure). Along with the removal of the distortion, it is important to recognize the dimensionality of the dataset prior to modeling. A property using strike estimates for each site is an indicator for dimensionality which is unaffected by local distortion. Mapping the local strike or a rose diagram is an effective visualization of the dimensionality.Two-dimensional inversion is becoming routine. For the fast calculation of derivatives, approximate calculation, reciprocity or conjugate gradient methods are used. In order to incorporate a priori information and to overcome the intrinsic ill-posed nature of the inversion problem, imposing constraints on the model structure is important. A proper tradeoff between the data fit and constraints should be optimized to obtain minimum structures that are required by the field data. However, the choice of constraints is rather subjective and depends on the geological situations. For field data, two-dimensional inversion has limits on modes, area, and period range. Special care must be taken for the structure outside the profile. Two-dimensional inversion incorporating anisotropy is interesting and becoming popular, but the structure may not be unique. Future development in three-dimensional inversion for real datasets should take the above points into consideration.     

Location of secondary faults from cross-correlation of the second vertical derivative of gravity anomalies1

A method is described to locate secondary faults, which can be difficult to identify on the Bouguer gravity map. The method is based on cross-correlation between the theoretical anomaly due to a vertical step and the second vertical derivative of the Bouguer anomaly. Faults are located from the closed maxima and minima on the cross-correlation contour map calculated for two perpendicular directions. One-dimensional model computations show that the magnitude of the extremum of the cross-correlation is related to the depth to the top of the hanging wall and the throw of the fault. Application of the method to the Bouguer gravity map of the former mouth of the Yellow River in the Shengli Oilfield area near the Bo Hai Sea shows the effectiveness of the method.     

临汾强震区地壳结构及发震背景研究

以诸城—宜川深地震测深速度剖面为约束, 对沿该剖面得到的高精度重力数据进行拟合, 并对临汾强震区平面布格重力异常进行处理, 得到了该地区地壳密度结构及平面重力异常分布． 利用上述结果分析了临汾强震区的地壳结构及构造环境, 结合前人相关研究成果, 认为临汾强震区地壳中存在塑性相对较强的介质, 洪洞和临汾两次历史地震皆发生在其与周边弹性介质的转换边界上． 另外, 临汾凹陷南北两侧局部构造环境存在差异, 在区域应力场作用下, 导致了洪洞地震和临汾地震的发生. 两次地震在发震时间、 地点和震级等地震要素上有所不同．      

Minimum relative entropy and probabilistic inversion in groundwater hydrology

The similarity between maximum entropy (MaxEnt) and minimum relative entropy (MRE) allows recent advances in probabilistic inversion to obviate some of the shortcomings in the former method. The purpose of this paper is to review and extend the theory and practice of minimum relative entropy. In this regard, we illustrate important philosophies on inversion and the similarly and differences between maximum entropy, minimum relative entropy, classical smallest model (SVD) and Bayesian solutions for inverse problems. MaxEnt is applicable when we are determining a function that can be regarded as a probability distribution. The approach can be extended to the case of the general linear problem and is interpreted as the model which fits all the constraints and is the one model which has the greatest multiplicity or “spreadout” that can be realized in the greatest number of ways. The MRE solution to the inverse problem differs from the maximum entropy viewpoint as noted above. The relative entropy formulation provides the advantage of allowing for non-positive models, a prior bias in the estimated pdf and `hard' bounds if desired. We outline how MRE can be used as a measure of resolution in linear inversion and show that MRE provides us with a method to explore the limits of model space. The Bayesian methodology readily lends itself to the problem of updating prior probabilities based on uncertain field measurements, and whose truth follows from the theorems of total and compound probabilities. In the Bayesian approach information is complete and Bayes' theorem gives a unique posterior pdf. In comparing the results of the classical, MaxEnt, MRE and Bayesian approaches we notice that the approaches produce different results. In␣comparing MaxEnt with MRE for Jayne's die problem we see excellent comparisons between the results. We compare MaxEnt, smallest model and MRE approaches for the density distribution of an equivalent spherically-symmetric earth and for the contaminant plume-source problem. Theoretical comparisons between MRE and Bayesian solutions for the case of the linear model and Gaussian priors may show different results. The Bayesian expected-value solution approaches that of MRE and that of the smallest model as the prior distribution becomes uniform, but the Bayesian maximum aposteriori (MAP) solution may not exist for an underdetermined case with a uniform prior.     

Using wind run to predict sand drift

Conventional aeolian sand transport models relate mass transport rate to wind speed or shear velocity, usually expressed and empirically tested on a 1-s time scale. Projections of total sand delivery over long time scales based on these models are highly sensitive to any small bias arising from statistical fitting on empirical data. We analysed time series of wind speed and sand transport rate collected at 14 independent measurement stations on a beach during a prior field experiment. The results show that relating total sand drift to cumulative above-threshold wind run yields models which are more statistically robust when fitted on empirical data, generating smaller prediction errors when projected to longer time scales. Testing of different power exponents indicates that a linear relationship between sand drift and above-threshold wind run yields the best results. These findings inspire a speculative novel phenomenological model relating the mass flow of air in the boundary layer to the mass transport of sand over the surface. © 2020 John Wiley & Sons, Ltd.     

Inversion of gravity and topography data for the crust thickness of China and its adjacent region

Introduction Since the middle of the century, gravitational isostasy has been a fundamental hypothesis for inverting the gravity data to find the crust thickness. Geophysicists have done a lot of researches on using gravity data to investigate the depth of Moho discontinuity. Since 1980, the International Lithosphere Program emphasized the importance of investigating the Moho depth variation. Thereafter a lot of results have been published in the world (Braitenberg et al, 2000; Kaban et al,…