Extrapolated Tikhonov method and inversion of 3D density images of gravity data

Tikhonov regularization（TR） method has played a very important role in the gravity data and magnetic data process. In this paper, the Tikhonov regularization method with respect to the inversion of gravity data is discussed. and the extrapolated TR method（EXTR） is introduced to improve the fitting error. Furthermore, the effect of the parameters in the EXTR method on the fitting error, number of iterations, and inversion results are discussed in details. The computation results using a synthetic model with the same and different densities indicated that. compared with the TR method, the EXTR method not only achieves the a priori fitting error level set by the interpreter but also increases the fitting precision, although it increases the computation time and number of iterations. And the EXTR inversion results are more compact than the TR inversion results, which are more divergent. The range of the inversion data is closer to the default range of the model parameters, and the model features and default model density distribution agree well.

Coastal bathymetry inversion using SAR-based altimetric gravity data:A case study over the South Sandwich Island

The global bathymetry models are usually of low accuracy over the coastline of polar areas due to the harsh climatic environment and the complex topography.Satellite altimetric gravity data can be a supplement and plays a key role in bathymetry modeling over these regions.The Synthetic Aperture Radar(SAR)altimeters in the missions like CryoSat-2 and Sentinel-3A/3B can relieve waveform contamination that existed in conventional altimeters and provide data with improved accuracy and spatial resolution.In this study,we investigate the potential application of SAR altimetric gravity data in enhancing coastal bathymetry,where the effects on local bathymetry modeling introduced from SAR altimetry data are quantified and evaluated.Furthermore,we study the effects on bathymetry modeling by using different scale factor calculation approaches,where a partition-wise scheme is implemented.The numerical experiment over the South Sandwich Islands near Antarctica suggests that using SARbased altimetric gravity data improves local coastal bathymetry modeling,compared with the model calculated without SAR altimetry data by a magnitude of 3:55 m within 10 km of offshore areas.Moreover,by using the partition-wise scheme for scale factor calculation,the quality of the coastal bathymetry model is improved by 7.34 m compared with the result derived from the traditional method.These results indicate the superiority of using SAR altimetry data in coastal bathymetry inversion.

Three-dimensional conjugate gradient inversion of magnetotelluric full information data

Based on the analysis of impedance tensor data, tipper data, and the conjugate gradient algorithm, we develop a three-dimensional （3D） conjugate gradient algorithm for inverting magnetotelluric full information data determined from five electric and magnetic field components and discuss the method to use the full information data for quantitative interpretation of 3D inversion results. Results from the 3D inversion of synthetic data indicate that the results from inverting full information data which combine the impedance tensor and tipper data are better than results from inverting only the impedance tensor data （or tipper data） in improving resolution and reliability. The synthetic examples also demonstrate the validity and stability of this 3D inversion algorithm.

3D inversion of borehole gravity data using cokriging

Borehole gravity has been used in mineral exploration recently with the advent of slim-hole gravimeters. It is logical to perform inversion to utilize the information in the newly acquired data. The inversions were carried out by using cokriging,which is a geostatistical method of estimation that minimizes the error variance by applying cross-correlation between several variables. In this study the estimated densities are derived by using boreholes gravity and known densities along the borehole. This method does not need iterative process and computes efficiently. The selection of examples demonstrates that this method has the ability to include physical property from borehole measurements in the inversion. The synthetic examples demonstrate the density variation along a borehole can be well determined without depth constraints in the inversion. The resolution of the recovered model can be further improved by including the densities along the borehole for inversion. However,this capability decreases dramatically with the increasing of distance between the anomalous body and the borehole.

Application of 3D Seismic Data Inversion to Coal Mining Prospecting

Seismic inversion is one of the most important methods for lithological prospecting . Seismic data with lowresolution is converted into impedance data of high resolution which can reflect the geological structure by inversionThe inversion technique of 3D seismic data is discussed from both methodological and theoretical aspects, and the in-version test is also carried out using actual logging data. The result is identical with the measured data obtained fromroadway of coal mine. The field tests and research results indicate that this method can provide more accurate data foridentifying thin coal seam and minor faults.

A 3D Geological Model Constrained by Gravity and Magnetic Inversion and its Exploration Implications for the World-class Zhuxi Tungsten Deposit, South China

The Zhuxi tungsten deposit in Jiangxi Province,South China,contains a total W reserve of about 2.86 Mt at an average grade of 0.54 wt%WO3,representing the largest W deposit in the world.Numerous studies on the metallogeny of the deposit have included its timing,the ore-controlling structures and sedimentary host rocks and their implications for mineral exploration.However,the deep nappe structural style of Taqian-Fuchun metallogenic belt that hosts the W deposit,and the spatial shape and scale of deeply concealed intrusions and their sedimentary host rocks are still poorly defined,which seriously restricts the discovery of new deposits at depth and in surrounding areas of the W deposit.Modern 3 D geological modeling is an important tool for the exploration of concealed orebodies,especially in brownfield environments.There are obvious density contrast and weak magnetic contrast in the ore-controlling strata and granite at the periphery of the deposit,which lays a physical foundation for solving the 3 D spatial problems of the ore-controlling geological body in the deep part of the study area through gravity and magnetic modeling.Gravity data(1:50000)and aeromagnetic data(1:50000)from the latest geophysical surveys of 2016-2018 have been used,firstly,to carry out a potential field separation to obtain residual anomalies for gravity and magnetic interactive inversion.Then,on the basis of the analysis of the relationship between physical properties and lithology,under the constraints of surface geology and borehole data,human-computer interactive gravity and magnetic inversion for 18 cross-sections were completed.Finally,the 3 D geological model of the Zhuxi tungsten deposit and its periphery have been established through these 18 sections,and the spatial shape of the intrusions and strata with a depth of 5 km underground were obtained,initially realizing―transparency‖for ore-controlling bodies.According the analysis of the geophysical,geochemical,and geological characteristics of the Zhuxi tungsten deposit,we discern three principles for prospecting and prediction in the research area,and propose five new exploration targets in its periphery.

Optimization algorithm for rapid 3D gravity inversion

The practical application of 3D inversion of gravity data requires a lot of computation time and storage space.To solve this problem,we present an integrated optimization algorithm with the following components:(1)targeting high accuracy in the space domain and fast computation in the wavenumber domain,we design a fast 3D forward algorithm with high precision;and(2)taking advantage of the symmetry of the inversion matrix,the main calculation in gravity conjugate gradient inversion is decomposed into two forward calculations,thus optimizing the computational efficiency of 3D gravity inversion.We verify the calculation accuracy and efficiency of the optimization algorithm by testing various grid-number models through numerical simulation experiments.

FAST APPROXIMATE INVERSION OF MAGNETOTELLURIC(FAIMT) DATA FOR A HORIZONTALLY LAYERED EARTH WITH NEAR-SURFACE INHOMOGENEITIES

This paper discusses use of approximations and the Integral Mean Value Theorem to show that 6 coefficients approximately describe the distortions of near surface inhomogeneities on the MT field of a horizontally layered earth model. When these 6 coefficients are considered together with those of the magnetic field of a horizontally layered earth model,the analytic and approximate wave impedance equations can be derived for the MT response of a horizontally layered earth model with near-surface 2-D and 3-D inhomogeneities. These approximate wave impedance equations are used with inverted MT data for 2-D and 3-D forward modelling. Although these 6 coefficients cannot be determined before inversion,initial estimates can be used. The 6 coefficients and the asistivity and thickness of each layer of a horizontally layered earth can be obtained by using published inversion methods. The 6 coefficients give important informaion (depths and resistivities) on the near-surface inhomogenelties.The authors inverted 2-D and 3-D theoretical models for Fast Approximate Inversion of Magnetotelluric (FAIMT) data for a horizontally layered earth with near-surface inhomogeneities compares favorably with traditional invrsion methods, especially for inverting regional or basin structures. This method simplifies computation and gives a reasonable 1 -D geological model with fewer nonuniquenas problems.

Inversion of gravity gradient data based on spatial gradient weighting

Compared with traditional gravity measurement data,gravity gradient tensor data contain more high frequency information,which can be used to understand the earth's interior structure,mineral resources distribution etc. In this study,the authors present an algorithm for inverting gravity gradiometer data to recover the three-dimensional( 3-D) distributions of density. Spatial gradient weighting was used to constrain the extent of the body horizontally and vertically. A more accurate inversion result can be obtained by combining the prior information into the weighting function and applying it in inversion. This method was tested on synthetic models and the inverted results showed that the resolution was significantly improved. Moreover,the algorithm was applied to the inversion of empirical data from a salt dome located in Texas,USA,which demonstrated the validity of the proposed method.

ACQUIREMENT AND COMPUTER PROCESSING OF 3-D SURFACE SHAPE DATA

The laser scanning and CCD image-transmitting measurement method and principle on acquiring 3-D curved surface shape data are discussed. Computer processing technique of 3-D curved surface shape(be called“ 3 - D surface shape”for short) data is analysed. This technique in- cludes these concrete methods and principles such as data smoothing, fitting, reconstructing ,elimi- nating and so on. The example and result about computer processing of 3- D surface shape data are given .

3-D velocity structure in the central-eastern part of Qilianshan

The 3-D velocity tomography image of the central-eastern part of Qilianshan is obtained by the joint inversion of 3-D velocity structure and focal parameters based on the S-P data of micro-earthquakes recorded by the digital seismic network set up for a Sino-French cooperation program since 1996. The inversed velocity structure does primarily reflect some important features of the deep structure in the region and provide the scientific background for the further study of active tectonic structure and the calculation of earthquake parameters.

Earthquake relocation and 3-dimensional crustal structure of P-wave velocity in central-western China

A simultaneous inversion of earthquake relocation and three-dimensional crustal structure of P-wave velocity in central-western China (21癗~36癗, 98癊~112癊) were performed in this paper. The crustal P-wave velocity model and earthquake relocation for this region are obtained using Pg and Sg phase readings of 9 988 earthquakes from 1992 to 1999 recorded at 193 seismic stations within central-western China by SPHYPIT90 and SPHREL3D90 programs. A lateral inhomogeneous structure of P-wave velocity in this region was obtained. Ob-vious contrast of P-wave velocities was revealed on both sides of active fault zones. Relocated epicenters of 6 459 events show clear lineation along active faults, which indicated a close correlation between seismicity and the active faults in this region. Focal depths of 82% relocated events ranged from 0 to 20 km, which is in good agreement with that from double-difference earthquake location algorithm.

3D motion and geometric information system of single-antenna radar based on incomplete 1D range data

A 3D motion and geometric information system of single-antenna radar is proposed,which can be supported by spotlight synthetic aperture radar（SAR） system and inverse SAR（ISAR） system involving relative 3D motion of the rigid target.In this system,applying the geometry invariance of the rigid target,the unknown 3D shape and motion of the radar target can be reconstructed from the 1D range data of some scatterers extracted from the high-resolution range image.Compared with the current 1D-to-3D algorithm,in the proposed algorithm,the requirement of the 1D range data is expanded to incomplete formation involving large angular motion of the target and hence,the quantity of the scatterers and the abundance of 3D motion are enriched.Furthermore,with the three selected affine coordinates fixed,the multi-solution problem of the reconstruction is solved and the technique of nonlinear optimization can be successfully utilized in the system.Two simulations are implemented which verify the higher robustness of the system and the better performance of the 3D reconstruction for the radar target with unknown relative motion.

3-D seismic tomography for velocity and interface structure of the crust and upper mantle(theoreticalpart)

A method of three dimensional (3-D) model parameterization is presented that makes forward and inverse problems become easy. The velocity and interface structure of crust and upper mantle are described by a set of highly smoothed functions. Shooting ray tracing method is chosen to calculate the ray paths for both forward and inverse problems. The partial derivatives of traveltime with respect to parameters of the model grids are calculated analytically while rays are being traced. Because velocity and interface functions have second-order continuous partial derivatives, the geometrical shadow zones at the surface caused by scattering and focusing of ray paths can be prevented. After ray tracing, an equation consisting of matrix and vectors for inverse problem is obtained. We use singular value decomposition method with damped factor to solve the equation. A synthetic data set which consists of several in-line profiles is used to test the methods. The results show that the methods are robust. Compared with the two dimensional method, the 3-D inversion method can give the right position of interfaces and the velocity structure when the crustal model is complicated.

Reconstruction of Temperature Field in 3-D, Absorbing, Emitting, and Anisotropically Scattering Medium

The soft measurement technology of flame temperature field is an efficient method to learn the combustion status in furnace. Generally, it reconstructs the temperature field in furnace through the image of flame, which is a process to solve radiative inverse problem. In this paper, the flame of pulverized coal is considered as 3-D, absorbing, emitting, and anisotropically scattering non-gray medium. Through the study on inverse problem of radiative heat transfer, the temperature field in this kind of medium has been reconstructed. The mechanism of 3-D radiative heat transfer in a rectangular media, which is 2 m×3 m× 5 m and full of CO2, N2 and carbon particles, is studied with Monte Carlo method. The 3-D temperature field in this rectangular space is reconstructed and the influence of particles density profile is discussed.

Advanced Computational Methods of Rapid and Rigorous 3-D Inversion of Airborne Electromagnetic Data

We develop a new computational method for modeling and inverting frequency domain airborne electromagnetic(EM)data.Our method is based on the contraction integral equation method for forward EM modeling and on inversion using the localized quasi-linear(LQL)approximation followed by the rigorous inversion,if necessary.The LQL inversion serves to provide a fast image of the target.These results are checked by a rigorous update of the domain electric field,allowing a more accurate calculation of the predicted data.If the accuracy is poorer than desired,rigorous inversion follows,using the resulting conductivity distribution and electric field from LQL as a starting model.The rigorous inversion iteratively solves the field and domain equations,converting the non-linear inversion into a series of linear inversions.We test this method on synthetic and field data.The results of the inversion are very encouraging with respect to both the speed and the accuracy of the algorithm,showing this is a useful tool for airborne EM interpretation.

基于Worldview-3与Sentinel-1 SAR数据的草原矿区复垦植被生物量反演方法研究

利用多源遥感数据定量反演矿区复垦植被生物量是高效、动态、大面积监测土地复垦和生态恢复效果的必要手段之一。本文以内蒙古草原露天煤矿为研究区,联合遥感光学与雷达数据各自的优势,探索基于Worldview-3(WV-3)与Sentinel-1 SAR数据的矿区复垦植被生物量反演方法,选择主成分小波变换(W-PCA)算法对WV-3与Sentinel-1 SAR数据进行融合,揭示波段反射率、植被指数、后向散射系数及纹理特征等参数与生物量之间的相关关系,建立多变量的生物量反演模型,并分析不同生物量模型的空间不确定性。结果表明:(1)通过W-PCA算法得到融合后的图像,信息熵的提高反映了融合图像与光学WV-3图像相比具有更多的细节信息,平均梯度的提高反映了融合图像与Sentinel-1 SAR图像相比具有更高的清晰度和更丰富的纹理信息。融合后的第8波段相关系数最高、光谱扭曲度最低、光谱保真度最高。(2)通过相关性分析,发现增强型植被指数(EVI)、归一化植被指数(NDVI)、VH极化、VH均值纹理以及融合后第8波段与生物量显著正相关。WV-3的NDVI与Sentinel-1的VH ME建模精度(R 2=0.8340,RMSE=16.4646 g/m^(2),Ac=81.52%)最高,融合后的第8波段验证精度(R 2=0.7983,RMSE=22.8283 g/m^(2),Ac=74.64%)最高。(3)基于不同模型的残差不确定性分析,Sentinel-1 SAR数据变量建立的模型估测结果更容易出现高估及饱和现象,两者联合变量建立的模型可实现优势互补,利用融合数据建立的模型明显改善生物量小于40 g/m^(2)时的高估计现象以及生物量大于100 g/m^(2)时的两者饱和现象,其不确定性降低2.42~9.68 g/m^(2)。因此,利用光学和雷达遥感融合能够有效提高复垦植被生物量的估算精度,为草原矿区复垦植被精细监测提供有效的数据支持。

AN INTEGRATED DATA MODEL IN THREE DIMENSIONAL GIS

The current GIS can only deal with 2-D or 2.5-D information on the earth surface. A new 3-D data structure and data model need to be designed for the 3-D GIS. This paper analyzes diverse 3-D spatial phenomena from mine to geology and their complicated relations, and proposes several new kinds of spatial objects including cross-section, column body and digital surface model to represent some special spatial phenomena like tunnels and irregular surfaces of an ore body. An integrated data structure including vector, raster and object-oriented data models is used to represent various 3-D spatial objects and their relations. The integrated data structure and object-oriented data model can be used as bases to design and realize a 3-D geographic information system.

Geophysical Modeling with Satellite Gravity Data: Eigen-6C4 vs. GGM Plus

Satellite data sets are an asset in global gravity collections;their characteristics vary in coverage and resolution. New collections appear often, and the user must adapt fast to their characteristics. Their use in geophysical modeling is rapidly increasing;with this in mind we compare two of the most densely populated sets: EIGEN-6C4 and GGMplus. We characterize them in terms of their frequency histograms, Free Air anomalies, power spectrum, and simple Bouguer anomalies. The nature of the digital elevation models used for data reduction is discussed. We conclude that the GGMplus data set offers a better spatial resolution. To evaluate their effect in geophysical modelling, we chose an inland region with a prominent volcanic structure in which we perform 3D inversions of the respective Bouguer anomalies, obtaining density variations that in principle can be associated with the geologic materials and the structure of the volcanic edifice. Model results are analyzed along sections of the inverted data;we conclude that the GGMplus data set offers higher resolution in the cases analyzed.

Leveraging machine learning to generate a unified and complete building height dataset for Germany

Building geometry data is crucial for detailed, spatially-explicit analyses of the building stock in energy systems analysis and beyond. Despite the existence of diverse datasets and methods, a standardized and validated approach for creating a nation-wide unified and complete dataset of German building heights is not yet available. This study develops and validates such a methodology, combining different data sources for building footprints and heights and filling gaps in height data using an XGBoost machine learning algorithm. The XGBoost model achieves a mean absolute error of 1.78 m at the national level and between 1.52 m and 3.47 m at the federal state level. The goal is proving the applicability of the methodology at a large scale and creating a useful dataset. The resulting dataset is thoroughly evaluated on a building-by-building level and spatially resolved statistics on the quality of the dataset are reported. This detailed validation found that the building number and footprint area of German building stock is 90.31 % and 94.84 % correct, respectively, and the building height accuracy is 0.59 m at the national level. However, errors are not homogeneous across Germany and further research is needed into the impact of including additional datasets, especially for regions and building types with lower accuracies. This study proves that the chosen methodology is useful for generating a building height dataset and the workflow, with some modifications for regional data availability, can be transferred to other countries. The generated building dataset for Germany constitutes a valuable data basis for the research community in fields such as energy research, urban planning and building decarbonization policy development.