Joint inversion of gravity and magnetic data for a two-layer model

Based on the synchronous joint gravity and magnetic inversion of single interface by Pilkington and the need of revealing Cenozoic and crystalline basement thickness in the new round of oil-gas exploration, we propose a joint gravity and magnetic inversion methodfor two-layer models by concentrating on the relationship between the change of thicknessI and position of the middle layer and anomaly and discuss the effects of the key parameters. Model tests and application to field data show the validity of this method.

Multi-scale data joint inversion of minerals and porosity in altered igneous reservoirs—A case study in the South China Sea

There are abundant igneous gas reservoirs in the South China Sea with significant value of research,and lithology classification,mineral analysis and porosity inversion are important links in reservoir evaluation.However,affected by the diverse lithology,complicated mineral and widespread alteration,conventional logging lithology classification and mineral inversion become considerably difficult.At the same time,owing to the limitation of the wireline log response equation,the quantity and accuracy of minerals can hardly meet the exploration requirements of igneous formations.To overcome those issues,this study takes the South China Sea as an example,and combines multi-scale data such as micro rock slices,petrophysical experiments,wireline log and element cutting log to establish a set of joint inversion methods for minerals and porosity of altered igneous rocks.Specifically,we define the lithology and mineral characteristics through core slices and mineral data,and establish an igneous multi-mineral volumetric model.Then we determine element cutting log correction method based on core element data,and combine wireline log and corrected element cutting log to perform the lithology classification and joint inversion of minerals and porosity.However,it is always difficult to determine the elemental eigenvalues of different minerals in inversion.This paper uses multiple linear regression methods to solve this problem.Finally,an integrated inversion technique for altered igneous formations was developed.The results show that the corrected element cutting log are in good agreement with the core element data,and the mineral and porosity results obtained from the joint inversion based on the wireline log and corrected element cutting log are also in good agreement with the core data from X-ray diffraction.The results demonstrate that the inversion technique is applicable and this study provides a new direction for the mineral inversion research of altered igneous formations.

The distribution of deep source rocks in the GS Sag:joint MT-gravity modeling and constrained inversion

The coal-bearing strata of the deep Upper Paleozoic in the GS Sag have high hydrocarbon potential. Because of the absence of seismic data, we use electromagnetic （MT） and gravity data jointly to delineate the distribution of deep targets based on well logging and geological data. First, a preliminary geological model is established by using three-dimensional （3D） MT inversion results. Second, using the formation density and gravity anomalies, the preliminary geological model is modified by interactive inversion of the gravity data. Then, we conduct MT-constrained inversion based on the modified model to obtain an optimal geological model until the deviations at all stations are minimized. Finally, the geological model and a seismic profile in the middle of the sag is analysed. We determine that the deep reflections of the seismic profile correspond to the Upper Paleozoic that reaches thickness up to 800 m. The processing of field data suggests that the joint MT-gravity modeling and constrained inversion can reduce the multiple solutions for single geophysical data and thus improve the recognition of deep formations. The MT-constrained inversion is consistent with the geological features in the seismic section. This suggests that the joint MT and gravity modeling and constrained inversion can be used to delineate deep targets in similar basins.

3D inversion modeling of joint gravity and magnetic data based on a sinusoidal correlation constraint

Joint inversion based on a correlation constraint utilizes a linear correlation function as a structural constraint.The linear correlation function contains a denominator,which may result in a singularity as the objective function is optimized,leading to an unstable inversion calculation.To improve the robustness of this calculation,this paper proposes a new method in which a sinusoidal correlation function is employed as the structural constraint for joint inversion instead of the conventional linear correlation function.This structural constraint does not contain a denominator,thereby preventing a singularity.Compared with the joint inversion method based on a cross-gradient constraint,the joint inversion method based on a sinusoidal correlation constraint exhibits good performance.An application to actual data demonstrates that this method can process real data.

Joint inversion of gravity and seismic data along a profile across the seismogenic fault of 2010 Yushu Ms7. 1 earthquake

Yushu Ms7.1 earthquake occurred on the Ganzi-Yushu fault zone, across which we carried out a joint relative-gravity and seismic-reflection survey, and then performed a gravity inversion constrained by the seismic-reflection result. Based on the data of complete Bouguer gravity anomaly and seismic reflection, we obtained a layered interface structure in deep crust down to Moho. Our study showed that the inversion could reveal the interfaces of strata along the survey profile and the directions of regional faults in two-dimension. From the characteristics of the observed topography of the Moho basement, we tentatively confirmed that the uplift of eastern edge of Qinghai-Tibet plateau was caused by the subduetion of the Indian plate.

3D joint inversion of surface and borehole gravity data using zeroth-order minimum entropy regularization

Surface and borehole gravity data contain complementary information.Thus,the joint inversion of these two data types can help retrieve the real spatial distributions of density bodies.When a sharp boundary exists between an anomalous density body and its surrounding rock,the interface recovered by smooth inversion with Tikhonov regularization is not clear,leading to difficulties in the subsequent geological interpretation.In this work,we develop a joint inversion of surface and borehole gravity data using zeroth-order minimum entropy regularization.The method takes advantage of the complementary information from surface and borehole gravity data to enhance the imaging resolution of density bodies.It also produces a focused imaging of bodies through the zeroth-order minimum entropy regularization without requiring a preselection of a proper focusing parameter.We apply the developed joint inversion approach to three diff erent synthetic data sets.Inversion results show that the focusing inversion with the zeroth-order minimum entropy regularization provides a good description of the true spatial extent of anomalous density bodies.Meanwhile,the joint focusing inversion reconstructs a more reliable density model with a relatively high resolution when a density body is passed through by one or more boreholes.

3D Joint inversion of gravity and gravity tensor data

The processing and interpretation of gravity and gradient data plays an important role in geophysics.The cross gradient joint inversion is usually used for achieving structure coupling of multiple geophysical models. In order to realize the coupling of gravity and gravity tensor data,the authors analyzed each component.The results show that different types of data contain different direction information,and derived the joint inversion based on cross gradient function and applied it to model data. The theoretical model results show that the cross gradient method can reduce the multi solution and significantly improve the resolution of the inversion.The method was also applied to inverse the gravity tensor data in Vinton salt dome,showing that this method can get higher resolution results than the separate linear inversion,and be closer to the real density from drilling data.

Fast 3D joint inversion of gravity and magnetic data based on cross gradient constraint

The gravity and magnetic data can be adopted to interpret the internal structure of the Earth.To improve the calculation efficiency during the inversion process and the accuracy and reliability of the reconstructed physical property models,the triple strategy is adopted in this paper to develop a fast cross-gradient joint inversion for gravity and magnetic data.The cross-gradient constraint contains solving the gradients of the physical property models and performing the cross-product calculation of their gradients.The sparse matrices are first obtained by calculating the gradients of the physical property models derived from the first-order finite difference.Then,the triple method is applied to optimize the storages and the calculations related to the gradients of the physical property models.Therefore,the storage compression amount of the calculations related to the gradients of the physical property models and the cross-gradient constraint are reduced to one-fold of the number of grid cells at least,and the compression ratio increases with the increase of the number of grid cells.The test results from the synthetic data and field data prove that the structural coupling is achieved by using the fast cross-gradient joint inversion method to effectively reduce the multiplicity of solutions and improve the computing efficiency.

Simultaneous Structure-Coupled Joint Inversion of Gravity and Magnetic Data Based on a Damped Least-Squares Technique

The structure-coupled joint inversion method of gravity and magnetic data is a powerful tool for?developing improved physical property models with high resolution and compatible features;?however, the conventional procedure is inefficient due to the truncated singular values decomposition?(SVD) process at each iteration. To improve the algorithm, a technique using damped leastsquares?is adopted to calculate the structural term of model updates, instead of the truncated SVD. This?produces structural coupled density and magnetization images with high efficiency. A so-called?coupling factor is introduced to regulate the tuning of the desired final structural similarity level.?Synthetic examples show that the joint inversion results are internally consistent and achieve?higher?resolution than separated. The acceptable runtime performance of the damped least squares?technique used in joint inversion indicates that it is more suitable for practical use than the truncated SVD method.

Joint inversion of gravity and vertical gradient data based on modified structural similarity index for the structural and petrophysical consistency constraint

Joint inversion is one of the most effective methods for reducing non-uniqueness for geophysical inversion.The current joint inversion methods can be divided into the structural consistency constraint and petrophysical consistency constraint methods,which are mutually independent.Currently,there is a need for joint inversion methods that can comprehensively consider the structural consistency constraints and petrophysical consistency constraints.This paper develops the structural similarity index(SSIM)as a new structural and petrophysical consistency constraint for the joint inversion of gravity and vertical gradient data.The SSIM constraint is in the form of a fraction,which may have analytical singularities.Therefore,converting the fractional form to the subtractive form can solve the problem of analytic singularity and finally form a modified structural consistency index of the joint inversion,which enhances the stability of the SSIM constraint applied to the joint inversion.Compared to the reconstructed results from the cross-gradient inversion,the proposed method presents good performance and stability.The SSIM algorithm is a new joint inversion method for petrophysical and structural constraints.It can promote the consistency of the recovered models from the distribution and the structure of the physical property values.Then,applications to synthetic data illustrate that the algorithm proposed in this paper can well process the synthetic data and acquire good reconstructed results.

A MATLAB-Based Numerical and GUI Implementation of Cross-Gradients Joint Inversion of Gravity and Magnetic Data

The cross-gradients joint inversion technique has been applied to multiple geophysical data with a significant improvement on compatibility, but its numerical implementation for practical use is rarely discussed in the literature. We present a MATLAB-based three-dimensional cross-gradients joint inversion program with application to gravity and magnetic data. The input and output information was examined with care to create a rational, independent design of a graphical user interface (GUI) and computing kernel. For 3D visualization and data file operations, UBC-GIF tools are invoked using a series of I/O functions. Some key issues regarding the iterative joint inversion algorithm are also discussed: for instance, the forward difference of cross gradients, and matrix pseudo inverse computation. A synthetic example is employed to illustrate the whole process. Joint and separate inversions can be performed flexibly by switching the inversion mode. The resulting density model and susceptibility model demonstrate the correctness of the proposed program.

Robust inversion analysis of local gravity anomalies caused by geological dislocation model of faults

Theoretical analysis and practical observations show that fault dislocations can change the gravity field around the fault. Gravity changes which were caused by the repeated dislocations over a long period of time were superimposed on the Bougeur gravity anomalies. These anomalies became the evidence of historical movement of fault as well as provide a way for the study of paleo earthquakes. This paper investigates inversion methods for the geological dislocation modeling of faults using the local Bouguer's gravity anomalies. To remove the effects of the irrelevant part of gravity anomalies to fault movements, we propose the robust nonlinear inversion method and set up the corresponding algorithm. Modeling examples indicate that the Marquardt's and Baye's least squares solutions depart from the true solution due to the attraction of gross errors in the data. The more seriously the data is contaminated, the more seriously the solutions are biased. In contrast, the proposed robust Marquardt's and Baye's inversion solutions can still maintain consistency with the solution without gross errors, even though 50 percent of the data is contaminated. This indicates that the proposed robust methods are effective. Using the proposed methods, we invert the geological dislocation models of the faults around the Erhai Lake in West Yunnan. The results show that the Northern Cangdong fault and the Erhai fault are normal dip slip faults with about 4 to 5 km dislocations; and that the Southern Cangdong fault has a less dip slip compared with the former two. A satisfactory fitting between the theoretical values of the inversion solution and the actual local gravity field is achievable.

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.

Effective elastic thickness of the lithosphere from joint inversion in western China and its implications

The western China lies in the convergence zone between Eurasian and Indian plates.It is an ideal place to study the lithosphere dynamics and tectonic evolutions on the continental Earth.The lithospheric strength is a key factor in controlling the lithosphere dynamics and deformations.The effective elastic thickness(T_(e))of the lithosphere can be used to address the lithospheric strength.Previous researchers only used one of the admittance or coherence methods to investigate the T_(e) in the western China.Moreover,most of them ignored the internal loads of the lithosphere during the T_(e) calculation,which can produce large biases in the T_(e) estimations.To provide more reliable T_(e) estimations,we used a new joint inversion method that integrated both admittance and coherence techniques to compute the T_(e) in this study,with the WGM2012 gravity data,the ETOPO1 topographic data,and the Moho depths from the CRUST1.0 model.The internal loads are considered and investigated using the load ratio(F).Our results show that the joint inversion method can yield reliable T_(e) and F values.Based on the analysis of T_(e) and F distributions,we suggest(1)the northern Tibetan Plateau could be the front edge of the plate collision of Eurasian and Indian plates;(2)the southern and part of central Tibetan Plateau have a strong lithospheric mantle related to the rigid underthrusting Indian plate;(3)the southeastern Tibetan Plateau may be experiencing the delamination of lithosphere and upwelling of asthenosphere.

Earthquake safety assessment of concrete arch and gravity dams

Based on research studies currently being carried out at Dalian University of Technology, some important aspects for the earthquake safety assessmcnt of concrete dams are reviewed and discussed. First, the rate-dependent behavior of concrcte subjected to earthquake loading is examined, emphasizing the properties of concrete under cyclic and biaxial loading conditions. Second, a modified four-parameter Hsieh-Ting-Chen viscoplastic consistency model is developed to simulate the rate-dependent behavior of concrete. The earthquake response of a 278m high arch dam is analyzed, and the results show that the strain-rate effects become noticeable in the inelastic range, Third, a more accurate non-smooth Newton algorithm for the solution of three-dimensional frictional contact problems is developed to study the joint opening effects of arch dams during strong earthquakes. Such effects on two nearly 300m high arch dams have been studied. It was found that the canyon shape has great influence on the magnitude and distribution of the joint opening along the dam axis. Fourth, the scaled boundary finite element method presented by Song and Wolf is employed to study the dam-reservoir-foundation interaction effects of concrete dams. Particular emphases were placed on the variation of foundation stiffness and the anisotropic behavior of the foundation material on the dynamic response of concrete dams. Finally, nonlinear modeling of concrete to study the damage evolution of concrete dams during strong earthquakes is discussed. An elastic-damage mechanics approach for damage prediction of concrete gravity dams is described as an example. These findings are helpful in understanding the dynamic behavior of concrete dams and promoting the improvement of seismic safety assessment methods.

Tomographic determination of 3－D crustal structure──Joint inversion of explosion and earthquake data

In this paper, the theory and method, obtaining the tomographic determination of three-dimensional velocity structure of the crust by use of the joint inversion of explosion and earthquake data, are given. The velocity distribution of the crust is regarded as a continuous function of the spatial coordinates without parametrization of the velocity model ahead, so that the inversion solution would not be influenced by different parametrization procedures.The expressions of integration kernels, which relates the two kinds of data sets, are also given. The authors have processed the observed data in Tangshan earthquake region by the method proposed in this paper, and obtained the tomographic results of the middle and upper crust structures in this region. The comparison of these results with the result obtained only by the explosion data, has also been made.

Multi-component joint inversion of gravity gradient based on fast forward calculation

With the development of gravity gradient full tensor measurement technique,three-dimensional( 3D) inversion based on gravity gradient tensor can provide more accurate information. But the forward calculation of 3D full tensor sensitivity matrix is very time-consuming,which restricts its development and application.According to the symmetry of the kernel function,the authors reconstruct the underground source of geological body to avoid repeat computation of the same value,and work out the corresponding relationship between the response of geological body to the observation point and the response of reconstructed geological body to the observation point. According to the relationship,rapid calculation of full tensor gravity sensitivity matrix can be achieved. The model calculation shows that this method can increase the speed of 30-45 times compared with the traditional calculation method. The sensitivity matrix is applied to the multi-component inversion of gravity gradient. The application of this method on the measured data provides the basis for the promotion of the method.

Joint inversion of Rayleigh group and phase velocities for S-wave velocity structure of the 2021 M_(S)6.0 Luxian earthquake source area,China

On September 16,2021,a MS6.0 earthquake struck Luxian County,one of the shale gas blocks in the Southeastern Sichuan Basin,China.To understand the seismogenic environment and its mechanism,we inverted a fine three-dimensional S-wave velocity model from ambient noise tomography using data from a newly deployed dense seismic array around the epicenter,by extracting and jointly inverting the Rayleigh phase and group velocities in the period of 1.6–7.2 s.The results showed that the velocity model varied significantly beneath different geological units.The Yujiasi syncline is characterized by low velocity at depths of~3.0–4.0 km,corresponding to the stable sedimentary layer in the Sichuan Basin.The eastern and western branches of the Huayingshan fault belt generally exhibit high velocities in the NE-SW direction,with a few local low-velocity zones.The Luxian MS6.0 earthquake epicenter is located at the boundary between the high-and low-velocity zones,and the earthquake sequences expand eastward from the epicenter at depths of 3.0–5.0 km.Integrated with the velocity variations around the epicenter,distribution of aftershock sequences,and focal mechanism solution,it is speculated that the seismogenic mechanism of the main shock might be interpreted as the reactivation of pre-existing faults by hydraulic fracturing.

Source rupture model of the 2018 M_(W)6.7 Iburi,Hokkaido earthquake from joint inversion of strong motion and InSAR observations

The 2018 M_(W)6.7 Iburi earthquake shocked the eastern Iburi region to the west of the Hidaka Collision Zone in Hokkaido,which is a destructive inland earthquake.We resolved the kinematic rupture process of the event by combining strong motions(SM)and synthetic aperture radar(SAR)images in a joint inversion.The results reveal that the duration of the whole rupture is about 17s,yielding a total seismic moment of 1.4×10^(19)N·m(M_(W)=6.7).The main slip area is located at a depth of approximately 24 km with a peak slip of~0.8m above the hypocenter.The comparison with the regional velocity model shows the earthquake was initiated in the upper mantle,while the majority of slips are located in the lower crust,which is an“aseismic”domain in the typical sandwich model.The location of the major slip area is consistent with a high-conductivity volume.We proposed a mechanism of low frictional property(<0.3)produced by high pore pressure to explain the abnormal high dip angle and centroid depth located in the ductile lower-crust.Aftershocks are distributed in areas where the Coulomb frictional stress increases due to co-seismic displacement with a mechanism conjugating to the mainshock.

COMPREHENSIVE INTEGRATION METHODS AND APPLICATION OF GRAVITY-MAGNETIC DATA IMAGE

the technique of image processing and analysis of gravity and magnetic data is one of themost effective ways to extract geological information from gravity and msanetic data. The presentpaper investigates, from an angle of generalized joint inversion, thc methods and procedures ofcomprehensive processing of multi-source geological image , and a specific example in Huai Nan coalfield is given here as well.