Lithological Characterization and Its Application Based on Three-Dimensional Structure-Coupled Joint Inversion of Gravity and Magnetic Data

Incorporating structural-coupling constraint, known as the cross-gradients criterion, helps to improve the focussing trend in cross-plot of multiple physical properties. Based on this feature, a?post-processing technique is studied to characterize the lithological types of subsurface geological materials after joint inversion. A simple domain transform, which converts two kinds of participant physical properties into an artificial complex array, is adopted to extract anomalies manually from homogenous host rock. A synthetic example shows that structure-coupled joint inverted results tend to concentrate on the feature trends in the cross-plot, and the main geological targets are recovered well by a radius-azimuth plot. In a field data example, the lithological characterization?reveals that the main rock types interpreted in the study area agree with the geological information, thus demonstrating the feasibility of this technique.

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.

Crustal and uppermost mantle structure of the northeastern Qinghai-Xizang Plateau from joint inversion of surface wave dispersions and receiver functions with P velocity constraints

Lithospheric structure beneath the northeastern Qinghai-Xizang Plateau is of vital significance for studying the geodynamic processes of crustal thickening and expansion of the Qinghai-Xizang Plateau. We conducted a joint inversion of receiver functions and surface wave dispersions with P-wave velocity constraints using data from the Chin Array Ⅱ temporary stations deployed across the Qinghai-Xizang Plateau. Prior to joint inversion, we applied the H-κ-c method(Li JT et al., 2019) to the receiver function data in order to correct for the back-azimuthal variations in the arrival times of Ps phases and crustal multiples caused by crustal anisotropy and dipping interfaces. High-resolution images of vS, crustal thickness, and vP/vSstructures in the Qinghai-Xizang Plateau were simultaneously derived from the joint inversion. The seismic images reveal that crustal thickness decreases outward from the Qinghai-Xizang Plateau. The stable interiors of the Ordos and Alxa blocks exhibited higher velocities and lower crustal vP/vSratios. While, lower velocities and higher vP/vSratios were observed beneath the Qilian Orogen and Songpan-Ganzi terrane(SPGZ), which are geologically active and mechanically weak, especially in the mid-lower crust.Delamination or thermal erosion of the lithosphere triggered by hot asthenospheric flow contributes to the observed uppermost mantle low-velocity zones(LVZs) in the SPGZ. The crustal thickness, vS, and vP/vSratios suggest that whole lithospheric shortening is a plausible mechanism for crustal thickening in the Qinghai-Xizang Plateau, supporting the idea of coupled lithospheric-scale deformation in this region.

An empirical method for joint inversion of wave and wind parameters based on SAR and wave spectrometer data

Synthetic aperture radar(SAR)and wave spectrometers,crucial in microwave remote sensing,play an essential role in monitoring sea surface wind and wave conditions.However,they face inherent limitations in observing sea surface phenomena.SAR systems,for instance,are hindered by an azimuth cut-off phenomenon in sea surface wind field observation.Wave spectrometers,while unaffected by the azimuth cutoff phenomenon,struggle with low azimuth resolution,impacting the capture of detailed wave and wind field data.This study utilizes SAR and surface wave investigation and monitoring(SWIM)data to initially extract key feature parameters,which are then prioritized using the extreme gradient boosting(XGBoost)algorithm.The research further addresses feature collinearity through a combined analysis of feature importance and correlation,leading to the development of an inversion model for wave and wind parameters based on XGBoost.A comparative analysis of this model with ERA5 reanalysis and buoy data for of significant wave height,mean wave period,wind direction,and wind speed reveals root mean square errors of 0.212 m,0.525 s,27.446°,and 1.092 m/s,compared to 0.314 m,0.888 s,27.698°,and 1.315 m/s from buoy data,respectively.These results demonstrate the model’s effective retrieval of wave and wind parameters.Finally,the model,incorporating altimeter and scatterometer data,is evaluated against SAR/SWIM single and dual payload inversion methods across different wind speeds.This comparison highlights the model’s superior inversion accuracy over other methods.

Three-dimensional gravity inversion based on sparse recovery iteration using approximate zero norm

This research proposes a novel three-dimensional gravity inversion based on sparse recovery in compress sensing. Zero norm is selected as the objective function, which is then iteratively solved by the approximate zero norm solution. The inversion approach mainly employs forward modeling; a depth weight function is introduced into the objective function of the zero norms. Sparse inversion results are obtained by the corresponding optimal mathematical method. To achieve the practical geophysical and geological significance of the results, penalty function is applied to constrain the density values. Results obtained by proposed provide clear boundary depth and density contrast distribution information. The method's accuracy, validity, and reliability are verified by comparing its results with those of synthetic models. To further explain its reliability, a practical gravity data is obtained for a region in Texas, USA is applied. Inversion results for this region are compared with those of previous studies, including a research of logging data in the same area. The depth of salt dome obtained by the inversion method is 4.2 km, which is in good agreement with the 4.4 km value from the logging data. From this, the practicality of the inversion method is also validated.

Three-dimensional frequency-domain full waveform inversion based on the nearly-analytic discrete method

The nearly analytic discrete(NAD)method is a kind of finite difference method with advantages of high accuracy and stability.Previous studies have investigated the NAD method for simulating wave propagation in the time-domain.This study applies the NAD method to solving three-dimensional(3D)acoustic wave equations in the frequency-domain.This forward modeling approach is then used as the“engine”for implementing 3D frequency-domain full waveform inversion(FWI).In the numerical modeling experiments,synthetic examples are first given to show the superiority of the NAD method in forward modeling compared with traditional finite difference methods.Synthetic 3D frequency-domain FWI experiments are then carried out to examine the effectiveness of the proposed methods.The inversion results show that the NAD method is more suitable than traditional methods,in terms of computational cost and stability,for 3D frequency-domain FWI,and represents an effective approach for inversion of subsurface model structures.

Electrical Structure of Wulingshan and Middle Jiangnan Orogen by Three-Dimensional Magnetotelluric Data Inversion

Funded by The National Key Research and Development Program of China,China Deep Exploration(Sinoprobe)and The China Geological Suvery Project on 2009–2019,a large scale magnetotelluric sounding(MT)survey grid(Fig.1)has covered whole south China.

Three-dimensional gravity inversion based on 3D U-Net++

The gravity inversion is to restore genetic density distribution of the underground target to be explored for explaining the internal structure and distribution of the Earth.In this paper,we propose a new 3D gravity inversion method based on 3D U-Net++.Compared with two-dimensional gravity inversion,three-dimensional(3D)gravity inversion can more precisely describe the density distribution of underground space.However,conventional 3D gravity inversion method input is two-dimensional,the input and output of the network proposed in our method are three-dimensional.In the training stage,we design a large number of diversifi ed simulation model-data pairs by using the random walk method to improve the generalization ability of the network.In the test phase,we verify the network performance by using the model-data pairs generated by the simulation.To further illustrate the eff ectiveness of the algorithm,we apply the method to the inversion of the San Nicolas mining area,and the inversion results are basically consistent with the borehole measurement results.Moreover,the results of the 3D U-Net++inversion and the 3D U-Net inversion are compared.The density models of the 3D U-Net++inversion have higher resolution,more concentrated inversion results,and a clearer boundary of the density model.

Inversion of source mechanism of 1989 Loma Prieta earthquake by three-dimensional FEM Green's function

Based on three-dimensional joint finite element, this paper discusses the theory and methodology about inversionof geodetic data. The FEM and inversion formula is given in detail; also a related code is developed. By use of theGreen's function about 3-D FEM, we invert geodetic measurementS of coseismic deformation of the 1989 Ms=7. 1Loma Prieta earthquake to datermine itS source mechanism. The result indicates that the slip on the fault plane isvery heterogeneous. The maximum slip and shear stress are located about 10 kin to northwest of the eathquakesource, the stress drop is about more than 1 MPa.

Concealed porphyry delineation based on nonlinear three-dimensional densitydifference inversion: An example in the Beiya mine area, Western Yunnan, China

Intermediate acid-complex rock masses with low-density characteristics are the most important prospecting sign in the Beiya area, of western Yunnan province, and provide a physical basis for good gravity exploration. It is usually difficult to obtaining solutions in connection with actual geological situations due to the ambiguity of the conventional gravity-processing results and lack of deep constraints. Thus, the three-dimensional (3D) inversion technology is considered as the main channel for reducing the number of solutions and improving the vertical resolution at the current stage. The current study starts from a model test and performs nonlinear 3D density-difference inversion called “model likelihood exploration”, which performs 3D inversion imaging and inversion of the known model while considering the topographic effects. The inversion results are highly consistent with those of the known models. Simultaneously, we consider the Beiya gold mine in Yunnan as an example. The nonlinear 3D densitydifference inversion technology, which is restricted by geological information, is explored to obtain the 3D density body structure below 5 km in the mine area, and the 3D structure of the deep and concealed rock masses are obtained using the density constraints of the intermediate-acid-complex rock masses. The results are well consistent with the surface geological masses and drilling-controlled deep geological masses. The model test and examples both show that the 3D density-difference nonlinear inversion technology can reduce inversion ambiguity, improve resolution, optimize the inversion results, and realize “transparency” in deeply concealed rock masses in ore-concentrated areas,which is useful in guiding the deep ore prospecting.

Joint PP and PS AVO inversion based on Bayes theorem

Based on the Aki-Richards approximate equations for reflection coefficients and Bayes theorem, we developed an inversion method to estimate P- and S-wave velocity contrasts and density contrast from combined PP and PS data. This method assumes that the parameters satisfy a normal distribution and introduces the covariance matrix to describe the degree of correlation between the parameters and thus to improve the inversion stability. Then, we suppose that the parameter sequence is subject to the Cauchy distribution and employs another matrix Q to describe the parameter sequence sparseness to improve the inversion result resolution. Tests on both synthetic and real multi-component data prove that this method is valid, efficient, more stable, and more accurate compared to methods using PP data only.

Generalized linear joint PP-PS inversion based on two constraints

Conventional joint PP-PS inversion is based on approximations of the Zoeppritz equations and assumes constant VP/VS;therefore,the inversion precision and stability cannot satisfy current exploration requirements.We propose a joint PP-PS inversion method based on the exact Zoeppritz equations that combines Bayesian statistics and generalized linear inversion.A forward model based on the exact Zoeppritz equations is built to minimize the error of the approximations in the large-angle data,the prior distribution of the model parameters is added as a regularization item to decrease the ill-posed nature of the inversion,low-frequency constraints are introduced to stabilize the low-frequency data and improve robustness,and a fast algorithm is used to solve the objective function while minimizing the computational load.The proposed method has superior antinoising properties and well reproduces real data.

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.

AVO approximation for PS-wave and its application in PP/PS joint inversion

Multi-component exploration has many advantages over ordinary P-wave exploration. PP/PS joint AVO analysis and inversion are useful and powerful methods to discriminate between reservoir and non-productive lithology. In this paper, we derive a new PS-wave reflection coefficient approximation equation which is more accurate at larger incidence angles. The equation is simplified for small incidence angles, which makes AVO analysis clearer and easier for angles less than 30 degrees. Based on this approximation, a PP/PS joint inversion is introduced. A real data example shows that oil sands, brine sands and shales can be differentiated based on the P- to S-wave velocity ratio from the PP/PS joint inversion. Fluid factors and Poisson＇s ratio also indicate an anomaly in the target zone at the oil well location.

Nonlinear joint PP-PS AVO inversion based on improved Bayesian inference and LSSVM

Multiwave seismic technology promotes the application of joint PP–PS amplitude versus offset (AVO) inversion;however conventional joint PP–PS AVO inversioan is linear based on approximations of the Zoeppritz equations for multiple iterations. Therefore the inversion results of P-wave, S-wave velocity and density exhibit low precision in the faroffset;thus, the joint PP–PS AVO inversion is nonlinear. Herein, we propose a nonlinear joint inversion method based on exact Zoeppritz equations that combines improved Bayesian inference and a least squares support vector machine (LSSVM) to solve the nonlinear inversion problem. The initial parameters of Bayesian inference are optimized via particle swarm optimization (PSO). In improved Bayesian inference, the optimal parameter of the LSSVM is obtained by maximizing the posterior probability of the hyperparameters, thus improving the learning and generalization abilities of LSSVM. Then, an optimal nonlinear LSSVM model that defi nes the relationship between seismic refl ection amplitude and elastic parameters is established to improve the precision of the joint PP–PS AVO inversion. Further, the nonlinear problem of joint inversion can be solved through a single training of the nonlinear inversion model. The results of the synthetic data suggest that the precision of the estimated parameters is higher than that obtained via Bayesian linear inversion with PP-wave data and via approximations of the Zoeppritz equations. In addition, results using synthetic data with added noise show that the proposed method has superior anti-noising properties. Real-world application shows the feasibility and superiority of the proposed method, as compared with Bayesian linear inversion.

Stepwise joint inversion of surface wave dispersion,Rayleigh wave ZH ratio,and receiver function data for 1D crustal shear wave velocity structure

Accurate determination of seismic velocity of the crust is important for understanding regional tectonics and crustal evolution of the Earth. We propose a stepwise joint linearized inversion method using surface wave dispersion, Rayleigh wave ZH ratio （i.e., ellipticity）, and receiver function data to better resolve 1D crustal shear wave velocity （Vs） structure. Surface wave dispersion and Rayleigh wave ZH ratio data are more sensitive to absolute variations of shear wave speed at depths, but their sensi- tivity kernels to shear wave speeds are different and complimentary. However, receiver function data are more sensitive to sharp velocity contrast （e.g., due to the existence of crustal interfaces） and Vp/Vs ratios. The stepwise inversion method takes advantages of the complementary sensitivities of each dataset to better constrain the Vs model in the crust. We firstly invert surface wave dispersion and ZH ratio data to obtain a 1D smooth absolute vs model and then incorporate receiver function data in the joint inver- sion to obtain a finer Vs model with better constraints on interface structures. Through synthetic tests, Monte Carlo error analyses, and application to real data, we demonstrate that the proposed joint inversion method can resolve robust crustal Vs structures and with little initial model dependency.

Rupture process of the 2011 Tohoku earthquake from the joint inversion of teleseismic and GPS data

Teleseismic and GPS data were jointly inverted for the rupture process of the 2011 Tohoku earthquake. The inversion results show that it is a bilateral rupture event with an average rupture velocity less than 2.0 km/s along the fault strike direction. The source rupture process consists of three sub-events, the first oc- curred near the hypocenter and the rest two ruptured along the up-dip direction and broke the sea bed, causing a maximum slip of about 30 m. The large-scale sea bed breakage may account for the tremendous tsunami disaster which resulted in most of the death and missing in this mega earthquake.

2D joint inversion of CSAMT and magnetic data based on cross-gradient theory

A two-dimensional forward and backward algorithm for the controlled-source audio-frequency magnetotelluric （CSAMT） method is developed to invert data in the entire region （near, transition, and far） and deal with the effects of artificial sources. First, a regularization factor is introduced in the 2D magnetic inversion, and the magnetic susceptibility is updated in logarithmic form so that the inversion magnetic susceptibility is always positive. Second, the joint inversion of the CSAMT and magnetic methods is completed with the introduction of the cross gradient. By searching for the weight of the cross-gradient term in the objective function, the mutual influence between two different physical properties at different locations are avoided. Model tests show that the joint inversion based on cross-gradient theory offers better results than the single-method inversion. The 2D forward and inverse algorithm for CSAMT with source can effectively deal with artificial sources and ensures the reliability of the final joint inversion algorithm.

Source model of the 11th July 2004 Zhongba earthquake revealed from the joint inversion of InSAR and seismological data

We use interferometric synthetic aperture radar （InSAR） and broadband seismic waveform data to estimate a source model of the 11th July, 2004 M W 6.2 Zhongba earthquake, Tibet of China. This event occurred within the seismically active zone of southwestern Tibetan Plateau where the east-west extension of the upper crust is observed. Because of limitations in one pair of InSAR data available, there are trade-offs among centroid depth, rupture area and amount of slip. Available seismic data tightly constrain the focal mechanism and centroid depth of the earthquake but not the horizontal location. Together, two complementary data sets can be used to identify the actual fault plane, better constrain the slip model and event location. We first use regional seismic waveform to estimate point source mechanism, then InSAR data is used to obtain better location. Finally, a joint inversion of teleseismic P-waves and InSAR data is performed to obtain a distributed model. Our preferred point source mechanism indicates a seismic moment of ～2.2×10 18 N·m （～M W 6.2）, a fault plane solution of 171° （342 ° ）/42 ° （48 ° ）/-83 ° （-97 ° ）, corresponding to strike/dip/rake, and a depth of 11 km. The fault plane with strike of 171 ？ and dip of 42° is identified as the ruptured fault with the aid of InSAR data. The preferred source model features compact area of slips between depth of 5–11 km and 10 km along strike with maximum slip amplitude of about 1.5 m.

Elastic modulus extraction based on generalized pre-stack PP–PS wave joint linear inversion

Joint PP–PS inversion offers better accuracy and resolution than conventional P-wave inversion. P-and S-wave elastic moduli determined through data inversions are key parameters for reservoir evaluation and fluid characterization. In this paper, starting with the exact Zoeppritz equation that relates P-and S-wave moduli, a coefficient that describes the reflections of P-and converted waves is established. This method effectively avoids error introduced by approximations or indirect calculations, thus improving the accuracy of the inversion results. Considering that the inversion problem is ill-posed and that the forward operator is nonlinear, prior constraints on the model parameters and modified low-frequency constraints are also introduced to the objective function to make the problem more tractable. This modified objective function is solved over many iterations to continuously optimize the background values of the velocity ratio, which increases the stability of the inversion process. Tests of various models show that the method effectively improves the accuracy and stability of extracting P and S-wave moduli from underdetermined data. This method can be applied to provide inferences for reservoir exploration and fluid extraction.