Geostatistical seismic inversion and 3D modelling of metric flow units,porosity and permeability in Brazilian presalt reservoir

Flow units(FU)rock typing is a common technique for characterizing reservoir flow behavior,producing reliable porosity and permeability estimation even in complex geological settings.However,the lateral extrapolation of FU away from the well into the whole reservoir grid is commonly a difficult task and using the seismic data as constraints is rarely a subject of study.This paper proposes a workflow to generate numerous possible 3D volumes of flow units,porosity and permeability below the seismic resolution limit,respecting the available seismic data at larger scales.The methodology is used in the Mero Field,a Brazilian presalt carbonate reservoir located in the Santos Basin,who presents a complex and heterogenic geological setting with different sedimentological processes and diagenetic history.We generated metric flow units using the conventional core analysis and transposed to the well log data.Then,given a Markov chain Monte Carlo algorithm,the seismic data and the well log statistics,we simulated acoustic impedance,decametric flow units(DFU),metric flow units(MFU),porosity and permeability volumes in the metric scale.The aim is to estimate a minimum amount of MFU able to calculate realistic scenarios porosity and permeability scenarios,without losing the seismic lateral control.In other words,every porosity and permeability volume simulated produces a synthetic seismic that match the real seismic of the area,even in the metric scale.The achieved 3D results represent a high-resolution fluid flow reservoir modelling considering the lateral control of the seismic during the process and can be directly incorporated in the dynamic characterization workflow.

UAV-based transient electromagnetic 3D forward modeling and inversion and analysis of exploration capability

Unmanned aerial vehicle transient electromagnetic(UAV-TEM)is a novel airborne exploration method that offers advantages such as low cost,simple operation,high exploration efficiency and suitability for near-surface exploration in complex terrain areas.To improve the accuracy of data interpretation in this method,the authors conducted a systematic three-dimensional(3D)forward modeling and inversion of the UAV-TEM.This study utilized the finite element method based on unstructured tetrahedral elements and employed the second-order backward Euler method for time discretization.This allowed for accurate 3D modeling and accounted for the effects of complex terrain.Based on these,the influence characteristics of flight altitudes and the sizes,burial depths,and resistivities of anomalies are compared and analyzed to explore the UAV-TEM systems’exploration capability.Lastly,four typical geoelectrical models of landslides are designed,and the inversion method based on the Gauss-Newton optimization method is used to image the landslide models and analyze the imaging effect of the UAV-TEM method on landslide geohazards.Numerical results showed that UAV-TEM could have better exploration resolution and fine imaging of nearsurface structures,providing important technical support for monitoring,early warning,and preventing landslides and other geological hazards.

3D magnetotelluric inversions with unstructured finite-element and limited-memory quasi-Newton methods

Traditional 3D Magnetotelluric(MT) forward modeling and inversions are mostly based on structured meshes that have limited accuracy when modeling undulating surfaces and arbitrary structures. By contrast, unstructured-grid-based methods can model complex underground structures with high accuracy and overcome the defects of traditional methods, such as the high computational cost for improving model accuracy and the difficulty of inverting with topography. In this paper, we used the limited-memory quasi-Newton(L-BFGS) method with an unstructured finite-element grid to perform 3D MT inversions. This method avoids explicitly calculating Hessian matrices, which greatly reduces the memory requirements. After the first iteration, the approximate inverse Hessian matrix well approximates the true one, and the Newton step(set to 1) can meet the sufficient descent condition. Only one calculation of the objective function and its gradient are needed for each iteration, which greatly improves its computational efficiency. This approach is well-suited for large-scale 3D MT inversions. We have tested our algorithm on data with and without topography, and the results matched the real models well. We can recommend performing inversions based on an unstructured finite-element method and the L-BFGS method for situations with topography and complex underground structures.

Parallel rapid relaxation inversion of 3D magnetotelluric data

We implement a parallel algorithm with the advantage of MPI （Message Passing Interface） to speed up the rapid relaxation inversion for 3D magnetotelluric data. We test the parallel rapid relaxation algorithm with synthetic and real data. The execution efficiency of the algorithm for several different situations is also compared. The results indicate that the parallel rapid relaxation algorithm for 3D magnetotelluric inversion is effective. This parallel algorithm implemented on a common PC promotes the practical application of 3D magnetotelluric inversion and can be suitable for the other geophysical 3D modeling and inversion.

Estimating primaries by sparse inversion of the 3D Curvelet transform and the L1-norm constraint

In this paper, we built upon the estimating primaries by sparse inversion （EPSI） method. We use the 3D curvelet transform and modify the EPSI method to the sparse inversion of the biconvex optimization and Ll-norm regularization, and use alternating optimization to directly estimate the primary reflection coefficients and source wavelet. The 3D curvelet transform is used as a sparseness constraint when inverting the primary reflection coefficients, which results in avoiding the prediction subtraction process in the surface-related multiples elimination （SRME） method. The proposed method not only reduces the damage to the effective waves but also improves the elimination of multiples. It is also a wave equation- based method for elimination of surface multiple reflections, which effectively removes surface multiples under complex submarine conditions.

Contrast between 2D inversion and 3D inversion based on 2D high-density resistivity data

The 2D data processing adopted by the high-density resistivity method regards the geological structures as two degrees, which makes the results of the 2D data inversion only an approximate interpretation;the accuracy and effect can not meet the precise requirement of the inversion. Two typical models of the geological bodies were designed, and forward calculation was carried out using finite element method. The forward-modeled profiles were obtained. 1% Gaussian random error was added in the forward models and then 2D and 3D inversions using a high-density resistivity method were undertaken to realistically simulate field data and analyze the sensitivity of the 2D and 3D inversion algorithms to noise. Contrast between the 2D and 3D inversion results of least squares inversion shows that two inversion results of high-density resistivity method all can basically reflect the spatial position of an anomalous body. However, the 3D inversion can more effectively eliminate the influence of interference from Gaussian random error and better reflect the distribution of resistivity in the anomalous bodies. Overall, the 3D inversion was better than 2D inversion in terms of embodying anomalous body positions, morphology and resistivity properties.

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.

Three-dimensional constrained gravity inversion of Moho depth and crustal structural characteristics at Mozambique continental margin

Mozambique's continental margin in East Africa was formed during the break-off stage of the east and west Gondwana lands. Studying the geological structure and division of continent-ocean boundary(COB) in Mozambique's continental margin is considered of great significance to rebuild Gondwana land and understand its movement mode. Along these lines, in this work, the initial Moho was fit using the known Moho depth from reflection seismic profiles, and a 3D multi-point constrained gravity inversion was carried out. Thus, highaccuracy Moho depth and crustal thickness in the study area were acquired. According to the crustal structure distribution based on the inversion results, the continental crust at the narrowest position of the Mozambique Channel was detected. According to the analysis of the crustal thickness, the Mozambique ridge is generally oceanic crust and the COB of the whole Mozambique continental margin is divided.

3D LBFGS inversion of controlled source extremely low frequency electromagnetic data

The controlled source extremely low frequency （CSELF） electromagnetic method is characterized by extremely long and powerful sources and a huge measurement range. Its electromagnetic field can therefore be affected by the ionosphere and displacement current. Research on 3D forward modeling and inversion of CSELF electromagnetic data is currently in its infancy. This paper makes exploratory attempts to firstly calculate the 1D extremely low frequency electromagnetic field under ionosphere-air-earth coupling circumstances, and secondly analyze the propagation characteristics of the background electromagnetic field. The 3D staggered-grid finite difference scheme for solving for the secondary electric field is adopted and incorporated with the 1D modeling algorithm to complete 3D forward modeling. Considering that surveys can be carried out in the near field and transition zone for lower frequencies, the 3D Limited-memory Broyden-Fletcher-Goldfarb-Shanno （LBFGS） inversion of CSELF electromagnetic data is presented （in which the sources, or primary fields, are included）, with the aim of directly inverting the impedance data, regardless of where it is acquired. Derivation of the objective functional gradient is the core component in the inversion. Synthetic tests indicate that the well-chosen approximation to the Hessian can significantly speed up the inversion. The model responses corresponding to the coexistence of conductive and resistive blocks show that the off-diagonal components of tensor impedance are much more sensitive to the resistivity variation than the diagonal components. In comparison with conventional scalar inversion, tensor inversion is superior in the recoveries of electric anomalies and background resistivity.

3D Step-by-step inversion strategy for audio magnetotellurics data based on unstructured mesh

A three-dimensional(3D)step-by-step inversion strategy for audio magnetotellurics(AMT)is investigated in this study.The objective function is minimized by iteratively solving the Gauss-Newton normal equation,and the inversion region is discretized with unstructured tetrahedral elements.The inversion proceeds step-by-step from a coarse mesh to a fine mesh.In the inversion iteration process,a mesh is adaptively optimized according to the spatial gradient information about the model resistivity to fine delineate the boundaries of abnormal bodies.In the early stage of inversion execution,a coarse mesh is used for inversion,and the inversion stability is improved by reducing the number of inversion elements.In addition,mesh refinement is performed in the iterative inversion process.The inversion results obtained from the previous mesh are used as the reference and initial models for the next mesh iterative inversion.The step-by-step inversion strategy can ensure that the inversion is performed in the correct direction,improving the inversion stability and results gradually.Synthetic results show that the step-by-step inversion strategy with a Gauss-Newton method for 3D AMT inversion is stable and reliable,which lays a foundation for further practical 3D AMT data inversion.

3D inversion of audio-magnetotelluric data for mineral exploration:A case study of Layikeleke buried porphyry copper deposit,Xinjiang,China

Layikeleke copper deposit is a large-scale porphyry copper polymetallic buried deposit,which has been discovered recently in the eastern Junggar area of Xinjiang.Mineralization occurred in the Late Silurian and Early Devonian with the copper body mainly confined to tonalite.To find new ore bodies,it is necessary to map the 3D spatial distribution of the tonalite.For this reason,we deployed audio-magnetotelluric(AMT)sounding in the research area,collected 26 profi les and 1198 measuring points,carried out 3D inversion calculations of off-diagonal elements in the impedance tensor data using the nonlinear conjugate gradient method,and obtained a 3D electrical structure model.The electrical structure reveals two groups of NW-SE trending middle and middle low resistivity anomaly zones,which intersect the high resistivity bedrock area in the northwest of the study area.Based on the electrical data,it can be inferred that the medium low resistance tonalite in the northern part of the study area is the host rock of the porphyry copper polymetallic deposit,which has been verifi ed by borehole data.The results of 3D AMT inversion depict the spatial distribution and depth variation characteristics of the tonalite electrical structure model,providing a basis for further prospecting and exploration.Therefore,this method of identifying lithology by 3D inversion can provide an important basis for mineral exploration and mining of buried rock masses,and is an effective prospecting method.

3D variable-grid full-waveform inversion on GPU

Full-waveform inversion(FWI)is a powerful tool to reconstruct subsurface geophysical parameters with high resolution.As3 D surveys become widely implemented,corresponding 3 D processing techniques are required to solve complex geological cases,while a large amount of computation is the most challenging problem.We propose an adaptive variable-grid 3 D FWI on graphics processing unit devices to improve computational efficiency without losing accuracy.The irregular-grid discretization strategy is based on a dispersion relation,and the grid size adapts to depth,velocity,and frequency automatically.According to the transformed grid coordinates,we derive a modified acoustic wave equation and apply it to full wavefield simulation.The 3 D variable-grid modeling is conducted on several 3 D models to validate its feasibility,accuracy and efficiency.Then we apply the proposed modeling method to full-waveform inversion for source and residual wavefield propagation.It is demonstrated that the adaptive variable-grid FWI is capable of decreasing computing time and memory requirements.From the inversion results of the 3 D SEG/EAGE overthrust model,our method retains inversion accuracy when recovering both thrust and channels.

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.

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.

Seismic traveltime inversion of 3D velocity model with triangulated interfaces

Seismic traveltime tomographic inversion has played an important role in detecting the internal structure of the solid earth. We use a set of blocks to approximate geologically complex media that cannot be well described by layered models or cells. The geological body is described as an aggregate of arbitrarily shaped blocks,which are separated by triangulated interfaces. We can describe the media as homogenous or heterogeneous in each block. We define the velocities at the given rectangle grid points for each block,and the heterogeneous velocities in each block can be calculated by a linear interpolation algorithm. The parameters of the velocity grid positions are independent of the model parameterization,which is advantageous in the joint inversion of the velocities and the node depths of an interface. We implement a segmentally iterative ray tracer to calculate traveltimes in the 3D heterogeneous block models.The damped least squares method is employed in seismic traveltime inversion,which includes the partial derivatives of traveltime with respect to the depths of nodes in the triangulated interfaces and velocities defined in rectangular grids. The numerical tests indicate that the node depths of a triangulated interface and homogeneous velocity distributions can be well inverted in a stratified model.

Inversion of 3D density interface with PSO-BP method

BP( Back Propagation) neural network and PSO( Particle Swarm Optimization) are two main heuristic optimization methods,and are usually used as nonlinear inversion methods in geophysics. The authors applied BP neural network and BP neural network optimized with PSO into the inversion of 3D density interface respectively,and a comparison was drawn to demonstrate the inversion results. To start with,a synthetic density interface model was created and we used the proceeding inversion methods to test their effectiveness. And then two methods were applied into the inversion of the depth of Moho interface. According to the results,it is clear to find that the application effect of PSO-BP is better than that of BP network. The BP network structures used in both synthetic and field data are consistent in order to obtain preferable inversion results. The applications in synthetic and field tests demonstrate that PSO-BP is a fast and effective method in the inversion of 3D density interface and the optimization effect is evident compared with BP neural network merely,and thus,this method has practical value.

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.

3D joint inversion of controlled-source audio-frequency magnetotelluric and magnetotelluric data

Different geophysical exploration methods have significant differences in terms of exploration depth,especially in frequency domain electromagnetic(EM)exploration.According to the definition of skin depth,this difference will increase with the effective detection frequency of the method.As a result,when performing three-dimensional inversion on single type of EM data,it is not possible to effectively distinguish the subsurface geoelectric structure at the full scale.Therefore,it is necessary to perform joint inversion on different type of EM data.In this paper we combine the magnetotelluric method(MT)with the controlled-source audio-magnetotelluric method(CSAMT)to study the frequency-domain three-dimensional(3D)joint inversions,and we use the unstructured finite-element method to do the forward modeling for them,so that the numerical simulation accuracies of different electromagnetic methods can be satisfied.By combining the two sets of data,we can obtain the sensitivity of the electrical structure at different depths,and depict the full-scale subsurface geoelectric structures.In actual mineral exploration,the 3D joint inversion is more useful for identifying subsurface veins in the shallow part and blind mines in the deep part.It can delineate the morphological distribution of ore bodies more completely and provide reliable EM interpretations to guide the mining of minerals.

Location and moment tensor inversion of small earthquakes using 3D Green＇s functions in models with rugged topography： application to the Longmenshan fault zone

With dense seismic arrays and advanced imaging methods, regional three-dimensional （3D） Earth models have become more accurate. It is now increasingly feasible and advantageous to use a 3D Earth model to better locate earthquakes and invert their source mechanisms by fitting synthetics to observed waveforms. In this study, we develop an approach to determine both the earthquake location and source mechanism from waveform information. The observed waveforms are filtered in different frequency bands and separated into windows for the individual phases. Instead of picking the arrival times, the traveltime differences are measured by cross-correlation between synthetic waveforms based on the 3D Earth model and observed waveforms. The earthquake location is determined by minimizing the cross-correlation traveltime differences. We then fix the horizontal location of the earthquake and perform a grid search in depth to determine the source mechanism at each point by fitting the synthetic and observed waveforms. This new method is verified by a synthetic test with noise added to the synthetic waveforms and a realistic station distribution. We apply this method to a series of Mw3.4-5.6 earthquakes in the Longmenshan fault （LMSF） zone, a region with rugged topography between the eastern margin of the Tibetan plateau and the western part of the Sichuan basin. The results show that our solutions result in improved waveform fits compared to the source parameters from the catalogs we used and the location can be better constrained than the amplitude-only approach. Furthermore, the source solutions with realistic topography provide a better fit to the observed waveforms than those without the topography, indicating the need to take the topography into account in regions with rugged topography.