Two-dimensional inversion of spectral induced polarization data using MPI parallel algorithm in data space

Traditional two-dimensional（2D） complex resistivity forward modeling is based on Poisson＇s equation but spectral induced polarization（SIP） data are the coproducts of the induced polarization（IP） and the electromagnetic induction（EMI） effects.This is especially true under high frequencies,where the EMI effect can exceed the IP effect.2D inversion that only considers the IP effect reduces the reliability of the inversion data.In this paper,we derive differential equations using Maxwell＇s equations.With the introduction of the Cole-Cole model,we use the finite-element method to conduct2 D SIP forward modeling that considers the EMI and IP effects simultaneously.The data-space Occam method,in which different constraints to the model smoothness and parametric boundaries are introduced,is then used to simultaneously obtain the four parameters of the Cole-Cole model using multi-array electric field data.This approach not only improves the stability of the inversion but also significantly reduces the solution ambiguity.To improve the computational efficiency,message passing interface programming was used to accelerate the 2D SIP forward modeling and inversion.Synthetic datasets were tested using both serial and parallel algorithms,and the tests suggest that the proposed parallel algorithm is robust and efficient.

Multiobjective particle swarm inversion algorithm for two-dimensional magnetic data

Regularization inversion uses constraints and a regularization factor to solve ill- posed inversion problems in geophysics. The choice of the regularization factor and of the initial model is critical in regularization inversion. To deal with these problems, we propose a multiobjective particle swarm inversion （MOPSOI） algorithm to simultaneously minimize the data misfit and model constraints, and obtain a multiobjective inversion solution set without the gradient information of the objective function and the regularization factor. We then choose the optimum solution from the solution set based on the trade-off between data misfit and constraints that substitute for the regularization factor. The inversion of synthetic two-dimensional magnetic data suggests that the MOPSOI algorithm can obtain as many feasible solutions as possible; thus, deeper insights of the inversion process can be gained and more reasonable solutions can be obtained by balancing the data misfit and constraints. The proposed MOPSOI algorithm can deal with the problems of choosing the right regularization factor and the initial model.

Two-dimensional frequency-domain acoustic fullwaveform inversion with rugged topography

We studied finite-element-method-based two-dimensional frequency-domain acoustic FWI under rugged topography conditions. The exponential attenuation boundary condition suitable for rugged topography is proposed to solve the cutoff botmdary problem as well as to consider the requirement of using the same subdivision grid in joint multifrequency inversion. The proposed method introduces the attenuation factor, and by adjusting it, acoustic waves are sufficiently attenuated in the attenuation layer to minimize the cutoff boundary effect. Based on the law of exponential attenuation, expressions for computing the attenuation factor and the thickness of attenuation layers are derived for different frequencies. In multifrequency-domain FWI, the conjugate gradient method is used to solve equations in the Gauss-Newton algorithm and thus minimize the computation cost in calculating the Hessian matrix. In addition, the effect of initial model selection and frequency combination on FWI is analyzed. Examples using numerical simulations and FWI calculations are used to verify the efficiency of the proposed method.

Two-dimensional regularized inversion of AMT data based on rotation invariant of Central impedance tensor

Considering the uncertainty of the electrical axis for two-dimensional audo-magnetotelluric(AMT) data processing, an AMT inversion method with the Central impedance tensor was presented. First, we present a calculation expression of the Central impedance tensor in AMT, which can be considered as the arithmetic mean of TE-polarization mode and TM-polarization mode in the twodimensional geo-electrical model. Second, a least-squares iterative inversion algorithm is established, based on a smoothnessconstrained model, and an improved L-curve method is adopted to determine the best regularization parameters. We then test the above inversion method with synthetic data and field data. The test results show that this two-dimensional AMT inversion scheme for the responses of Central impedance is effective and can reconstruct reasonable two-dimensional subsurface resistivity structures. We conclude that the Central impedance tensor is a useful tool for two-dimensional inversion of AMT data.

Comparison of different inversion methods of D-T_(2)two-dimensional nuclear magnetic resonance logging and applicability analysis

D-T_(2)two-dimensional nuclear magnetic resonance(2D NMR)logging technology can distinguish pore fluid types intuitively,and it is widely used in oil and gas exploration.Many 2D NMR inversion methods(e.g.,truncated singular value decomposition(TSVD),Butler-Reds-Dawson(BRD),LM-norm smoothing,and TIST-L1 regularization methods)have been proposed successively,but most are limited to numerical simulations.This study focused on the applicability of different inversion methods for NMR logging data of various acquisition sequences,from which the optimal inversion method was selected based on the comparative analysis.First,the two-dimensional NMR logging principle was studied.Then,these inversion methods were studied in detail,and the precision and computational efficiency of CPMG and diffusion editing(DE)sequences obtained from oil-water and gas-water models were compared,respectively.The inversion results and calculation time of truncated singular value decomposition(TSVD),Butler-Reds-Dawson(BRD),LM-norm smoothing,and TIST-L1 regularization were compared and analyzed through numerical simulations.The inversion method was optimized to process SP mode logging data from the MR Scanner instrument.The results showed that the TIST-regularization and LM-norm smoothing methods were more accurate for the CPMG and DE sequence echo trains of the oil-water and gas-water models.However,the LM-norm smoothing method was less time-consuming,making it more suitable for logging data processing.A case study in well A25 showed that the processing results by the LM-norm smoothing method were consistent with GEOLOG software.This demonstrates that the LM-norm smoothing method is applicable in practical NMR logging processing.

Inversion of two-dimensional tidal open boundary conditions of M_2 constituent in the Bohai and Yellow Seas

Two-dimensional tidal open boundary conditions of the M2 constituent in the Bohai and Yellow Seas(BYS) have been estimated by assimilating T/P altimeter data.During inversion,independent point(IP) strategy was used,in which several IPs on the open boundary is assumed,values at these IPs can be optimized with an adjoint method,and those at other grid points are determined by linearly interpolating the values at IPs.The reasonability and feasibility of the model are tested by ideal twin experiments.In the practical experiment(PE) after assimilation,the cost function may reach 1% or less of its initial value.Mean absolute errors in amplitude and phase can be less than 5 cm and 5°,respectively,and the obtained co-chart can show the character of the M2 constituent in the BYS.The results of the PE indicate that using only two IPs on the open boundary can yield better simulated results.

Geometric Inversion of Two-Dimensional Stokes Flows – Application to the Flow between Parallel Planes

Geometric inversion is applied to two-dimensional Stokes flow in view to find new Stokes flow solutions. The principle of this method and the relations between the reference and inverse fluid velocity fields are presented. They are followed by applications to the flow between two parallel plates induced by a rotating or a translating cylinder. Thus hydrodynamic characteristics of flow around circular bodies obtained by inversion of the plates are thus deduced. Typically fluid flow patterns around two circular cylinders in contact placed in the centre of a rotating or a translating circular cylinder are illustrated.

Two-dimensional NMR inversion based on fast norm smoothing method

Two-dimensional(2D)nuclear magnetic resonance(NMR)inversion operates with massive echo train data and is an ill-posed problem.It is very important to select a suitable inversion method for the 2D NMR data processing.In this study,we propose a fast,robust,and effective method for 2D NMR inversion that improves the computational efficiency of the inversion process by avoiding estimation of some unneeded regularization parameters.Firstly,a method that combines window averaging(WA)and singular value decomposition(SVD)is used to compress the echo train data and obtain the singular values of the kernel matrix.Subsequently,an optimum regularization parameter in a fast manner using the signal-to-noise ratio(SNR)of the echo train data and the maximum singular value of the kernel matrix are determined.Finally,we use the Butler-Reeds-Dawson(BRD)method and the selected optimum regularization parameter to invert the compressed data to achieve a fast 2D NMR inversion.The numerical simulation results indicate that the proposed method not only achieves satisfactory 2D NMR spectra rapidly from the echo train data of different SNRs but also is insensitive to the number of the final compressed data points.

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.

THE WAVE EQUATION APPROACH TO THE TWO-DIMENSIONAL INVERSE PROBLEM FOR A GENERAL BOUNDED DOMAIN WITH PIECEWISE SMOOTH MIXED BOUNDARY CONDITIONS

The spectral distribution exp( ), where {} are the eigenvalues of the negative Laplacian -△=- in the (x^1,x^2)-plane, is studied for a variety of domains, where -∞< t <∞ and i=(1/2)(-1) . The dependence of (t)on the connectivity of a domain and the boundary conditions are analyzed. Particular attention is given to a general bounded domain Ω in R^2 with a smooth boundary Ω, where a finite number of piecewise smooth Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth parts Γj(j = 1,……,n) of Ω are considered such that Some geometrical properties of Ω(e.g., the area of Ω, the total lengths of the boundary, the curvature of its boundary, etc.) are determined, from the asymptotic expansions of (t) for |t| → 0.

Assessing the effects of model parameter assumptions on surface-wave inversion results

Surface-wave inversion is a powerful tool for revealing the Earth's internal structure.However,aside from shear-wave velocity(v_(S)),other parameters can influence the inversion outcomes,yet these have not been systematically discussed.This study investigates the influence of various parameter assumptions on the results of surface-wave inversion,including the compressional and shear velocity ratio(v_(P)/v_(S)),shear-wave attenuation(Q_(S)),density(ρ),Moho interface,and sedimentary layer.We constructed synthetic models to generate dispersion data and compared the obtained results with different parameter assumptions with those of the true model.The results indicate that the v_(P)/v_(S) ratio,Q_(S),and density(ρ) have minimal effects on absolute velocity values and perturbation patterns in the inversion.Conversely,assumptions about the Moho interface and sedimentary layer significantly influenced absolute velocity values and perturbation patterns.Introducing an erroneous Mohointerface depth in the initial model of the inversion significantly affected the v_(S) model near that depth,while using a smooth initial model results in relatively minor deviations.The assumption on the sedimentary layer not only affects shallow structure results but also impacts the result at greater depths.Non-linear inversion methods outperform linear inversion methods,particularly for the assumptions of the Moho interface and sedimentary layer.Joint inversion with other data types,such as receiver functions or Rayleigh wave ellipticity,and using data from a broader period range or higher-mode surface waves,can mitigate these deviations.Furthermore,incorporating more accurate prior information can improve inversion results.

Layer-Valley Hall Effect under Inversion and Time-Reversal Symmetries

Hall effects have been the central paradigms in modern physics,materials science and practical applications,and have led to many exciting breakthroughs,including the discovery of topological Chern invariants and the revolution of metrological resistance standard.To date,the Hall effects have mainly focused on a single degree of freedom(Do F),and most of them require the breaking of spatial-inversion and/or time-reversal symmetries.Here we demonstrate a new type of Hall effect,i.e.,layer-valley Hall effect,based on a combined layer-valley Do F characterized by the product of layer and valley indices.The layer-valley Hall effect has a quantum origin arising from the layer-valley contrasting Berry curvature,and can occur in nonmagnetic centrosymmetric crystals with both spatial-inversion and time-reversal symmetries,transcending the symmetry constraints of single Do F Hall effect based on the constituent layer or valley index.Moreover,the layer-valley Hall effect is highly tunable and shows a W-shaped pattern in response to the out-of-plane electric fields.Additionally,we discuss the potential detection approaches and material-specific design principles of layer-valley Hall effect.Our results demonstrate novel Hall physics and open up exotic paradigms for new research direction of layer-valleytronics that exploits the quantum nature of the coupled layer-valley DoF.

Progress on two-dimensional ferrovalley materials

The electron's charge and spin degrees of freedom are at the core of modern electronic devices. With the in-depth investigation of two-dimensional materials, another degree of freedom, valley, has also attracted tremendous research interest. The intrinsic spontaneous valley polarization in two-dimensional magnetic systems, ferrovalley material, provides convenience for detecting and modulating the valley. In this review, we first introduce the development of valleytronics.Then, the valley polarization forms by the p-, d-, and f-orbit that are discussed. Following, we discuss the investigation progress of modulating the valley polarization of two-dimensional ferrovalley materials by multiple physical fields, such as electric, stacking mode, strain, and interface. Finally, we look forward to the future developments of valleytronics.

An illustrated guide to:Parsimonious multi-scale full-waveform inversion

Having been a seemingly unreachable ideal for decades,3-D full-waveform inversion applied to massive seismic datasets has become reality in recent years.Often achieving unprecedented resolution,it has provided new insight into the structure of the Earth,from the upper few metres of soil to the entire globe.Motivated by these successes,the technology is now being translated to medical ultrasound and non-destructive testing.Despite remarkable progress,the computational cost of fullwaveform inversion continues to be a major concern.It limits the amount of data that can be exploited,and it largely inhibits quantitative and comprehensive uncertainty analyses.These notes complement a presentation on recent developments in full-waveform inversion that are intended to reduce computational cost and assimilate more data,thereby improving tomographic resolution.The suite of strategies includes flexible and user-friendly spectral-element simulations,the design of wavefieldadapted meshes that harness prior information on wavefield geometry,dynamic mini-batch optimisation that naturally takes advantage of data redundancies,and collaborative multi-scale updating to jointly constrain crustal and mantle structure.

Recent advances in two-dimensional photovoltaic devices

Two-dimensional(2D)materials have attracted tremendous interest in view of the outstanding optoelectronic properties,showing new possibilities for future photovoltaic devices toward high performance,high specific power and flexibility.In recent years,substantial works have focused on 2D photovoltaic devices,and great progress has been achieved.Here,we present the review of recent advances in 2D photovoltaic devices,focusing on 2D-material-based Schottky junctions,homojunctions,2D−2D heterojunctions,2D−3D heterojunctions,and bulk photovoltaic effect devices.Furthermore,advanced strategies for improving the photovoltaic performances are demonstrated in detail.Finally,conclusions and outlooks are delivered,providing a guideline for the further development of 2D photovoltaic devices.

Alternating spin splitting of electronic and magnon bands in two-dimensional altermagnetic materials

Unconventional antiferromagnetism dubbed as altermagnetism was first discovered in rutile structured magnets,which is featured by spin splitting even without the spin–orbital coupling effect.This interesting phenomenon has been discovered in more altermagnetic materials.In this work,we explore two-dimensional altermagnetic materials by studying two series of two-dimensional magnets,including MF4 with M covering all 3d and 4d transition metal elements,as well as TS2 with T=V,Cr,Mn,Fe.Through the magnetic symmetry operation of RuF4 and MnS2,it is verified that breaking the time inversion is a necessary condition for spin splitting.Based on symmetry analysis and first-principles calculations,we find that the electronic bands and magnon dispersion experience alternating spin splitting along the same path.This work paves the way for exploring altermagnetism in two-dimensional materials.

Unlocking the potential of ultra-thin two-dimensional antimony materials:Selective growth and carbon coating for efficient potassium-ion storage

Antimony-based anodes have attracted wide attention in potassium-ion batteries due to their high theoretical specific capacities(∼660 mA h g^(-1))and suitable voltage platforms.However,severe capacity fading caused by huge volume change and limited ion transportation hinders their practical applications.Recently,strategies for controlling the morphologies of Sb-based materials to improve the electrochemical performances have been proposed.Among these,the two-dimensional Sb(2D-Sb)materials present excellent properties due to shorted ion immigration paths and enhanced ion diffusion.Nevertheless,the synthetic methods are usually tedious,and even the mechanism of these strategies remains elusive,especially how to obtain large-scale 2D-Sb materials.Herein,a novel strategy to synthesize 2D-Sb material using a straightforward solvothermal method without the requirement of a complex nanostructure design is provided.This method leverages the selective adsorption of aldehyde groups in furfural to induce crystal growth,while concurrently reducing and coating a nitrogen-doped carbon layer.Compared to the reported methods,it is simpler,more efficient,and conducive to the production of composite nanosheets with uniform thickness(3–4 nm).The 2D-Sb@NC nanosheet anode delivers an extremely high capacity of 504.5 mA h g^(-1) at current densities of 100 mA g^(-1) and remains stable for more than 200 cycles.Through characterizations and molecular dynamic simulations,how potassium storage kinetics between 2D Sb-based materials and bulk Sb-based materials are explored,and detailed explanations are provided.These findings offer novel insights into the development of durable 2D alloy-based anodes for next-generation potassium-ion batteries.

Linearized waveform inversion for vertical transversely isotropic elastic media:Methodology and multi-parameter crosstalk analysis

Seismic migration and inversion are closely related techniques to portray subsurface images and identify hydrocarbon reservoirs.Seismic migration aims at obtaining structural images of subsurface geologic discontinuities.More specifically,seismic migration estimates the reflectivity function(stacked average reflectivity or pre-stack angle-dependent reflectivity)from seismic reflection data.On the other hand,seismic inversion quantitatively estimates the intrinsic rock properties of subsurface formulations.Such seismic inversion methods are applicable to detect hydrocarbon reservoirs that may exhibit lateral variations in the inverted parameters.Although there exist many differences,pre-stack seismic migration is similar with the first iteration of the general linearized seismic inversion.Usually,seismic migration and inversion techniques assume an acoustic or isotropic elastic medium.Unconventional reservoirs such as shale and tight sand formation have notable anisotropic property.We present a linearized waveform inversion(LWI)scheme for weakly anisotropic elastic media with vertical transversely isotropic(VTI)symmetry.It is based on two-way anisotropic elastic wave equation and simultaneously inverts for the localized perturbations(ΔVp_(0)/Vp_(0)/Vs_(0)/Vs_(0)/,Δ∈,Δδ)from the long-wavelength reference model.Our proposed VTI-elastic LWI is an iterative method that requires a forward and an adjoint operator acting on vectors in each iteration.We derive the forward Born approximation operator by perturbation theory and adjoint operator via adjoint-state method.The inversion has improved the quality of the images and reduces the multi-parameter crosstalk comparing with the adjoint-based images.We have observed that the multi-parameter crosstalk problem is more prominent in the inversion images for Thomsen anisotropy parameters.Especially,the Thomsen parameter is the most difficult to resolve.We also analyze the multi-parameter crosstalk using scattering radiation patterns.The linearized waveform inversion for VTI-elastic media presented in this article provides quantitative information of the rock properties that has the potential to help identify hydrocarbon reservoirs.

Recent progress on valley polarization and valley-polarized topological states in two-dimensional materials

Valleytronics, using valley degree of freedom to encode, process, and store information, may find practical applications in low-power-consumption devices. Recent theoretical and experimental studies have demonstrated that twodimensional(2D) honeycomb lattice systems with inversion symmetry breaking, such as transition-metal dichalcogenides(TMDs), are ideal candidates for realizing valley polarization. In addition to the optical field, lifting the valley degeneracy of TMDs by introducing magnetism is an efficient way to manipulate the valley degree of freedom. In this paper, we first review the recent progress on valley polarization in various TMD-based systems, including magnetically doped TMDs,intrinsic TMDs with both inversion and time-reversal symmetry broken, and magnetic TMD heterostructures. When topologically nontrivial bands are empowered into valley-polarized systems, valley-polarized topological states, namely valleypolarized quantum anomalous Hall effect can be realized. Therefore, we have also reviewed the theoretical proposals for realizing valley-polarized topological states in 2D honeycomb lattices. Our paper can help readers quickly grasp the latest research developments in this field.

Global dust density in two-dimensional complex plasma

The driven-dissipative Langevin dynamics simulation is used to produce a two-dimensional(2D) dense cloud, which is composed of charged dust particles trapped in a quadratic potential. A 2D mesh grid is built to analyze the center-to-wall dust density. It is found that the local dust density in the outer region relative to that of the inner region is more nonuniform,being consistent with the feature of quadratic potential. The dependences of the global dust density on equilibrium temperature, particle size, confinement strength, and confinement shape are investigated. It is found that the particle size, the confinement strength, and the confinement shape strongly affect the global dust density, while the equilibrium temperature plays a minor effect on it. In the direction where there is a stronger confinement, the dust density gradient is bigger.