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.

A Comprehensive Overview of the ELECTRE Method in Multi-Criteria Decision-Making

The ELECTRE(ELimination Et Choix Traduisant la REalite)method has gained widespread recognition as one of the most effective multi-criteria decision-making(MCDM)methods.Its versatility allows it to be applied in a wide range of areas such as engineering,economics,business,environmental management and many others.This paper aims to provide an overview of the ELECTRE method,including its fundamental concepts,applications,advantages,and limitations.At its core,the ELECTRE method is an outranking family of MCDM techniques,which allows for the direct comparison of alternatives based on a set of criteria.The method takes into account the preferences and importance of decision-makers and generates a ranking of the alternatives based on their relative strengths and weaknesses.The ELECTRE method is a powerful tool for decision-making,and its applicability to a wide range of fields demonstrates its versatility and adaptability.By understanding its concepts,applications,merits,and demerits,decision-makers can use the ELECTRE method to make informed and effective decisions in a variety of contexts.

STRAIGHTFORWARD MULTI-SCALE BOUNDARY ELEMENT METHOD FOR GLOBAL/LOCAL MECHANICAL ANALYSIS OF ELASTIC HETEROGENEOUS MATERIAL

A straightforward multi-scale boundary element method is proposed for global and local mechanical analysis of heterogeneous material.The method is more accurate and convenient than finite element based multi-scale method.The formulations of this method are derived by combining the homogenization approach and the fundamental equations of boundary element method.The solution gives the convenient formulations to compute global elastic constants and the local stress field.Finally,two numerical examples of porous material are presented to prove the accuracy and the efficiency of the proposed method.The results show that the method does not require the iteration to obtain the solution of the displacement in micro level.

The Multi-scale Method for Solving Nonlinear Time Space Fractional Partial Differential Equations

In this paper, we present a new algorithm to solve a kind of nonlinear time space-fractional partial differential equations on a finite domain. The method is based on B-spline wavelets approximations, some of these functions are reshaped to satisfy on boundary conditions exactly. The Adams fractional method is used to reduce the problem to a system of equations. By multiscale method this system is divided into some smaller systems which have less computations. We get an approximated solution which is more accurate on some subdomains by combining the solutions of these systems. Illustrative examples are included to demonstrate the validity and applicability of our proposed technique, also the stability of the method is discussed.

AN ADAPTIVE MULTI-SCALE CONJUGATE GRADIENT METHOD FOR DISTRIBUTED PARAMETER ESTIMATION OF 2-D WAVE EQUATION

An adaptive multi-scale conjugate gradient method for distributed parameter estimations (or inverse problems) of wave equation is presented. The identification of the coefficients of wave equations in two dimensions is considered. First, the conjugate gradient method for optimization is adopted to solve the inverse problems. Second,the idea of multi-scale inversion and the necessary conditions that the optimal solution should be the fixed point of multi-scale inversion method isconsidered. An adaptive multi-scale inversion method for the inverse problem is developed in conjunction with the conjugate gradient method. Finally, some numerical results are shown to indicate the robustness and effectiveness of our method.

An Effective Numerical Calculation Method for Multi-Time-Scale Mathematical Models in Systems Biology

The improvements of high-throughput experimental devices such as microarray and mass spectrometry have allowed an effective acquisition of biological comprehensive data which include genome, transcriptome, proteome, and metabolome (multi-layered omics data). In Systems Biology, we try to elucidate various dynamical characteristics of biological functions with applying the omics data to detailed mathematical model based on the central dogma. However, such mathematical models possess multi-time-scale properties which are often accompanied by time-scale differences seen among biological layers. The differences cause time stiff problem, and have a grave influence on numerical calculation stability. In the present conventional method, the time stiff problem remained because the calculation of all layers was implemented by adaptive time step sizes of the smallest time-scale layer to ensure stability and maintain calculation accuracy. In this paper, we designed and developed an effective numerical calculation method to improve the time stiff problem. This method consisted of ahead, backward, and cumulative algorithms. Both ahead and cumulative algorithms enhanced calculation efficiency of numerical calculations via adjustments of step sizes of each layer, and reduced the number of numerical calculations required for multi-time-scale models with the time stiff problem. Backward algorithm ensured calculation accuracy in the multi-time-scale models. In case studies which were focused on three layers system with 60 times difference in time-scale order in between layers, a proposed method had almost the same calculation accuracy compared with the conventional method in spite of a reduction of the total amount of the number of numerical calculations. Accordingly, the proposed method is useful in a numerical analysis of multi-time-scale models with time stiff problem.

A Comparison of Two Macroinvertebrate Multi-Plate Sampling Methods to Inform Great Lakes Monitoring and Remediation Efforts

Hester-Dendy (HD) multi-plate samplers have been widely used by state and federal government agencies for bioassessment of water quality through use of macroinvertebrate community data. To help guide remediation and restoration efforts at the Niagara River Great Lakes Area of Concern site, a multi-agency study was conducted in 2014 to assess the contribution of seven major urban tributaries on the US side of the river toward the impairment of the Niagara River. As part of this study, macroinvertebrate communities were sampled using two co-located versions of HD samplers: one version used by the New York State Department of Environmental Conservation (NYSDEC) and another by the US Environmental Protection Agency Office of Research and Development. Samplers were deployed in tributaries in highly developed watersheds with high percent impervious surface. The two sampling methods varied in terms of number and size of plates, between-plate spacing, and deployment method. Comparison of the similarity/grouping of communities with multivariate ordination techniques, Nonmetric Multidimensional Scaling and Multi-Response Permutation Procedure, showed that both methods were able to detect differences in communities at stations, despite some grouping by month and method. The indices and metrics derived from the two HD methods were found to give comparable but not identical assessments of water quality. Despite their differences, the methods were robust with respect to water quality categories derived from indices used nationally (HBI) and by NY state (BAP). For the common richness metrics, total taxa and EPT richness, there was no statistical difference between means from 3 samplings. Some metrics, especially percent tolerant collector-gatherer individuals, did show significant differences at certain stations. Indicator Species Analysis showed some taxa associated with each method. The observed community differences were thought mostly due to the difference in sampler deployment position. .

Solving Multi-Objective Linear Programming Problem by Statistical Averaging Method with the Help of Fuzzy Programming Method

A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming problem can be converted into the single objective function by various methods as Chandra Sen’s method, weighted sum method, ranking function method, statistical averaging method. In this paper, Chandra Sen’s method and statistical averaging method both are used here for making single objective function from multi-objective function. Two multi-objective programming problems are solved to verify the result. One is numerical example and the other is real life example. Then the problems are solved by ordinary simplex method and fuzzy programming method. It can be seen that fuzzy programming method gives better optimal values than the ordinary simplex method.

Study on spline wavelet finite-element method in multi-scale analysis for foundation

A new finite element method （FEM） of B-spline wavelet on the interval （BSWI） is proposed. Through analyzing the scaling functions of BSWI in one dimension, the basic formula for 2D FEM of BSWI is deduced. The 2D FEM of 7 nodes and 10 nodes are constructed based on the basic formula. Using these proposed elements, the multiscale numerical model for foundation subjected to harmonic periodic load, the foundation model excited by external and internal dynamic load are studied. The results show the pro- posed finite elements have higher precision than the tradi- tional elements with 4 nodes. The proposed finite elements can describe the propagation of stress waves well whenever the foundation model excited by extemal or intemal dynamic load. The proposed finite elements can be also used to con- nect the multi-scale elements. And the proposed finite elements also have high precision to make multi-scale analysis for structure.

Selection Method of Multi-Objective Problems Using Genetic Algorithm in Motion Plan of AUV

To research the effect of the selection method of multi-objects genetic algorithm problem on optimizing result, thismethod is analyzed theoretically and discussed by using an autonomous underwater vehicle(AUV) as an object. A changingweight vtlue method is put forward and a selection formula is modified. Some experiments were implemented on an AUV.TwinBurger. The results shows that this method is effective and feasible.

Formula for calculating spatial similarity degrees between point clouds on multi-scale maps taking map scale change as the only independent variable

The degree of spatial similarity plays an important role in map generalization, yet there has been no quantitative research into it. To fill this gap, this study first defines map scale change and spatial similarity degree/relation in multi-scale map spaces and then proposes a model for calculating the degree of spatial similarity between a point cloud at one scale and its gener- alized counterpart at another scale. After validation, the new model features 16 points with map scale change as the x coordinate and the degree of spatial similarity as the y coordinate. Finally, using an application for curve fitting, the model achieves an empirical formula that can calculate the degree of spatial similarity using map scale change as the sole independent variable, and vice versa. This formula can be used to automate algorithms for point feature generalization and to determine when to terminate them during the generalization.

A LEVEL SET METHOD FOR STRUCTURAL TOPOLOGY OPTIMIZATION WITH MULTI-CONSTRAINTS AND MULTI-MATERIALS

Combining the vector level set model,the shape sensitivity analysis theory with the gradient projection technique,a level set method for topology optimization with multi-constraints and multi-materials is presented in this paper.The method implicitly describes structural material in- terfaces by the vector level set and achieves the optimal shape and topology through the continuous evolution of the material interfaces in the structure.In order to increase computational efficiency for a fast convergence,an appropriate nonlinear speed mapping is established in the tangential space of the active constraints.Meanwhile,in order to overcome the numerical instability of general topology opti- mization problems,the regularization with the mean curvature flow is utilized to maintain the interface smoothness during the optimization process.The numerical examples demonstrate that the approach possesses a good flexibility in handling topological changes and gives an interface representation in a high fidelity,compared with other methods based on explicit boundary variations in the literature.

Explicit multi-symplectic method for the Zakharov-Kuznetsov equation

We propose an explicit multi-symplectic method to solve the two-dimensional Zakharov-Kuznetsov equation. The method combines the multi-symplectic Fourier pseudospectral method for spatial discretization and the Euler method for temporal discretization. It is verified that the proposed method has corresponding discrete multi-symplectic conservation laws. Numerical simulations indicate that the proposed scheme is characterized by excellent conservation.

Three-Dimensional Multi-mesh Material Point Method for Solving Collision Problems

为三维的材料点方法的一个新多网孔接触算法被介绍。接触算法忠实地恢复在碰撞身体之间的相反的代理力量。在常规身体或僵硬身体之间的碰撞过程在一样的框架以内被对待。动量和团的多值在每个节点上被定义描述接触 / 幻灯片 / 分离过程。在接触表面的每个粒子的正常、正切的速度在各自的单个网孔被计算。库仑磨擦被使用描述在联系身体之间滑动或滑倒。接触算法的效率是线性地与联系身体的数字有关因为当节的动量和团被形成在时，重叠节点被打扫所有身体的材料粒子标记每次走。数字模拟证明我们的接触算法拥有高精确性和低数字精力驱散，它为解决碰撞问题是很重要的。

Imaginary displacement method for analysis of multi-fingered robot hands grasping stability

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Multi-symplectic methods for membrane free vibration equation

In this paper, the multi-symplectic formulations of the membrane free vibration equation with periodic boundary conditions in Hamilton space are considered. The complex method is introduced and a semi-implicit twenty-seven-points scheme with certain discrete conservation laws-a multi-symplectic conservation law （CLS）, a local energy conservation law （ECL） as well as a local momentum conservation law （MCL） --is constructed to discrete the PDEs that are derived from the membrane free vibration equation. The results of the numerical experiments show that the multi-symplectic scheme has excellent long-time numerical behavior,

THE APPLICATION OF MULTI－SCALE PERTURBATION METHOD TO THE STABILITY ANALYSIS OF PLANE COUETTE FLOW

This paper applies the multi-scale perturbation method suggested by Ref [3] toinvestigate the linear stability behavior of distorted plane Couette .flow. Using thismethod, the unstable Tollmien-Schlichting wave in plane Couette flow can be found,but not the most unstable mode. By comparing the results of this paper with those ofRef. [3], the effectiveness of this method is investigated.

M-TIMES SECANT-LIKE MULTI-PROJCTION METHOD FOR SPARSE MINIMIZATION PROBLEM

In this paper, we present m time secant like multi projection algorithm for sparse unconstrained minimization problem. We prove this method are all q superlinearly convergent to the solution about m≥1 . At last, we from some numerical results, discuss how to choose the number m to determine the approximating matrix properly in practical use.