A Non-parametric Gradient-Based Shape Optimization Approach for Solving Inverse Problems in Directed Self-Assemblyof Block Copolymers

We consider the inverse problem of finding guiding pattern shapes that result in desired self-assembly morphologies of block copolymer melts.Specifically,we model polymer selfassembly using the self-consistent field theory and derive,in a non-parametric setting,the sensitivity of the dissimilarity between the desired and the actual morphologies to arbitrary perturbations in the guiding pattern shape.The sensitivity is then used for the optimization of the confining pattern shapes such that the dissimilarity between the desired and the actual morphologies is minimized.The efficiency and robustness of the proposed gradient-based algorithm are demonstrated in a number of examples related to templating vertical interconnect accesses(VIA).

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.

Multi-objective strategy to optimize dithering technique for high-quality three-dimensional shape measurement

Dithering optimization techniques can be divided into the phase-optimized technique and the intensity-optimized technique. The problem with the former is the poor sensitivity to various defocusing amounts, and the problem with the latter is that it cannot enhance phase quality directly nor efficiently. In this paper, we present a multi-objective optimization framework for three-dimensional(3D) measurement by utilizing binary defocusing technique. Moreover, a binary patch optimization technique is used to solve the time-consuming issue of genetic algorithm. It is demonstrated that the presented technique consistently obtains significant phase performance improvement under various defocusing amounts.

A method for phase reconstruction in optical three-dimensional shape measurement

In optical three-dimensional shape measurement, a method of improving the measurement precision for phase reconstruction without phase unwrapping is analyzed in detail. Intensities of any five consecutive pixels that lie in the x-axis direction of the phase domain are given. Partial derivatives of the phase function in the x- and y-axis directions are obtained with a phase-shifting mechanism, the origin of which is analysed. Furthermore, to avoid phase unwrapping in the phase reconstruction, we derive the gradient of the phase function and perform a two-dimensional integral along the x- and y-axis directions. The reconstructed phase can be obtained directly by performing numerical integration, and thus it is of great convenience for phase reconstruction. Finally, the results of numerical simulations and practical experiments verify the correctness of the proposed method.

Balanced Functional Maps for Three-Dimensional Non-Rigid Shape Registration

Three-dimensional(3D)shape registration is a challenging problem,especially for shapes under non-rigid transformations.In this paper,a 3D non-rigid shape registration method is proposed,called balanced functional maps(BFM).The BFM algorithm generalizes the point-based correspondence to functions.By choosing the Laplace-Beltrami eigenfunctions as the function basis,the transformations between shapes can be represented by the functional map(FM)matrix.In addition,many constraints on shape registration,such as the feature descriptor,keypoint,and salient region correspondence,can be formulated linearly using the matrix.By bi-directionally searching for the nearest neighbors of points’indicator functions in the function space,the point-based correspondence can be derived from FMs.We conducted several experiments on the Topology and Orchestration Specification for Cloud Applications(TOSCA)dataset and the Shape Completion and Animation of People(SCAPE)dataset.Experimental results show that the proposed BFM algorithm is effective and has superior performance than the state-of-the-art methods on both datasets.

3D parallel inversion of time-domain airborne EM data

To improve the inversion accuracy of time-domain airborne electromagnetic data, we propose a parallel 3D inversion algorithm for airborne EM data based on the direct Gauss-Newton optimization. Forward modeling is performed in the frequency domain based on the scattered secondary electrical field. Then, the inverse Fourier transform and convolution of the transmitting waveform are used to calculate the EM responses and the sensitivity matrix in the time domain for arbitrary transmitting waves. To optimize the computational time and memory requirements, we use the EM ＂footprint＂ concept to reduce the model size and obtain the sparse sensitivity matrix. To improve the 3D inversion, we use the OpenMP library and parallel computing. We test the proposed 3D parallel inversion code using two synthetic datasets and a field dataset. The time-domain airborne EM inversion results suggest that the proposed algorithm is effective, efficient, and practical.

An inversion of transient electromagnetic data from a conical source

Multiturn coils is an effective transmitter for transient electromagnetic method(TEM) used in narrow space and complex terrain at presently. However, its high mutual inductance coupling and long turn-off time affect the quality of later data processing and interpretation. Compared with multiturn coils, the new conical source has low mutual inductance and short turn-off time. Based on the superposition principle, we use Hankel transform and numerical filtering method for forward modelling of the conical source field in the layered-media and explore TEM characteristics excited by this source. We apply improved damped least square inversion to integrated transient electromagnetic(TEM) data. We first invert the induced voltage into similar resistivity and apparent depth, and then use the inverted results as input parameters in the initial model and transform the apparent resistivity data into the frequency domain. Then, damped least square inversion is performed in the frequency domain using the initial model. Subsequently, we use automated model building to search for the extremes and inflection points in the resistivity–depth data that are treated as critical layer parameters. The inversion of theoretical and observed data suggests that the method modifies the resistivity and depth and yields a model of the underground layers.

Nonstationary signal inversion based on shaping regularization for random noise attenuation

Prediction filtering is one of the most commonly used random noise attenuation methods in the industry;however,it has two drawbacks.First,it assumes that the seismic signals are piecewise stationary and linear.However,the seismic signal exhibits nonstationary due to the complexity of the underground structure.Second,the method predicts noise from seismic data by convolving with a prediction error filter(PEF),which applies inconsistent noise models before and after denoising.Therefore,the assumptions and model inconsistencies weaken conventional prediction filtering's performance in noise attenuation and signal preservation.In this paper,we propose a nonstationary signal inversion based on shaping regularization for random noise attenuation.The main idea of the method is to use the nonstationary prediction operator(NPO)to describe the complex structure and obtain seismic signals using nonstationary signal inversion instead of convolution.Different from the convolutional predicting filtering,the proposed method uses NPO as the regularization constraint to directly invert the eff ective signal from the noisy seismic data.The NPO varies in time and space,enabling the inversion system to describe complex(nonstationary and nonlinear)underground geological structures in detail.Processing synthetic and field data results demonstrate that the method eff ectively suppresses random noise and preserves seismic refl ection signals for nonstationary seismic data.

A fast and precise three-dimensional measurement system based on multiple parallel line lasers

This paper conducts a trade-off between efficiency and accuracy of three-dimensional(3 D)shape measurement based on the triangulation principle,and introduces a flying and precise 3 D shape measurement method based on multiple parallel line lasers.Firstly,we establish the measurement model of the multiple parallel line lasers system,and introduce the concept that multiple base planes can help to deduce the unified formula of the measurement system and are used in simplifying the process of the calibration.Then,the constraint of the line spatial frequency,which maximizes the measurement efficiency while ensuring accuracy,is determined according to the height distribution of the object.Secondly,the simulation analyzing the variation of the systemic resolution quantitatively under the circumstance of a set of specific parameters is performed,which provides a fundamental thesis for option of the four system parameters.Thirdly,for the application of the precision measurement in the industrial field,additional profiles are acquired to improve the lateral resolution by applying a motor to scan the 3 D surface.Finally,compared with the line laser,the experimental study shows that the present method of obtaining 41220 points per frame improves the measurement efficiency.Furthermore,the accuracy and the process of the calibration are advanced in comparison with the existing multiple-line laser and the structured light makes an accuracy better than 0.22 mm at a distance of 956.02 mm.

Shape Sensing of Thin Shell Structure Based on Inverse Finite Element Method

Shape sensing as a crucial component of structural health monitoring plays a vital role in real-time actuation and control of smart structures,and monitoring of structural integrity.As a model-based method,the inverse finite element method(iFEM)has been proved to be a valuable shape sensing tool that is suitable for complex structures.In this paper,we propose a novel approach for the shape sensing of thin shell structures with iFEM.Considering the structural form and stress characteristics of thin-walled structure,the error function consists of membrane and bending section strains only which is consistent with the Kirchhoff–Love shell theory.For numerical implementation,a new four-node quadrilateral inverse-shell element,iDKQ4,is developed by utilizing the kinematics of the classical shell theory.This new element includes hierarchical drilling rotation degrees-of-freedom(DOF)which enhance applicability to complex structures.Firstly,the reconstruction performance is examined numerically using a cantilever plate model.Following the validation cases,the applicability of the iDKQ4 element to more complex structures is demonstrated by the analysis of a thin wallpanel.Finally,the deformation of a typical aerospace thin-wall structure(the composite tank)is reconstructed with sparse strain data with the help of iDKQ4 element.

Three-dimensional lithospheric density distribution of China and surrounding regions

In this paper, we analyze lithospheric density distribution of China and surrounding regions on the basis of 30＇ × 30＇ gravity data and 1°×1 °P-wave velodty data, Firstly, we used the empirical equation be- tween the density and the P-wave velocity difference as the base of the initial model of the Asian lithospheric density. Secondly, we calculated the gravity anomaly, caused by the Moho discontinuity and the sedimentary layer discontinuity, by the Parker formula. Thirdly, the gravity anomaly of the spherical harmonics with 2 40 order for the anomalous body below the lithosphere is calculated based on the model of EGM96. Finally, by using Algebra Reconstruction Techniques （ART）, the inversion of 30＇ ~ 30＇ residual lithospheric Bouguer gravity anomaly caused by the lithosphere yields a rather detailed struc- tural model. The results show that the lithospheric density distribution of China and surrounding regions has a certain connection with the tectonic structure. The density is relatively high in the Philippine Sea plate, Japan Sea, the Indian plate, the Kazakhstan shield and the Western Siberia plain, whereas the Tibetan Plateau has low-density characteristics. The minimum value of density lies in the north of Philippines, in the Taiwan province and in the Ryukyu island arc.

Influence of sampling on three-dimensional surface shape measurement

In order to accurately measure an object’s three-dimensional surface shape,the influence of sampling on it was studied.First,on the basis of deriving spectra expressions through the Fourier transform,the generation of CCD pixels was analyzed,and its expression was given.Then,based on the discrete expression of deformation fringes obtained after sampling,its Fourier spectrum expression was derived,resulting in an infinitely repeated"spectra island"in the frequency domain.Finally,on the basis of using a low-pass filter to remove high-order harmonic components and retaining only one fundamental frequency component,the inverse Fourier transform was used to reconstruct the signal strength.A method of reducing the sampling interval,i.e.,reducing the number of sampling points per fringe,was proposed to increase the ratio between the sampling frequency and the fundamental frequency of the grating.This was done to reconstruct the object’s surface shape more accurately under the condition of m>4.The basic principle was verified through simulation and experiment.In the simulation,the sampling intervals were 8 pixels,4 pixels,2 pixels,and 1 pixel,the maximum absolute error values obtained in the last three situations were 88.80%,38.38%,and 31.50%in the first situation,respectively,and the corresponding average absolute error values are 71.84%,43.27%,and 32.26%.It is demonstrated that the smaller the sampling interval,the better the recovery effect.Taking the same four sampling intervals in the experiment as in the simulation can also lead to the same conclusions.The simulated and experimental results show that reducing the sampling interval can improve the accuracy of object surface shape measurement and achieve better reconstruction results.

基于自适应整形正则化的AVAz反演

高角度裂缝的存在导致地下介质呈现方位各向异性,具有水平对称轴的横向各向同性介质中反射系数随方位角的变化可以近似表示为傅里叶级数的形式.傅里叶系数的大小取决于背景介质和裂缝参数,傅里叶系数的相位角取决于裂缝对称轴方向.常规傅里叶级数分析利用逐个时间采样点的方位地震数据求和计算傅里叶系数,计算结果易受噪声影响.为了提高傅里叶系数估计的抗噪性和稳定性,将常规傅里叶级数分析与AVAz(振幅随方位角变化)反演方法相结合,提出一种基于整形正则化的AVAz二阶傅里叶系数反演方法.常规整形正则化约束中的整形算子形态固定,提出一种基于方位各向异性强度的自适应整形算子,利用基于常规傅里叶级数分析的二阶傅里叶系数初步估计结果计算阻尼因子,结合一阶差分矩阵构建自适应整形算子,达到在反演中自适应地调整整形算子形态的目的.理论测试表明,基于自适应整形正则化的AVAz反演方法具有较强的抗噪性,能够有效提高二阶傅里叶系数反演的稳定性.实际叠前地震数据应用结果显示裂缝预测结果与测井资料相吻合,证明了基于自适应整形正则化AVAz反演进行裂缝预测的有效性.

热载荷下星载天线逆有限元变形重构方法

为实现星载天线结构在服役过程中的实时变形监测,针对真实分布式热载荷下的星载天线板结构,研究了基于应变监测的逆有限元变形重构方法.首先,针对星载天线板结构提出了一种基于四节点四边形逆向壳单元的变形监测方法,通过建立基于位移梯度的单元划分方法,对逆有限元单元划分进行优化,采用最小二乘误差函数构造结构应变与位移的矩阵关系.其次,建立天线板热试验系统,获取典型热载荷下的结构温度分布.然后,建立典型实验温差状态下的复合材料星载天线板结构有限元模型,获取结构表面应变和位移.最后,在典型热载荷下,验证所提变形重构方法的有效性.结果表明,变形重构的位移误差不超过0.5 mm,说明逆有限元法能够在典型热载荷下准确重构天线板变形.

基于逆有限元方法和位移振型函数的薄板动载荷识别方法

动载荷识别对于结构设计和健康监测具有重要意义。利用在工程实践中容易获得的应变响应,提出了一种基于逆有限元方法和位移振型函数的薄板动载荷识别方法,能够同时识别动载荷空间分布和时间历程。首先,逆有限元方法可以利用离散应变数据重建离散位移场。然后,采用位移振型函数拟合得到连续位移场,将拟合良好的振型函数代入薄板微分控制方程中确定识别载荷。最后,通过薄板集中载荷和全局分布载荷识别的两个数值算例,验证该方法的可行性和准确性。结果表明,提出方法对于薄板动载荷的识别是有效且准确的。