抛物型方程的一种高精度区域分解有限差分算法

1引言近年来,区域分解算法以可以将大型问题分解为一系列小型问题以减少计算规模及算法可高度并行实现等特点受到了人们的广泛关注.前人也做了很多很好的工作:参考文献[1]中C.N.Dawson等人提出了显一隐格式的区域分解算法,在时间层不分层的内边界点采用大步长向前-中心差分显格式及在内点采用古典隐格式,取得的精度为O(△t+h2+H3).参考文献[2]中给出了[1]中区域分解算法对于内边界点为等距分布的多子区域时的新的误差估计,使含H3误差项的系数比[1]中缩小了一倍.还将采用大步长日的saulyev的非对称差分格式应用于内边界点,并给出了两个子区域和多个子区域情形下差分解的先验误差估计.

类Lyapunov理论在类人形机器人任务空间内跟踪的应用

考虑了类人形机器人的各种不确定因素,提出了其手臂控制的新方法.基于类Lyapunov方法,设计出具有鲁棒性功能的任务空间控制器.该方法得到的控制器不但在有限确定时间内达到稳定跟踪,而且不需要雅可比矩阵求逆,对一定类型的外部干扰具有鲁棒性功能.最后通过数值仿真显示了所得结果的有效性及其应用方法.

海洋机器人变参数大时延控制系统补偿方法的研究

本文提出一种变参数大时延系统的补偿方法，具有传输滞后系统的幅相频率特性和时域特性，流体动力学变参数的修正方法和具有传输滞后和零阶保持器滞后的补偿仿真。

裂缝性油气藏储层预测方法研究

In this paper, based on the E & P situation in the oilfield and the theory of geophysical exploration, a series researches are conducted on fracture reservoir prediction technology in general，and it especially focus on some difficult points. The technological series which integrated amplitude preserved data processing、interpretation and its comprehensive application research as a whole were developed and this new method can be applied to the other similar oilfield exploration and development. The contents and results in this paper are listed as follows: 1. An overview was given on the status and development of fracture reservoir estimation technique, compare and analyze those geophysical prediction methods. This will be very helpful to the similar reservoir researches. 2. Analyze and conclude the characters of geologies and well logging response of burial hills fracture reservoir, those conclusions are used to steer the geophysical research and get satisfying results. 3. Forward modeling anisotropy seismic response of fracture reservoir. Quantitatively describe the azimuthal amplitude variation. Amplitude ellipse at each incidence angle is used to identify the fracture orientation. 4. Numerical simulation of structure stress based on finite difference method is carried out. Quantitatively describe and analyze the direction and intensity of fracture. 5. Conventional attributes extraction of amplitude preserved seismic data、attributes with different azimuthal angle and different offset are used to determine the relationship between the results and fracture distribution. 6. With spectrum decomposition method based on wavelet transform， the author disclose the reservoir distribution in space. It is a powerful tool to display its anisotropy. 7. Integrated seismic wave impendence、elastic impendence、spectrum decomposition、attribute extraction、fracture analysis result as a whole to identify and evaluate the fracture reservoir. An optimum workflow is constructed. It is used to practical oil&gas production and good results are obtained. This can indicate the wide foreground of this technique series.

滩海过渡带地震资料拼接处理方法研究

The technology of seismic acquirement has been more and more intact in both land area and marine area, however, since the acquirement equipment can not handle the tasks in this both two kinds of prospects at the same time, it is very hard to acquire in the prospect of seashore area, and also the quality of the raw data is poor, the related work in seashore area has been a tough task. With the development of the level of exploration, acquired equipment and technology, a certain series of processing methods has been built up, which enhanced the resolving power, the ratio of signal to noise and the quality of imaging, these methods could meet most of the requirements of exploration and the development. What is more, more and more nowadays prospects are composed by two or more 3D sub-prospect, the differences between frequencies, energy levels and the ratios of signal to noise are definitely obvious, we can not perform finely construct analysis and interpretation of reservoir without solving these problems in matching different raw data. As for the prospect that composed by both seashore and marine ones, through the analysis on the characteristics on frequency, amplitude, polarity and multiples of land prospect and marine prospect, the methods on how to eliminate those differences mentioned above were researched, and this paper gives a series of methods includes the computing of matching factor, recognizing of time difference, recognizing of phase difference, matching frequency, collapsing of abnormal energy, frequency compensating and so on, to fulfill the attenuations of energy difference, frequency difference, time difference and phase difference, and what is more, improve the innovative methods: includes the quantities method to synthetically and automatically recognize time difference and phase difference on the basis of signal match technology and according to statistic rule. And distinct the differences on phase and frequency characteristics of received raw data between velocity seismometer and piezoelectricity seismometer, and deduces that there are 90 degrees gap between data from these two seismometers, thirdly, synthetically apply zone abnormal frequency processing, surface consistent abnormal frequency compensate, residual abnormal frequency compensate, stack time equilibrium and optimize the processing seis-flow, deal with the would-be problems, such as low signal and noise rate, low resolution, poor imaging and poor state of consistent. Gain excellent effect in Da-gang oil field.

二维自组织介质中地震波的传播特性

The topic of this study is simulation in the two dimensional self-organized media. The study in complexity of the earth plays an important role in structures, sources and energy seismic detection. And it mainly focuses on vertical or horizontal heterogeneous, anisotropic and linear media. Based on 2D self-organized velocity model and four-order finite-difference method, we simulate different types self-organized media and the same type mode with various parameters such as horizontal relative length, vertical relative length, variations, and velocity background gradient. Also we analyze the seismograms with complexity methods with instant information including amplitude, energy and frequency. The results can be summarized as the fallows: (1) The waveforms fluctuate with the velocity variations; (2) Different type self-organized media bring different effects on the amplitudes, energy and waveforms; (3) Different parameters also produce various influences to seismograms. (4) The layer contains their self-organized features, from which we can investigate the quality of the earth.

基于匹配追踪方法的地震信号时频分析研究

Seismic signal is a typical non-stationary signal, whose frequency is continuously changing with time and is determined by the bandwidth of seismic source and the absorption characteristic of the media underground. The most interesting target of seismic signal’s processing and explaining is to know about the local frequency’s abrupt changing with the time, since this kind of abrupt changing is indicating the changing of the physical attributes of the media underground. As to the seismic signal’s instantaneous attributes taken from time-frequency domain, the key target is to search a effective, non-negative and fast algorithm time-frequency distribution, and transform the seismic signal into this time-frequency domain to get its instantaneous power spectrum density, and then use the process of weighted adding and average etc. to get the instantaneous attributes of seismic signal. Time-frequency analysis as a powerful tool to deal with time variant non-stationary signal is becoming a hot researching spot of modern signal processing, and also is an important method to make seismic signal’s attributes analysis. This kind of method provides joint distribution message about time domain and frequency domain, and it clearly plots the correlation of signal’s frequency changing with the time. The spectrum decomposition technique makes seismic signal’s resolving rate reach its theoretical level, and by the method of all frequency scanning and imaging the three dimensional seismic data in frequency domain, it improves and promotes the resolving abilities of seismic signal vs. geological abnormal objects. Matching pursuits method is an important way to realize signal’s self-adaptive decomposition. Its main thought is that any signal can be expressed by a series of time-frequency atoms’ linear composition. By decomposition the signal within an over completed library, the time-frequency atoms which stand for the signal itself are selected neatly and self-adaptively according to the signal’s characteristics. This method has excellent sparse decomposition characteristics, and is widely used in signal de-noising, signal coding and pattern recognizing processing and is also adaptive to seismic signal’s decomposition and attributes analysis. This paper takes matching pursuits method as the key research object. As introducing the principle and implementation techniques of matching pursuits method systematically, it researches deeply the pivotal problems of atom type’s selection, the atom dictionary’s discrete, and the most matching atom’s searching algorithm, and at the same time, applying this matching pursuits method into seismic signal’s processing by picking-up correlative instantaneous messages from time-frequency analysis and spectrum decomposition to the seismic signal. Based on the research of the theory and its correlative model examination of the adaptively signal decomposition with matching pursuit method, this paper proposes a fast optimal matching time-frequency atom’s searching algorithm aimed at seismic signal’s decomposition by frequency-dominated pursuit method and this makes the MP method pertinence to seismic signal’s processing. Upon the research of optimal Gabor atom’s fast searching and matching algorithm, this paper proposes global optimal searching method using Simulated Annealing Algorithm, Genetic Algorithm and composed Simulated Annealing and Genetic Algorithm, so as to provide another way to implement fast matching pursuit method. At the same time, aimed at the characteristics of seismic signal, this paper proposes a fast matching atom’s searching algorithm by means of designating the max energy points of complex seismic signal, searching for the most optimal atom in the neighbor area of these points according to its instantaneous frequency and instantaneous phase, and this promotes the calculating efficiency of seismic signal’s matching pursuit algorithm. According to these methods proposed above, this paper implements them by programmed calculation, compares them with some open algorithm and proves this paper’s conclusions. It also testifies the active results of various methods by the processing of actual signals. The problems need to be solved further and the aftertime researching targets are as follows: continuously seeking for more efficient fast matching pursuit algorithm and expanding its application range, and also study the actual usage of matching pursuit method.

积分偏移的计算几何与并行实现

The Second Round of Oil & Gas Exploration needs more precision imaging method, velocity vs. depth model and geometry description on Complicated Geological Mass. Prestack time migration on inhomogeneous media was the technical basic of velocity analysis, prestack time migration on Rugged surface, angle gather and multi-domain noise suppression. In order to realize this technique, several critical technical problems need to be solved, such as parallel computation, velocity algorithm on ununiform grid and visualization. The key problem is organic combination theories of migration and computational geometry. Based on technical problems of 3-D prestack time migration existing in inhomogeneous media and requirements from nonuniform grid, parallel process and visualization, the thesis was studied systematically on three aspects: Infrastructure of velocity varies laterally Green function traveltime computation on ununiform grid, parallel computational of kirchhoff integral migration and 3D visualization, by combining integral migration theory and Computational Geometry. The results will provide powerful technical support to the implement of prestack time migration and convenient compute infrastructure of wave number domain simulation in inhomogeneous media. The main results were obtained as follows: 1. Symbol of one way wave Lie algebra integral, phase and green function traveltime expressions were analyzed, and simple 2-D expression of Lie algebra integral symbol phase and green function traveltime in time domain were given in inhomogeneous media by using pseudo-differential operators’ exponential map and Lie group algorithm preserving geometry structure. Infrastructure calculation of five parts, including derivative, commutating operator, Lie algebra root tree, exponential map root tree and traveltime coefficients , was brought forward when calculating asymmetry traveltime equation containing lateral differential in 3-D by this method. 2. By studying the infrastructure calculation of asymmetry traveltime in 3-D based on lateral velocity differential and combining computational geometry, a method to build velocity library and interpolate on velocity library using triangulate was obtained, which fit traveltime calculate requirements of parallel time migration and velocity estimate. 3. Combining velocity library triangulate and computational geometry, a structure which was convenient to calculate differential in horizontal, commutating operator and integral in vertical was built. Furthermore, recursive algorithm, for calculating architecture on lie algebra integral and exponential map root tree (Magnus in Math), was build and asymmetry traveltime based on lateral differential algorithm was also realized. 4. Based on graph theory and computational geometry, a minimum cycle method to decompose area into polygon blocks, which can be used as topological representation of migration result was proposed, which provided a practical method to block representation and research to migration interpretation results. 5. Based on MPI library, a process of bringing parallel migration algorithm at arbitrary sequence traces into practical was realized by using asymmetry traveltime based on lateral differential calculation and Kirchhoff integral method. 6. Visualization of geological data and seismic data were studied by the tools of OpenGL and Open Inventor, based on computational geometry theory, and a 3D visualize system on seismic imaging data was designed.

有源电磁扩散场克希霍夫积分偏移

As active electromagnetic method, field data of CSAMT method follow the equation of diffusion. Propagting in solid earth media, diffusion EM signal has strong attenuation and dispersion, otherwise seismic wave shows weak attenuation and dispersion, therefore the resolution power of CSAMT method is not better than seismic reflection method. However, there is consistence and similarity between EM signal and seismic wave in wave equation, we can apply Kirchhoff integral migration technique, a proven one in seismic method in time domain, to carry out seduo-seismic processing for CSAMT signal in frequency domain so that the attenuation and dispersion could be made compensated in some extent, and the resolution power and interpretation precision of active EM wave could be improved. Satisfying passive homogeneous Helmholtz quation, we proceed with Green theorem and combine the active inhomogenous Helmholtz quation, the Kirchhoff integral formula could be derived. Given practical problems, if we only consider the surface integral value, and assume that the intergral value in other interface is zero, combined with Green theorem in uniform half space, the expression could be simplified, and we can obtain frequency-domain Kirchhoff integral formula in surface, which is also called downward continuation of EM field in frequency domain. With image conditions and energy compensation considered, in order to get image conditions in time domain Fourier inverse transformation in frequency domain can be performed, so we can formulate the active Kirchhoff integral migration expression. At first, we construct relative stratified model, with different frequency series taken into account, then we change the distances between transmitter and reciever, the EM response can be obtained. Analyzing the EM properties, we can clarify near and far zone that can instruct us to carry out transmitter layout in practical application. Combined with field data surveyed in far zone, We perform Kirchhoff integral migration and compare the results with model to interpret. Secondly, with far field EM data, we apply TM mode to get EM response of given 2D model, then apply Kirchhoff integral migration on modelling data and interpret the results.

波动方程模拟与偏移的实用化方法研究

Along with the widespread and in-depth applications in petroleum prospecting and development, the seismic modeling and migration technologies are proposed with a higher requirement by oil industrial, and the related practical demand is getting more and more urgent. Based on theories of modeling and migration methods for wave equation, both related with velocity model, I thoroughly research and develop some methods for the goal of highly effective and practical in this dissertation. In the first part, this dissertation probes into the layout designing by wave equations modeling, focusing on the target-oriented layout designing method guided by wave equation modeling in complicated structure areas. It is implemented by using the fourth order staggered grid finite difference (FD) method in velocity-stress 2D acoustic wave equations plus perfectly matched layer (PML) absorbing boundary condition. To design target-oriented layout: (a) match the synthetic record on the surface with events of subsurface structures by analyzing the snapshots of theoretical model; (b) determine the shot-gather distance by tracking the events of target areas and measuring the receiving range when it reaches the surface; (c) restrict the range of valid shot-gather distance by drawing seismic windows in single shot records; (d) choose the best trace distance by comparing the resolution of prospecting targets from the simulated records with different trace distance. Eventually, we obtained the observation system parameters, which achieve the design requirements. In the second part, this dissertation presents the practical method to improve the 3D Fourier Finite Difference (FFD) migration, and carefully analyzes all the factors which influence 3D FFD migration’s efficiency. In which, one of the most important parameters of migration is the extrapolating step. This dissertation presents an efficient 3D FFD migration algorithm, which use FFD propagator to extrapolate wavefields over big layers, and use Born-Kirchhoff interpolator to image wavefields over small layers between the big ones. Finally, I show the effectiveness of this hybrid migration method by comparing migration results from 3D SEG/EAGE model with different methods.

旋转轴对称介质中的qP波一阶射线追踪

Elastic anisotropy is a very common phenomenon in the Earth’s interior, especial for sedimentary rock as important gas and oil reservoirs. But in the processing and interpretation of seismic data, it is assumption that the media in the Earth’s interior is completely elastic and isotropic, and then the methods based on isotropy are used to deal with anisotropic seismic data, so it makes the seismic resolution lower and the error on images is caused. The research on seismic wave simulation technology can improve our understanding on the rules of seismic wave propagation in anisotropic media, and it can help us to resolve problems caused by anisotropy of media in the processing and interpretation of seismic data. So researching on weakly anisotropic media with rotated axis of symmetry, we study systematically the rules of seismic wave propagation in this kind of media, simulate the process with numerical calculation, and get the better research results. The first-order ray tracing (FORT) formulas of qP wave derived can adapt to every anisotropic media with arbitrary symmetry. The equations are considerably simpler than the exact ray tracing equations. The equations allow qP waves to be treated independently from qS waves, just as in isotropic media. They simplify considerably in media with higher symmetry anisotropy. In isotropic media, they reduce to the exact ray tracing equations. In contrast to other perturbation techniques used to trace rays in weakly anisotropic media, our approach does not require calculation of reference rays in a reference isotropic medium. The FORT-method rays are obtained directly. They are computationally more effective than standard ray tracing equations. Moreover the second-order travel time corrections formula derived can be used to reduce effectively the travel time error, and improve the accuracy of travel time calculation. The tensor transformation equations of weak-anisotropy parameters in media with rotated axis of symmetry derived from the Bond transformation equations resolve effectively the problems of coordinate transformation caused by the difference between global system of coordinate and local system of coordinate. The calculated weak-anisotropy parameters are completely suitable to the first-order ray tracing used in this paper, and their forms are simpler than those from the Bond transformation. In the numerical simulation on ray tracing, we use the travel time table calculation method that the locations of the grids in the ray beam are determined, then the travel times of the grids are obtained by the reversed distance interpolation. We get better calculation efficiency and accuracy by this method. Finally we verify the validity and adaptability of this method used in this paper with numerical simulations for the rotated TI model with anisotropy of about 8% and the rotated ORTHO model with anisotropy of about 20%. The results indicate that this method has better accuracy for both media with different types and different anisotropic strength. Keywords: weak-anisotropy, numerical simulation, ray tracing equation, travel time, inhomogeneity

计算层状介质中电磁场的层矩阵法

As an important branch of electrical prospecting method, the artificial source frequency domain electromagnetism method has received more and more attention. But when conducts the fundamental research, people often isolated study some concrete method, so the research results of one method are very difficult to apply to another method directly. This article will possess the artificial source frequency domain EM method to an 1D model simply. It is stratified medium model, with an electric or magnetic source in or outside of it. Then take the horizontal electric dipole source as an example to introduce how to computing the EM field in stratified medium. Because layer matrix is the key of establishing equations, so we call it the layer-matrix method. The key of layer-matrix method is establishing equations by using layer matrixes in wavenumber(kx, ky, z) domain, then obtains the electromagnetic field value of wavenumber domain. After Fourier transform, we can get electromagnetic field of any position in spatial domain. The layer matrix technique theoretically can calculate electromagnetic field of any position for any source, is suitable for many kinds of electromagnetic method. After introduction of the layer matrix method, this article has done some CSAMT, MCSEM and Wireless Electro-Magnetic Method (WEM) modeling with layer matrix method separately. In CSAMT modeling, we get electromagnetic field dissemination characteristics considering wave number of the air, and obtain three-dimensional distribution characteristics of the electromagnetic field. In MCSEM modeling, we get electromagnetic field dissemination characteristics with and without considering the airwave, and obtain three-dimensional distribution characteristics of electromagnetic field. In WEM modeling, we get electromagnetic field’s difference between considering the ionosphere and not considering it, and recognize the ionosphere’s influence of electromagnetic field. With the layer matrix technique, we have got some new understandings of EM dissemination rules of different situations. All analysis results indicate that the layer-matrix technique is credible and effective, and are worthy of further thorough research and development.

锦屏一级水电站高应力大断面地下洞室稳定性分析

According to the feature of high stress and large size underground tunnel , a method named DEFLAC is put forward in this paper. DEFLAC is such a method that use disturbing energy as criteria, and based on the simulating software of FLAC. Finally, the method is applied in the underground powerhouse project of Jin-Ping First-level Hydropower Station. The result is well. And some conclusions are got. (1) Based on the geological features of excavation unloading phenomena, they are concluded to three types, what’s more three corresponding mechanical modes are proposed to explain the unloading phenomena. (2) The relation of two standards , which is called GB50287-99 (T) and BQ ,is studied. And the main difference of them ,when they are applied in high stress zone ,is researched. (3) .A method named DEFLAC is put forward , which is combined disturbing energy method and FLAC simulating software. The two dimension and three dimension explicit finite difference expressions are deduced in this paper. (4) Compared the instability area achieved by FLAC and DEFLAC with the measured result, a conclusion is got. That is a more accurate result can be got by DEFLAC. (5) According to the main powerhouse first layer excavation project, the method to search and analyze the instability blocks is studied in this paper. Finally, the results got by FLAC and DEFLAC are compared .A conclusion is got that DEFLAC can judge the stability of blocks induced by intermittent joints, but Block Theory can’t. So more accurate block amount can be got by DEFLAC. It is an effective method to judge stability of blocks

地下水流动数值模拟的并行计算方法研究

Numerical modeling of groundwater is very important for understanding groundwater flow and solving hydrogeological problem. Today, groundwater studies require massive model cells and high calculation accuracy, which are beyond single-CPU computer’s capabilities. With the development of high performance parallel computing technologies, application of parallel computing method on numerical modeling of groundwater flow becomes necessary and important. Using parallel computing can improve the ability to resolve various hydro-geological and environmental problems. In this study, parallel computing method on two main types of modern parallel computer architecture, shared memory parallel systems and distributed shared memory parallel systems, are discussed. OpenMP and MPI (PETSc) are both used to parallelize the most widely used groundwater simulator, MODFLOW. Two parallel solvers, P-PCG and P-MODFLOW, were developed for MODFLOW. The parallelized MODFLOW was used to simulate regional groundwater flow in Beishan, Gansu Province, which is a potential high-level radioactive waste geological disposal area in China. 1. The OpenMP programming paradigm was used to parallelize the PCG (preconditioned conjugate-gradient method) solver, which is one of the main solver for MODFLOW. The parallel PCG solver, P-PCG, is verified using an 8-processor computer. Both the impact of compilers and different model domain sizes were considered in the numerical experiments. The largest test model has 1000 columns, 1000 rows and 1000 layers. Based on the timing results, execution times using the P-PCG solver are typically about 1.40 to 5.31 times faster than those using the serial one. In addition, the simulation results are the exact same as the original PCG solver, because the majority of serial codes were not changed. It is worth noting that this parallelizing approach reduces cost in terms of software maintenance because only a single source PCG solver code needs to be maintained in the MODFLOW source tree. 2. P-MODFLOW, a domain decomposition–based model implemented in a parallel computing environment is developed, which allows efficient simulation of a regional-scale groundwater flow. The basic approach partitions a large model domain into any number of sub-domains. Parallel processors are used to solve the model equations within each sub-domain. The use of domain decomposition method to achieve the MODFLOW program distributed shared memory parallel computing system will process the application of MODFLOW be extended to the fleet of the most popular systems, so that a large-scale simulation could take full advantage of hundreds or even thousands parallel processors. P-MODFLOW has a good parallel performance, with the maximum speedup of 18.32 (14 processors). Super linear speedups have been achieved in the parallel tests, indicating the efficiency and scalability of the code. Parallel program design, load balancing and full use of the PETSc were considered to achieve a highly efficient parallel program. 3. The characterization of regional ground water flow system is very important for high-level radioactive waste geological disposal. The Beishan area, located in northwestern Gansu Province, China, is selected as a potential site for disposal repository. The area includes about 80000 km2 and has complicated hydrogeological conditions, which greatly increase the computational effort of regional ground water flow models. In order to reduce computing time, parallel computing scheme was applied to regional ground water flow modeling. Models with over 10 million cells were used to simulate how the faults and different recharge conditions impact regional ground water flow pattern. The results of this study provide regional ground water flow information for the site characterization of the potential high-level radioactive waste disposal.

人工源宽角地震资料中的广角效应及其对地壳速度成像的影响

The seismic wide-angle reflection/refraction method is the one of the most effective method for probing the crustal and upper mantle structure. It mainly uses the wide-angle reflection information from the boundary in the crust and the top boundary of the upper mantle to rebuild the crust and upper mantle structure. Through analyzing the reflection and transmission coefficients of various incident waves on the interface, we think relative to the pre-critical angle reflection information the post critical angle reflection information that received by wide-angle seismic data exists a time-shift effect with the offset variation, and then it must cause the error for velocity analysis and structure image. The feature of the wide-angle seismic wave field of the fourteen representative crust columns tell us that the wide-angle effects in the different representative tectonic units for the interface depth and the interval velocity in crust. We studied the features of the wide-angle seismic wave field through building the crust model and inverse its travel time by GA method to know the wide-angle influence on crustal velocity image. At last we finished the data processing of the Tunxi-Wenzhou wide-angle seismic profile. The results are as following: (1) Through building crust model, we labeled the travel time for all the phases by ray tracing method and remove wide-angle effects method, it revealed the wide-angle effect exists in the seismic data. (2) The travel time inversion by GA method can tell us that the depth by traditional ray tracing method is shallower than the result by remove wide-angle effects method, the latter can recover the crust structure model in effect. (3) We applied the two method mentioned before to the fourteen representative crust columns in China. It indicates that the removed wide-angle effect method in travel time inversion is reasonable and effective. (4) The real data processing from Tunxi-Wenzhou wide-angle seismic profile give us the basic structure through the two ways. The main influence exhibits in the difference of the interval velocity of the curst, and the wide-angle effects in shallow interface are stronger than the deep interface.