Currently,most rock physics models,used for evaluating the elastic properties of cracked or fractured media,take into account the crack properties,but not the background anisotropy.This creats the errors of in the ani...Currently,most rock physics models,used for evaluating the elastic properties of cracked or fractured media,take into account the crack properties,but not the background anisotropy.This creats the errors of in the anisotropy estimates by using fi eld logging data.In this work,based on the scattered wavefi eld theory,a sphere-equivalency method of elastic wave scattering was developed to accurately calculate the elastic properties of a vertical transversely isotropic solid containing aligned cracks.By setting the scattered wavefi eld due to a crack equal to that due to an equivalent sphere,an eff ective elastic stiff ness tensor was derived for the cracked medium.The stability and accuracy of the approach were determined for varying background anisotropy values.The results show that the anisotropy of the eff ective media is aff ected by cracks and background anisotropy for transversely isotropic background permeated by horizontally aligned cracks,especially for the elastic wave propagating along the horizontal direction.Meanwhile,the crack orientation has a signifi cant infl uence on the elastic wave velocity anisotropy.The theory was subsequently applied to model laboratory ultrasonic experimental data for artifi cially cracked samples and to model borehole acoustic anisotropy measurements.After considering the background anisotropy,the model shows an improvement in the agreement between theoretical predictions and measurement data,demonstrating that the present theory can adequately explain the anisotropic characteristics of cracked media.展开更多
Similarity for spatial directions plays an important role in GIS. In this paper, the conventional approaches are analyzed. Based on raster data areal objects, the authors propose two new methods for measuring similari...Similarity for spatial directions plays an important role in GIS. In this paper, the conventional approaches are analyzed. Based on raster data areal objects, the authors propose two new methods for measuring similarity among spatial directions. One is to measure the similarity among spatial directions based on the features of raster data and the changes of distances between spatial objects, the other is to measure the similarity among spatial directions according to the variation of each raster cell centroid angle. The two methods overcome the complexity of measuring similarity among spatial directions with direction matrix model and solve the limitation of small changes in direction. The two methods are simple and have broader applicability.展开更多
LetX 1,…,X n be iid observations of a random variableX with probability density functionf(x) on the q-dimensional unit sphere Ωq in Rq+1,q ? 1. Let $f_n (x) = n^{ - 1} c(h)\sum\nolimits_{i = 1}^n {K[(1 - x'X_i )...LetX 1,…,X n be iid observations of a random variableX with probability density functionf(x) on the q-dimensional unit sphere Ωq in Rq+1,q ? 1. Let $f_n (x) = n^{ - 1} c(h)\sum\nolimits_{i = 1}^n {K[(1 - x'X_i )/h^2 ]} $ be a kernel estimator off(x). In this paper we establish a central limit theorem for integrated square error off n under some mild conditions.展开更多
This paper proves the error reduction property （saturation property）, convergence and optimality of an adaptive mixed finite element method （AMFEM） for the Poisson equation. In each step of AMFEM, the local refine...This paper proves the error reduction property （saturation property）, convergence and optimality of an adaptive mixed finite element method （AMFEM） for the Poisson equation. In each step of AMFEM, the local refinement is performed basing on simple either edge-oriented residuals or edge-oriented data oscillations, depending only on the marking strategy, under some restriction of refinement. The main tools used here are the strict discrete local efficiency property given by Carstensen and Hoppe （2006） and the quasi-orthogonality estimate proved by Chen, Holst, and Xu （2009）. Numerical experiments fully confirm the theoretical analysis.展开更多
基金supported by the National Natural Science Foundation of China (No. 41821002)the Fundamental Research Funds for the Central Universities (Nos. 18CX02065A,20CX06046A)+3 种基金the Young Elite Scientist Sponsorship Program by the China Association for Science and TechnologyMajor Scientifi c and Technological Projects of CNPC (No. ZD2019-183-004)Qingdao Postdoctoral Applied Research Project (No. qdyy20190079)China Postdoctoral Science Foundation (No. 2020M672171)。
文摘Currently,most rock physics models,used for evaluating the elastic properties of cracked or fractured media,take into account the crack properties,but not the background anisotropy.This creats the errors of in the anisotropy estimates by using fi eld logging data.In this work,based on the scattered wavefi eld theory,a sphere-equivalency method of elastic wave scattering was developed to accurately calculate the elastic properties of a vertical transversely isotropic solid containing aligned cracks.By setting the scattered wavefi eld due to a crack equal to that due to an equivalent sphere,an eff ective elastic stiff ness tensor was derived for the cracked medium.The stability and accuracy of the approach were determined for varying background anisotropy values.The results show that the anisotropy of the eff ective media is aff ected by cracks and background anisotropy for transversely isotropic background permeated by horizontally aligned cracks,especially for the elastic wave propagating along the horizontal direction.Meanwhile,the crack orientation has a signifi cant infl uence on the elastic wave velocity anisotropy.The theory was subsequently applied to model laboratory ultrasonic experimental data for artifi cially cracked samples and to model borehole acoustic anisotropy measurements.After considering the background anisotropy,the model shows an improvement in the agreement between theoretical predictions and measurement data,demonstrating that the present theory can adequately explain the anisotropic characteristics of cracked media.
文摘Similarity for spatial directions plays an important role in GIS. In this paper, the conventional approaches are analyzed. Based on raster data areal objects, the authors propose two new methods for measuring similarity among spatial directions. One is to measure the similarity among spatial directions based on the features of raster data and the changes of distances between spatial objects, the other is to measure the similarity among spatial directions according to the variation of each raster cell centroid angle. The two methods overcome the complexity of measuring similarity among spatial directions with direction matrix model and solve the limitation of small changes in direction. The two methods are simple and have broader applicability.
文摘LetX 1,…,X n be iid observations of a random variableX with probability density functionf(x) on the q-dimensional unit sphere Ωq in Rq+1,q ? 1. Let $f_n (x) = n^{ - 1} c(h)\sum\nolimits_{i = 1}^n {K[(1 - x'X_i )/h^2 ]} $ be a kernel estimator off(x). In this paper we establish a central limit theorem for integrated square error off n under some mild conditions.
基金supported in part by the Natural Science Foundation of China under Grant No.10771150the National Basic Research Program of China under Grant No.2005CB321701the Natural Science Foundation of Chongqing City under Grant No.CSTC,2010BB8270
文摘This paper proves the error reduction property （saturation property）, convergence and optimality of an adaptive mixed finite element method （AMFEM） for the Poisson equation. In each step of AMFEM, the local refinement is performed basing on simple either edge-oriented residuals or edge-oriented data oscillations, depending only on the marking strategy, under some restriction of refinement. The main tools used here are the strict discrete local efficiency property given by Carstensen and Hoppe （2006） and the quasi-orthogonality estimate proved by Chen, Holst, and Xu （2009）. Numerical experiments fully confirm the theoretical analysis.
