The wave propagation behavior in an elastic wedge-shaped medium with an arbitrary shaped cylindrical canyon at its vertex has been studied.Numerical computation of the wave displacement field is carried out on and nea...The wave propagation behavior in an elastic wedge-shaped medium with an arbitrary shaped cylindrical canyon at its vertex has been studied.Numerical computation of the wave displacement field is carried out on and near the canyon surfaces using weighted-residuals(moment method).The wave displacement fields are computed by the residual method for the cases of elliptic,circular,rounded-rectangular and flat-elliptic canyons,The analysis demonstrates that the resulting surface displacement depends,as in similar previous analyses,on several factors including,but not limited,to the angle of the wedge,the geometry of the vertex,the frequencies of the incident waves,the angles of incidence,and the material properties of the media.The analysis provides intriguing results that help to explain geophysical observations regarding the amplification of seismic energy as a function of site conditions.展开更多
In order to obtain high order spectral moments, the residual moment M(w(n))(i) = integral(0)(wn) w(i)S(w)dw, as proposed by Denis s, is presented for approximate estimation of spectral moment m(i) = integral(0)(infini...In order to obtain high order spectral moments, the residual moment M(w(n))(i) = integral(0)(wn) w(i)S(w)dw, as proposed by Denis s, is presented for approximate estimation of spectral moment m(i) = integral(0)(infinity) w(i)S(w)dw. Glazman's partial averaging idea is discussed. It is pointed out that Glazman's method and definition of non-dimensional spectral moment can not be used to estimate spectral moments for engineering purposes and that method is not supported by theory and computation. The non-dimensional spectral moment of PM spectrum, which should be expressed as [GRAPHICS] is related to wind speed. The 0 - 8th moments of PM spectrum are estimated for wind speeds of 10, 20 and 30 m/s and some discussions are given.展开更多
An analysis of statistical expected values for transformations is performed in this study to quantify the effect of heterogeneity on spatial geological modeling and evaluations. Algebraic transformations are frequentl...An analysis of statistical expected values for transformations is performed in this study to quantify the effect of heterogeneity on spatial geological modeling and evaluations. Algebraic transformations are frequently applied to data from logging to allow for the modeling of geological properties. Transformations may be powers, products, and exponential operations which are commonly used in well-known relations （e.g., porosity-permeability transforms）. The results of this study show that correct computations must account for residual transformation terms which arise due to lack of independence among heterogeneous geological properties. In the case of an exponential porosity-permeability transform, the values may be positive. This proves that a simple exponential model back-transformed from linear regression underestimates permeability. In the case of transformations involving two or more properties, residual terms may represent the contribution of heterogeneous components which occur when properties vary together, regardless of a pair-wise linear independence. A consequence of power- and product-transform models is that regression equations within those transformations need corrections via residual cumulants. A generalization of this result is that transformations of multivariate spatial attributes require multiple-point random variable relations. This analysis provides practical solutions leading to a methodology for nonlinear modeling using correct back transformations in geology.展开更多
In reliability theory and survival analysis, the problem of point estimation based on the censored sample has been discussed in many literatures. However, most of them are focused on MLE, BLUE etc; little work has bee...In reliability theory and survival analysis, the problem of point estimation based on the censored sample has been discussed in many literatures. However, most of them are focused on MLE, BLUE etc; little work has been done on the moment-method estimation in censoring case. To make the method of moment estimation systematic and unifiable, in this paper, the moment-method estimators(abbr. MEs) and modified momentmethod estimators(abbr. MMEs) of the parameters based on type Ⅰ and type Ⅱ censored samples are put forward involving mean residual lifetime. The strong consistency and other properties are proved. To be worth mentioning, in the exponential distribution,the proposed moment-method estimators are exactly MLEs. By a simulation study, in the view point of bias and mean square of error, we show that the MEs and MMEs are better than MLEs and the “pseudo complete sample” technique introduced in Whitten et al.(1988). And the superiority of the MEs is especially conspicuous, when the sample is heavily censored.展开更多
文摘The wave propagation behavior in an elastic wedge-shaped medium with an arbitrary shaped cylindrical canyon at its vertex has been studied.Numerical computation of the wave displacement field is carried out on and near the canyon surfaces using weighted-residuals(moment method).The wave displacement fields are computed by the residual method for the cases of elliptic,circular,rounded-rectangular and flat-elliptic canyons,The analysis demonstrates that the resulting surface displacement depends,as in similar previous analyses,on several factors including,but not limited,to the angle of the wedge,the geometry of the vertex,the frequencies of the incident waves,the angles of incidence,and the material properties of the media.The analysis provides intriguing results that help to explain geophysical observations regarding the amplification of seismic energy as a function of site conditions.
基金This work was financially supported by the National Natural Science Foundation of China(Grant No.49776282)
文摘In order to obtain high order spectral moments, the residual moment M(w(n))(i) = integral(0)(wn) w(i)S(w)dw, as proposed by Denis s, is presented for approximate estimation of spectral moment m(i) = integral(0)(infinity) w(i)S(w)dw. Glazman's partial averaging idea is discussed. It is pointed out that Glazman's method and definition of non-dimensional spectral moment can not be used to estimate spectral moments for engineering purposes and that method is not supported by theory and computation. The non-dimensional spectral moment of PM spectrum, which should be expressed as [GRAPHICS] is related to wind speed. The 0 - 8th moments of PM spectrum are estimated for wind speeds of 10, 20 and 30 m/s and some discussions are given.
文摘An analysis of statistical expected values for transformations is performed in this study to quantify the effect of heterogeneity on spatial geological modeling and evaluations. Algebraic transformations are frequently applied to data from logging to allow for the modeling of geological properties. Transformations may be powers, products, and exponential operations which are commonly used in well-known relations （e.g., porosity-permeability transforms）. The results of this study show that correct computations must account for residual transformation terms which arise due to lack of independence among heterogeneous geological properties. In the case of an exponential porosity-permeability transform, the values may be positive. This proves that a simple exponential model back-transformed from linear regression underestimates permeability. In the case of transformations involving two or more properties, residual terms may represent the contribution of heterogeneous components which occur when properties vary together, regardless of a pair-wise linear independence. A consequence of power- and product-transform models is that regression equations within those transformations need corrections via residual cumulants. A generalization of this result is that transformations of multivariate spatial attributes require multiple-point random variable relations. This analysis provides practical solutions leading to a methodology for nonlinear modeling using correct back transformations in geology.
基金This research is partially supported by National Science Foundation of China (No. 69971016).
文摘In reliability theory and survival analysis, the problem of point estimation based on the censored sample has been discussed in many literatures. However, most of them are focused on MLE, BLUE etc; little work has been done on the moment-method estimation in censoring case. To make the method of moment estimation systematic and unifiable, in this paper, the moment-method estimators(abbr. MEs) and modified momentmethod estimators(abbr. MMEs) of the parameters based on type Ⅰ and type Ⅱ censored samples are put forward involving mean residual lifetime. The strong consistency and other properties are proved. To be worth mentioning, in the exponential distribution,the proposed moment-method estimators are exactly MLEs. By a simulation study, in the view point of bias and mean square of error, we show that the MEs and MMEs are better than MLEs and the “pseudo complete sample” technique introduced in Whitten et al.(1988). And the superiority of the MEs is especially conspicuous, when the sample is heavily censored.
