Empirical Equations of P-Wave Velocity in the Shallow and Semi-Deep Sea Sediments from the South China Sea

Three-hundred and thirty-one sediment cores,including six sediment types(clayey-and sandy-silt,silty-and sandy-clay,clayey-and silty-sand)were collected from the shallow and semi-deep seas of the South China Sea,and the P-wave velocities and physical properties of core sediments were measured under standard laboratory conditions.To eliminate the influence of environ-mental factors,the empirical sound speed ratio equations were established.Compared with several equations from literature,the po-rosity and wet bulk density empirical equations established in this paper agree well with Richardson and Briggs(2004)’s in-situ equations,which implies that our empirical equations can be used in the similar region of world’s oceans under certain conditions and will be useful in areas lacking first-hand P-wave speed data.However,the mean grain size equations established in this study,similar to the previous studies,have low accuracy,which may be due to the different particle arrangements and degrees of compac-tion in sediments.The results also show that for different sediment types,the equation based on all sediment data is in good agree-ment with the measured data in the study area,as there are both siliciclastic and carbonate sediments on the studied seabed.It is sug-gested that appropriate empirical equations should be selected according to sediment types and sedimentary environment in future works,and the empirical equation of porosity or the two-parameter equation of porosity and grain size should be preferred.

A Novel Empirical Equation for Relative Permeability in Low Permeability Reservoirs

In this paper, a novel empirical equation is proposed to calculate the relative permeability of low permeability reservoir. An improved item is introduced on the basis of Rose empirical formula and Al-Fattah empirical formula, with one simple model to describe oil/water relative permeability. The position displacement idea of bare bones particle swarm optimization is applied to change the mutation operator to improve the RNA genetic algorithm. The parameters of the new empirical equation are optimized with the hybrid RNA genetic algorithm(HRGA) based on the experimental data. The data is obtained from a typical low permeability reservoir well 54 core 27-1 in Gu Dong by unsteady method. We carry out matlab programming simulation with HRGA. The comparison and error analysis show that the empirical equation proposed is more accurate than the Rose empirical formula and the exponential model. The generalization of the empirical equation is also verified.

Is the Two-Color Method Superior to Empirical Equations in Refractive Index Compensation?

The Edlén empirical equations and the two-color method are the commonly used approaches to converting a length measured in air to the corresponding length in vacuum to eliminate the influence of the refractive index of air. However, it is not well known whether the two-color method is superior to empirical equations in refractive index compensation. We investigated the uncertainties of these approaches via numerical calculations of their sensitivity coefficients of environmental parameters. On the basis of a comparison of their uncertainties, we found that in a 0% humidity environment, the two-color method had potential to provide greater measurement accuracy than the empirical equations.

Empirical Development of the Rock Mass Deformation Modulus

Rock mass deformation modulus is a fundamental factor for a safe and economical design of rock structures like large underground openings, tunneling, and open pit mine as well as foundations in both the initial state of stresses act on rock mass and its strength characteristics. The rock mass deformation modulus recently has been measured by in-situ loading tests and has been estimated by use of empirical equation based on classification systems and data of laboratory tests. In-situ tests to measure modulus directly are so expensive, times consuming and the reliability of the results of these tests is sometimes doubtful; subsequently, many researches have been carried out to estimate this parameter based on classification systems. In this study, a new empirical equation was proposed by use of statistical analyses based on a database of more than 142 in-situ tests, like plate load tests, dilatometer tests, flat jack tests, and classification systems; in addition, properties of the intact rock.

Evaluation of empirical estimation of uniaxial compressive strength of rock using measurements from index and physical tests

The uniaxial compressive strength(UCS) of rock is an important parameter required for design and analysis of rock structures,and rock mass classification.Uniaxial compression test is the direct method to obtain the UCS values.However,these tests are generally tedious,time-consuming,expensive,and sometimes impossible to perform due to difficult rock conditions.Therefore,several empirical equations have been developed to estimate the UCS from results of index and physical tests of rock.Nevertheless,numerous empirical models available in the literature often make it difficult for mining engineers to decide which empirical equation provides the most reliable estimate of UCS.This study evaluates estimation of UCS of rocks from several empirical equations.The study uses data of point load strength(Is(50)),Schmidt rebound hardness(SRH),block punch index(BPI),effective porosity(n) and density(ρ)as inputs to empirically estimate the UCS.The estimated UCS values from empirical equations are compared with experimentally obtained or measured UCS values,using statistical analyses.It shows that the reliability of UCS estimated from empirical equations depends on the quality of data used to develop the equations,type of input data used in the equations,and the quality of input data from index or physical tests.The results show that the point load strength(Is(50)) is the most reliable index for estimating UCS among the five types of tests evaluated.Because of type-specific nature of rock,restricting the use of empirical equations to the similar rock types for which they are developed is one of the measures to ensure satisfactory prediction performance of empirical equations.

Viscosity prediction in selected Iranian light oil reservoirs:Artificial neural network versus empirical correlations

Viscosity is a parameter that plays a pivotal role in reservoir fluid estimations. Several approaches have been presented in the literature （Beal, 1946; Khan et al, 1987; Beggs and Robinson, 1975; Kartoatmodjo and Schmidt, 1994; Vasquez and Beggs, 1980; Chew and Connally, 1959; Elsharkawy and Alikhan, 1999; Labedi, 1992） for predicting the viscosity of crude oil. However, the results obtained by these methods have significant errors when compared with the experimental data. In this study a robust artificial neural network （ANN） code was developed in the MATLAB software environment to predict the viscosity of Iranian crude oils. The results obtained by the ANN and the three well-established semi-empirical equations （Khan et al, 1987; Elsharkawy and Alikhan, 1999; Labedi, 1992） were compared with the experimental data. The prediction procedure was carried out at three different regimes： at, above and below the bubble-point pressure using the PVT data of 57 samples collected from central, southern and offshore oil fields of lran. It is confirmed that in comparison with the models previously published in literature, the ANN model has a better accuracy and performance in predicting the viscosity of Iranian crudes.

“Refractivity-from-clutter” based on local empirical refractivity model

Constructing sophisticated refractivity models is one of the key problems for the RFC(refractivity from clutter)technology. If prior knowledge of the local refractivity environment is available, more accurate parameterized model can be constructed from the statistical information, which in turn can be used to improve the quality of the local refractivity retrievals. The validity of this proposal was demonstrated by range-dependent refractivity profile inversions using the adjoint parabolic equation method to the Wallops’ 98 experimental data.

An accurate empirical correlation for predicting natural gas compressibility factors

The compressibility factor of natural gas is an important parameter in many gas and petroleum engineering calculations. This study presents a new empirical model for quick calculation of natural gas compressibility factors. The model was derived from 5844 experimental data of compressibility factors for a range of pseudo reduced pressures from 0.01 to 15 and pseudo reduced temperatures from 1 to 3. The accuracy of the new empirical correlation has been compared with commonly used existing methods. The comparison indicates the superiority of the new empirical model over the other methods used to calculate compressibility factor of natural gas with average absolute relative deviation percent （AARD%） of 0.6535.

Novel empirical correlations for estimation of bubble point pressure,saturated viscosity and gas solubility of crude oils

Knowledge of petroleum fluid properties is crucial for the study of reservoirs and their development. Estimation of reserves in an oil reservoir or determination of its performance and economics requires a good knowledge of the fluid physical properties. Bubble point pressure, gas solubility and viscosity of oils are the most important parameters in use for petroleum and chemical engineers. In this study a simple-to-use, straight-forward mathematical model was correlated on a set of 94 crude oil data. Three correlations were achieved based on an exponential regression, which were different from conventional empirical correlations, and were evaluated against 12 laboratory data other than those used for the regression. It is concluded that the new exponential equation is of higher precision and accuracy than the conventional correlations and is a more convenient mathematical formulation.

Robust Element-Wise Empirical Likelihood Estimation Method for Longitudinal Data

For the regression model about longitudinal data, we combine the robust estimation equation with the elemental empirical likelihood method, and propose an efficient robust estimator, where the robust estimation equation is based on bounded scoring function and the covariate depended weight function. This method reduces the influence of outliers in response variables and covariates on parameter estimation, takes into account the correlation between data, and improves the efficiency of estimation. The simulation results show that the proposed method is robust and efficient.

Empirical Likelihood Based Longitudinal Data Analysis

In longitudinal data analysis, our primary interest is in the estimation of regression parameters for the marginal expectations of the longitudinal responses, and the longitudinal correlation parameters are of secondary interest. The joint likelihood function for longitudinal data is challenging, particularly due to correlated responses. Marginal models, such as generalized estimating equations (GEEs), have received much attention based on the assumption of the first two moments of the data and a working correlation structure. The confidence regions and hypothesis tests are constructed based on the asymptotic normality. This approach is sensitive to the misspecification of the variance function and the working correlation structure which may yield inefficient and inconsistent estimates leading to wrong conclusions. To overcome this problem, we propose an empirical likelihood (EL) procedure based on a set of estimating equations for the parameter of interest and discuss its characteristics and asymptotic properties. We also provide an algorithm based on EL principles for the estimation of the regression parameters and the construction of its confidence region. We have applied the proposed method in two case examples.

Assessment of Rock Mass Quality and Deformation Modulus by Empirical Methods along Kandiah River, KPK, Pakistan

The pivotal aim of this study is to evaluate the rock mass characterization and deformation modulus. It is vital for rock mass classification to investigate important parameters of discontinuities. Therefore, Rock Mass Rating (RMR) and Tunneling quality index (Q) classification systems are applied to analyze 22 segments along proposed tunnel routes for hydropower in Kandiah valley, Khyber Pakhtunkhwa, Pakistan. RMR revealed the range of fair to good quality rocks, whereas Q yielded poor to fair quality rocks for investigated segments of the rock mass. Besides, Em values were acquired by empirical equations and computer-aided program RocLab, and both methods presented almost similar variation trend of their results. Hence, the correlations of Em with Q and RMR were carried out with higher values of the regression coefficient. This study has scientific significance to initially understand the rock mass conditions of Kandiah valley.

Space-time objective decomposition of vortex equations and mechanism analysis of subtropical high abnormal activities

To analyze the dynamic mechanism of unusual activities of the subtropical high, the space-time varible separation of the partial differential vortex equations is carried out with Galerkin methods based on the heat force and the whirl movement dissipation effect. Aiming at the subjective and man-made conventional method of choice in the space basis functions, we propose to combine the empirical orthogonal function （EOF） analysis with the genetic algorithm to inverse the space basis functions from the actual sequence of fields. A group of trigonometric functions are chosen as a generalized space basis function. With the least-squares error of the basis function and EOF typical fields, and with the complete orthogonality of basis functions, we can get the dual-bound function. A genetic algorithm is then introduced to carry out surface fitting and coefficient optimization of the basis function. As a result, the objective and reasonable constant differential equation of the subtropical high is obtained by inversion. Finally, based on the obtained nonlinear dynamics model, the dynamic behavior and mechanism of the subtropical high is analyzed and discussed under the influence of heat force. We find that solar radiation and zonal differences in land and sea are important factors impacting the potential field and flow field changes of the subtropical areas. These factors lead to strength changes of the subtropical high and medium-term advance/retreat activities. The former is a gradual change, while the latter shows more break characteristics. Meaningful results are obtained in the analysis.

Empirical study on the antecedents of multinational enterprises’ oversea subsidiaries staffing

Based on probing into the literature on multinational enterprise (MNE) staffing, we set up a concept model for MNEs’ subsidiary staffing by two groups of influencing factors: the national differences bwteen the parent country and the host country, and the strategies employed by MNEs. We also tested the model and proposed propositions by a sample evaluation method, specifically with 1 000 copies of questionnaires given out to managers or directors of MNEs’ subsidiaries in China Mainland and resulting in 151 sets of valid answers. The empirical study supports that national differences between the parent country and the host country and the strategies employed by MNEs do have impact on the subsidiary staffing, and MNE headquarters should make different staffing plans according to the difference of nations and strategies. We welcome testing our model by peer researchers in other country.

基于物理模型试验的库岸散粒体滑坡涌浪特性

滑坡涌浪灾害具有历时短、地形条件复杂、规模大的特点,是国内外研究的重要地质和工程问题之一。本文以库岸滑坡失稳入水涌浪过程为研究对象,考虑水上滑坡与淹没滑坡两种情景,设计并开展散粒体滑坡涌浪3维物理模型试验,量测滑坡入水运动堆积过程及涌浪产生、传播过程特征,并进一步分析沿滑坡运动方向传播的离岸波与沿河道上下游传播的侧向波波幅、传播规律特性等。结果表明:当滑坡从淹没工况到水上工况时,涌浪波幅最大值特征逐渐从波峰小于波谷转向波峰大于波谷;沿滑坡运动方向产生的涌浪波幅大于沿库岸传播的涌浪波幅,侧向波传播过程中波幅高度衰减程度小于离岸波;进一步分析发现,涌浪沿河道上下游传播时,侧向波最大浪高为其首浪高度的2.5倍;散粒体滑坡涌浪最大高度与散粒体质量成正相关,与散粒体初始淹没率成负相关;受滑坡体入水时相对厚度的影响,涌浪最大高度与入水高差成负相关;在此基础上,利用无量纲分析方法与多元非线性回归方法,推导出散粒体滑坡涌浪最大高度经验公式,并采用提出的经验公式对三峡库区巫山红岩子滑坡与加拿大切哈利斯湖滑坡涌浪案例最大浪高进行计算分析,验证该公式具有较好的适用性和准确性。

新疆地区回弹法预测岩石单轴抗压强度可靠性研究

单轴抗压强度(UCS)是岩土工程勘察中必须确认的重要参数之一。以回弹法为代表的间接法因其成本低、耗时少,在预测岩石单轴抗压强度方面得到了广泛应用。然而,基于此法建立的经验方程存在诸多局限性,其可靠性尚未得到充分验证。选取新疆地区的砂岩、花岗岩、片麻岩为研究对象,通过N型回弹锤试验测得每种岩性的回弹高度,结合单轴压缩试验结果检查了现有的测试程序和预测模型;并在验证既有经验方程可靠性的基础上,探讨了一种考虑试样初始损伤的回弹法预测岩石UCS值的新方法。结果表明:回弹后试样的UCS值平均下降了8.06~23.95 MPa,不同节理方向的UCS值平均差距为25.57 MPa;在现行测试程序中,Hucka等提出的方法在本研究中显示出最小的离散性;岩石UCS测试新方法能显著提升预测精度,并赋予经验方程实际物理含义。研究结果可为降低该地区岩土工程勘察的时间成本提供参考。

Bayesian Empirical Likelihood Estimation of Quantile Structural Equation Models

Structural equation model(SEM) is a multivariate analysis tool that has been widely applied to many fields such as biomedical and social sciences. In the traditional SEM, it is often assumed that random errors and explanatory latent variables follow the normal distribution, and the effect of explanatory latent variables on outcomes can be formulated by a mean regression-type structural equation. But this SEM may be inappropriate in some cases where random errors or latent variables are highly nonnormal. The authors develop a new SEM, called as quantile SEM(QSEM), by allowing for a quantile regression-type structural equation and without distribution assumption of random errors and latent variables. A Bayesian empirical likelihood(BEL) method is developed to simultaneously estimate parameters and latent variables based on the estimating equation method. A hybrid algorithm combining the Gibbs sampler and Metropolis-Hastings algorithm is presented to sample observations required for statistical inference. Latent variables are imputed by the estimated density function and the linear interpolation method. A simulation study and an example are presented to investigate the performance of the proposed methodologies.

Minimum Reservoir Water Level in Hydropower Dams

Vortex formation over the intakes is an unde- sirable phenomenon within the water withdrawal process from a dam reservoir. Calculating the minimum operating water level in power intakes by empirical equations is not a safe way and sometimes contains some errors. Therefore, current method to calculate the critical submergence of a power intake is construction of a scaled physical model in parallel with numerical model. In this research some pro- posed empirical relations for prediction of submergence depth in power intakes were validated with experimental data of different physical and numerical models of power intakes. Results showed that, equations which involved the geometry of intake have better correspondence with the experimental and numerical data.

Empirical likelihood inference for estimating equation with missing data

In this article, empirical likelihood inference for estimating equation with missing data is considered. Based on the weighted-corrected estimating function, an empirical log-likelihood ratio is proved to be a standard chiqsquare distribution asymptotically under some suitable conditions. This result is different from those derived before. So it is convenient to construct confidence regions for the parameters of interest. We also prove that our proposed maximum empirical likelihood estimator θ is asymptotically normal and attains the semiparametric efficiency bound of missing data. Some simulations indicate that the proposed method performs the best.

EMPIRICAL LIKELIHOOD INFERENCE FOR LOGISTIC EQUATION WITH RANDOM PERTURBATION

Empirical likelihood(EL) combined with estimating equations(EE) provides a modern semi-parametric alternative to classical estimation techniques such as maximum likelihood estimation(MLE). This paper not only uses closed form of conditional expectation and conditional variance of Logistic equation with random perturbation to perform maximum empirical likelihood estimation(MELE) for the model parameters, but also proposes an empirical likelihood ratio statistic(ELRS) for hypotheses concerning the interesting parameter. Monte Carlo simulation results show that MELE and ELRS provide competitive performance to parametric alternatives.