| 曲线拟合新技术在分析高温高压实验数据中的试用 |
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| 引用本文： | 张启锐,王信和.曲线拟合新技术在分析高温高压实验数据中的试用[J].地质科学,1985,0(4):391-400. |
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| 作者姓名： | 张启锐 王信和 |
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| 作者单位： | 中国科学院地质研究所 |
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| 摘 要： | Kern(1982)和 Kern 与 Richter(1981)介绍了他们通过高温高压实验测定的、多种岩石在不同温度和压力条件下模拟地震 P 波和 S 波的波速 Vp 和 Vs,这些资料对于探索地壳内的岩石矿物组成和各种物理性质是十分宝贵的。我们知道,Vp 和 Vs 既依赖于温度,也依赖于压力。
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| 关 键 词： | , |
| 收稿时间： | 1983-02-28 |
| 修稿时间： | 1983-02-28; |
A NEW TECHNIQUE FOR CURVE FITTING——A TRIAL TO PART OF THE DATA FROM HIGH TEMPERATURE AND HIGH PRESSURE EXPERIMENTS |
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| Zhang Qirui,Wang Xinhe.A NEW TECHNIQUE FOR CURVE FITTING——A TRIAL TO PART OF THE DATA FROM HIGH TEMPERATURE AND HIGH PRESSURE EXPERIMENTS[J].Chinese Journal of Geology,1985,0(4):391-400. |
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| Authors: | Zhang Qirui Wang Xinhe |
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| Institution: | Institute of Geology, Academia Sinica, Beijing |
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| Abstract: | Kern (1982) and Kern and Riehter (1981) introduced their researches on velocities of simulated P- and S-wave under different temperature and confining pressure. The work is important for understanding the mineral composition as well as their physical properties in the earth interior. Based upon the great amount of observations, they suggested a unique best fit formula for various rock-types Vp(P, T) = Vp0 + (dVp/dP)T·P + (dVp/dT)p·T where the pressure (P) varies from 2 to 6 kbar under room temperature and the temperature (T) is limited at 20℃to 500℃ under the 6 kbar confining pressure. In terms of such conditions, the coefficients Vp0, (dVp/dP)T, and dVp/dP)T of examined rock-types were also estimated and shown in Kern, and Richter (1981).However, after close examination, it was found that the formula did not fit the original observations. Therefore, a new technique, i.e. Box-Cox method was adopted. The method and results of the granite sample no. 876 are illustrated in detail in this paper. Actually, Box-Cox transformation reprasents a family of power transformation as follow:y*{(yλ-1)/λ,λ≠0 logy, λ=0 If we take y* to be the dependent variable, then a general regression model could be:Y* = A + Bx + u Assumming the error term u to be independent, normal, homogeneous and u~N (0, σ2), then the corresponding maximum log likelihood estimate could be expressed as  If an appropriate series of X values is given, a maximum value of L Lmax may be obtained and the related X value will be the estimated transformation power parameter. The calculation may be proceeded recurrsively with an ordinary least-square regression analysis program.The results of applying Box-Cox regression method to data of sample 876 is good. Comparing with results of orthogonal polynomial regression method, it may be concluded that the equation achieved by Box-Cox method is simpler and will be more useful in quantitative processing and interpretation. Moreover, it is believed that the fit of similar data, with Box-Cox method will be adequate too. |
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| Keywords: | , |
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