泰斯公式性态分析与误差估计方法

主要目的是分析在原始数据具有随机误差的情况下,利用泰斯公式进行正逆问题计算时,公式本身对误差的传递作用,即对泰斯公式的性态进行分析。研究中采用了函数对数据随机误差传递作用的随机性分析方法。通过较为简单的数学推导,建立了泰斯公式正逆计算问题的原始数据与计算结果所具有随机误差的统计参数之间的近似关系式,并推导出了两类计算问题的条件数。指出在u值较小的情况下,计算_的问题属于"病态"的;在u=0.438点及其附近,计算T的问题为"病态"的;在u值和_的相对误差与T的相对误差的比值很大的情况下,正问题为"病态"的。其它条件下的计算问题属于"良态"的。据此建议利用抽水试验后期资料计算T值,利用前期资料计算_值。另一方面,还提出了在原始数据的误差为已知的情况下,进行误差估计的方法。 

THE PERFORMANCE ANALYSIS OF THEIS EQUATION AND ERROR ESTIMATION METHOD

As a main purpose,the transfer of errors by the Theis equation itself under the situation that the input data has the random errors and utilizing the Theis equation to the direct and inverse computation problems,i.e.,the performance of Theis equation,is analyzed.Applying the randomness analysis method of the data random errors transfer by the functions and the simpler mathematical derivation,the approximate expressions between the statistic parameters of the random errors of input and output data have been established,and the conditional function for both kinds of computation problem are derived.It is indicated that in the case of smaller value of u ,the condition for computing u is bad performance;in the case of BX]u =0438 and nearby,that for computing T is bad performance;and in the case of larger u value and large ratio of relative errors of and T ,the direct computation problem is bad performance too.The computation problems under other conditions belong to good performance.On this basis,it is recommended that the calculation of ]T value utilizes the data from later stage of pumping test,and that of the value utilizes the data from early stage.In addition,the errors estimation method is presented if the errors of original data is known.