摘要
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μ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μ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μ值。另一方面，还提出了在原始数据的误差为已知的情况下。
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.
出处
《煤田地质与勘探》
CAS
CSCD
北大核心
1999年第4期38-42,共5页
Coal Geology & Exploration
