巷道对全空间瞬变电磁场影响的边界元数值模拟

Numerical simulation of the roadway effect on whole-space transient electromagnetic fields by boundary element method

巷道空间对全空间瞬变电磁场的影响特征是矿井瞬变电磁法中尚未妥善解决的理论问题.从电磁场满足的麦克斯韦方程组和边界条件出发,推导洛伦兹规范和库伦规范下位函数满足的控制方程和边界条件,作为含三维巷道全空间水平层状介质模型的边值问题.用边界元法模拟了含巷道的典型3层地电模型的瞬变电磁响应特征,分析了有无巷道时视电阻率的变化规律及模型参数的变化对巷道响应特征的影响规律,提出了改变巷道所在层参数时巷道影响变化最大,即巷道围岩介质导电性是决定巷道影响大小的最直接因素的观点.结果表明：巷道空间的存在使得视电阻率值发生显著变化,与无巷道时相比其值变大,巷道影响大小介于1.0~2.5之间;当发射源放置在巷道底板上时,底板岩层的电阻率越小,巷道影响变化越大,顶板岩层电阻率所引起的巷道影响变化最小.研究结果为进一步建立巷道影响校正算法提供了理论依据.

It is an unsolved theoretical problem that the roadway space how to influence the characteristics of electromagnetic fields of mine transient electromagnetic method. Using Max- well＇s equations of electromagnetic fields and their boundary conditions deduced one couple of potential functions in terms of Lorentz and Coulomb gauges, and the governing equations and boundary conditions were taken as the boundary value problem for numerical simulation of elec- tromagnetic fields in the case of three dimensional roadway in whole-space layered model. U- sing the boundary element method simulated the responses of transient electromagnetic field in a typical 3qayer geoelectrical model, and analyzed the variations of apparent resistivity when the roadway was existent or inexistent , and proposed that roadway effect changed greatly with different conductivity of the layer in which the roadway existed. It means that the conductivity of the layer in which the roadway exists is the most direct factor that determines the character- istics of roadway effect.the results show that theexistence of roadway space makes the apparent resistivity change greatly, and the value is bigger than that of without roadway, and the values of roadway effect are between 1.0 and 2.5; when the transmitting loop putting on the floor of roadway, the smaller the resistivity of floor is, the greater the roadway effect changes, and the variation of resistivity of roof has little influences on the roadway effect. Above results provide the theoretical foundation of the proposal of correction algorithm for roadway effect.