声诱导电磁场的赫兹矢量表示与多极声电测井模拟

在假设声场不受电磁场影响的前提下，将Pride声电耦合方程组化为具有电流源的麦克斯韦方程组.与空间位置固定的电流源产生的电磁场不同，孔隙地层中声波诱导的电磁场是由空间波动的电流源产生的.通过引入赫兹矢量，将求解麦克斯韦方程组问题转化为求解关于赫兹矢量的非齐次矢量赫姆霍兹方程组.通过求解该方程组，得出电磁场表达式.利用此方法，针对声电效应测井，分别计算了由单极声源、偶极声源、四极声源激发的井内声场及其诱导电磁场的全波波形. 关键词： 孔隙介质 诱导电磁场 测井 多极声源

Formulation of the acoustically-induced electromagnetic field in a porous formation in terms of Hertz vectors and simulation of the borehole electromagnetic field excited by an acoustic multipole source

The electromagnetic field induced by acoustic waves in a porous formation is investigated. By supposing the acoustic field is not influenced by its induced electromagnetic field, the governing equations for the coupled acoustic and electromagnetic fields are reduced to a set of Maxwell equations with a propagation current source. The Maxwell equations are then transformed into inhomogeneous vector Helmholtz equations by introducing Hertz vectors. Finally the electromagnetic field is formulated in terms of the solutions to the Helmholtz equations. This method is used to evaluate the electromagnetic field during seismoelectric logging in a porous formation. The full waveforms of the acoustic field and the electromagnetic field in the borehole are calculated when the borehole acoustic sources are respectively a monopole, a dipole and a quadrupole.