Simulation Of Seismoelectric Wavefields With Quasi-static Electromagnetic Approximation And Error Analysis

Because of the existence of the double electrical layer^[1],there is a coupling between the elastic wave and the electromagnetic wave in the fluid saturated porous medium.When the elastic wave propagates in the porous medium,it will generate electromagnetic field.In addition,when the elastic wave meets the interface of the medium,it will also excite electromagnetic waves independent of the propagation of seismic waves.These two kinds of electromagnetic signals are called seismoelectric signals.The seismoelectric is an effective mechanism for the generation of seismic electromagnetic fields.The study of seismoelectric is of great significance to the interpretation of geophysical exploration and seismic electromagnetic phenomena.In the study of seismoelectric phenomena,theoretical simulation is one of the most important means.In the seismoelectric field simulation,especially the time-domain numerical method is used to calculate the seismic wave field of the source.In order to avoid the computation difficulty caused by the large difference in the velocity between the elastic wave and the electromagnetic wave,the electromagnetic approximation is usually adopted.Sometimes it is also called quasi static approximation.But the former did not study the error analysis of quasi-static electromagnetic approximation.By studying and comparing the exact and approximate solution,we study the error and its influencing factors,explore the suitable conditions for using the approximation.In this study,we investigate the error caused by the quasi-static EM approximation based on a horizontally layered model.With such an approximation we obtain a simplified set of Pride's equations and present an analytically-based algorithm to solve the seismoelectric responses to an explosive source.First,we solve the seismic wavefields by ignoring the influence of the converted EM fields on the propagation of the seismic waves.Second,we simplify Maxwell equations to a Poisson equation of the electric potential,from which the EM signals are solved.The EM responses resulting from the quasi-static method were compared with those calculated by the full-coupling method that solves the full Pride's equations without any assumption.?1?For receivers that are located far from the free surface,the coseismic EM signals are generated by body seismic waves.We found that:the quasi-static EM approximation causes the missing of the coseismic electric field accompanying the body S waves;it causes negligible error in simulating the coseismic electric fields accompanying the body P waves;the quasi-static EM approximation causes obvious errors in simulating the coseismic magnetic field accompanying the body S waves.The errors increase with the increase of the salinity and decreases with the increase of the frequency;this implies that under high-frequency condition,the quasistatic method seems to produce more accurate coseismic magnetic fields.?2?For receivers that are located near the free surface,as discussed below:under the low-frequency and low-salinity conditions or under high-frequency conditions,the quasi-static approximation causes small errors in simulating the horizontal coseismic electric field;under low-frequency but high-salinity conditions,the quasi-static EM approximation causes significant errors in simulating the horizontal coseismic electric field;the quasi-static EM approximation nearly cause no error in simulating the vertical electric field when the receiver is located close the free surface.?3?We also investigated the interfacial EM waves that are generated by the direct P wave at the free surface.We find that only under the condition that the wavelength of the EM wave is much larger than the source-receiver distance,the quasi-static method is accurate in simulating the EM wave.In this paper,we study the error,influence factors and the conditions of quasi-static electromagnetic approximation.The obtained results can provide important theoretical basis for future seismic phenomena and the interpretation of electromagnetic signals.In addition,this paper also studied the VESP model and the Twin-well model experiment,it is found that the two not only provide high resolution,but also can observe different kinds of waves conveniently.Besides,we can directly study various wave generation and transformation process,which pave the way for future research.This study was funded by the National Natural Science Foundation?No.41474038 and 41774048?.