Research On 1D Forward And Inversion Of Transient Electromagnetic Method When Considering Displacement Current

Engineering and environmental geological problems have become the focus of researches.And most of the issues involve the detection of the shallow geological structure.Because of the turn-off time of the transient electromagnetic apparatus,the early shallow data is lost,which causes the “blind area” –the depth of about 20 meters underground that cannot be detected.With the development of the apparatus and devices,the turn-off time of the emission current has been shortened to microsecond level,or even nanosecond level,which provides the opportunity for blind area detection.However,the frequency of the fast turn-off current has become 10MHz~100MHz level.So,the influence of the displacement current cannot be ignored.Smoke loop inversion and optimization inversion are two widely used methods in one-dimensional inversion of transient electromagnetic.Smoke loop inversion is a fast approximate inversion method with no need for initial model.Nevertheless,it cannot fit the observed data.Least square method is commonly used in optimization inversion.It can fit the observed data but has a poor precision and slow speed with the increase of the layers.For the issues above,the paper derives the frequency domain response of vertical magnetic dipole and large-loop source when considering displacement current in the first.Then acquire the time domain response through time-frequency transform.Hankel transform is involved when solving the frequency domain response.This paper introduced a kernel function decomposition method base on haar wavelets.The method has a good anti-noise property and remarkable computational stability,which realizes the combination of transform and denoising.This paper adopts Gaver-Stehfest inverse Laplace transform(G-S transform)when obtaining the time domain response.Simulation results show that the G-S transform with 16 filter coefficient has a higher precision,which can be used in the solution of time domain response.The influence of observed parameters on displacement current effect and transient response in the typical stratum model is discussed based on the theoretical derivation and numerical computation.In homogeneous half space,the time that influenced by displacement current is between dozens of nanoseconds to hundreds of nanoseconds.The vertical magnetic field and its time derivative will change.The effect of displacement current on the response is more obvious with the decrease of electrical resistivity and dielectric constant.What's more,the increase of transmitter coil will delay the time influenced by displacement current.In the layer model,when the top layer has a high resistance,the electrical resistivity and dielectric constant of the lower layers will affect the displacement current effect.While the top layer has low resistance,the electrical resistivity and dielectric constant of the lower layers has no influence on displacement current.In homogeneous half space,the greater the electrical resistivity is,the sooner the decline time of the vertical magnetic field will be.But the decay rate of the vertical magnetic field will stay the same when the resistivity is different.Besides,the peak of early vertical magnetic time derivative will become greater and the decline time in later period will be earlier with the increase of electrical resistivity.In addition,as the radius of the transmitting coil augments,the vertical magnetic and the peak of its time derivative will decrease,as well as the response decay rate,and the decline will ahead of time.Dielectric constant almost has no influence on vertical magnetic and has a slight effect on its time derivative.In layer model,the high resistance of the top layer leads to great sensitivity of response to the resistivity of the lower layers.And it will be contrary when it comes to the fact that the top layer has a low resistance,which results in a great difficulty to search for the high resistance target covered by the low resistance top layer in practical work.Plus,only the dielectric constant in top layer has impact on the time derivative of vertical magnetic will make it harder to do inversion.Moreover,the increase of the turn-off time will delay the decline time of the vertical magnetic field and expedite the decay rate.At the same time,the peak of the time derivative will decrease and the decline time will be delayed.In terms of transient electromagnetic inversion,this paper adopts the smoke loop inversion and the particle swarm optimization inversion.Smoke loop inversion can reflect the geological structure roughly and highlight the low-resistant anomalous bodies effectively.Compared with the least square method,the particle swarm optimization inversion has a higher precision and time saving,which means it is better than least square method.What's more,the inversion precision of relative dielectric constant is not high generally because of the slight influence of relative dielectric constant on the response.Although the transient electromagnetic method is insensitive to the high-resistivity formation,the particle swarm optimization algorithm can still be obtained in accordance with the theoretical model.