One-dimensional Modeling And Inversion For Time-domainairborne Electromagnetic Problems

Time-domain airborne electromagnetic(AEM) systems generally have a high spatial sampling rate, resulting in AEM systems’ high lateral resolution. The large amount of data also brings challenges and difficulties to the two dimensional or three dimensional electromagnetic inversion methods. So the practical data processing methods now mainly are conductivity-depth-imaging and one dimensional inversion. In this paper, we use the fast Hankel transformation to calculate the frequency-domain magnetic field response and get the time-domain AEM response via sine or cosine transformation and the convolution algorithm. We conduct the image procedure based on half-space model and pseudolayer half-space model. Then we introduce the traditional damped least squares inversion method used in AEM. At last, we show our research on weighted laterally-constrained inversion method and its new progress and new application for time-domain AEM data. We compare the advantages and shortcomings of laterally-constrained inversion and damped least squares inversion. This paper is organized as follows:(1) Time-domain AEM modeling algorithm for arbitrary transmitting waveform. We calculate the magnetic field produced by the transmitting dipole of a fixed wing AEM system or the transmitting loop of a helicopter AEM system via zero and one order Hankel transform. We formulate the Fourier transform as half order Hankel transformation and transform the frequency-domain AEM response to time-domain impulse response and step response. We model the time-domain AEM response with arbitrary transmitting waveform according to the convolution theorem and the relationship between impulse response and step response.(2) Conductivity-depth-imaging algorithm for time-domain AEM data. We transform the AEM survey data into some intermediate parameters like apparent conductivity via the imaging algorithm. By plotting the apparent conductivity against certain transformed depths, we can get the profile which generally provide a good indication on how the electrical properties in the underground vary.(3) Single site damped least squares inversion. We present the basic theory of single site damped least squares inversion, two methods to calculate the Jacob matrix, the selection criterion for damping factor, the method to update the model and the workflow of the inversion.(4) Weighted laterally-constrained inversion. We introduce how to consider data fitting, lateral constraints on resistivity, thickness and depth at the same time and adjust the constraint strength using weighting factors. By testing our algorithm on both synthetic and survey data and comparing our results with those from conventional inversions, we show that laterally-constrained inversion algorithm is a very reliable and effective tool to process the time-domain AEM data.