Direct synthesis of time domain pseudo-random 3D electromagnetic response with a band-limited source

Abstract

Methods based on pseudo-random coded emission technology can effectively suppress the noise in electromagnetic exploration and improve the depth and resolution of the detection. Additionally, the synthesis of electromagnetic response signals excited by pseudo-random code sources can provide not only theoretical data for data processing but also intermediate results for evaluations of field data. Currently, pseudo-random signal simulations ignore the presence of source effects generated by band-limited sources in the Earth's impulse response. Furthermore, the simulation methods are mainly completed based on one-dimensional and two-dimensional formats and thus cannot accurately reflect the pseudo-random response of three-dimensional geoelectric structures. In this paper, 3D pseudo-random electromagnetic signals with a band-limited source were synthesized according to the propagating routine of the electromagnetic field. First, Maxwell's Equations were solved using a three-dimensional time-domain finite volume method. To avoid the singularity of the source and incorporate source effect response, the Gaussian function was introduced to simulate the band-limited impulse sources. The Earth's impulse response was obtained, which contained source effects under three-dimensional geoelectric structures. Then, ideal pseudo-random electromagnetic signals could be composed by convoluting the Earth's impulse response with a pseudo-random source waveform. Since the transmitter and receiver instruments were band-limited, a low-pass filter with a Blackman window was introduced to simulate the instrument's system response. The simulated pseudo-random signals were obtained by adding noise and the ideal pseudo-random electromagnetic signals were filtered using a low-pass filter. By comparison with signals acquired in the field, the correctness of the pseudo-random signal synthesis with source effects was successfully verified.