De-noising CSEM data using least-squares method based on mixed basis of Fourier series and Legendre polynomials

Controlled-source electromagnetic (CSEM) surveys are widely used, but due to the influence of instrumental or environmental factors, the data obtained from CSEM surveys is often disturbed by noise. To address this problem, a de-noising method based on least-squares inversion has been proposed to effectively deal with the non-periodic noise in CSEM data. This method selects special reconstruction areas in the time domain and establishes an over-determined equation to obtain the noise. However, the condition in selecting reconstruction areas is rigorous, according to which only an area merely consists of signal and white Gaussian noise can be chosen as an ideal reconstruction area, limiting the application of this method. In this paper, an improved method was proposed by introducing Legendre polynomials into the over-determined equation. Using this improved method, areas containing other kinds of noise can also be chosen as reconstruction areas, extending the scope of application. To avoid the possible calculation error that comes from an ill-conditioned matrix, a regularization factor is introduced into the over-determined equation as an option. Meanwhile, to quantitatively evaluate the effect of this proposed method, the envelope evaluation method is involved and a "collapse algorithm" is proposed to evaluate the de-noising effect through residual noise. Through simulation and real case study, the validity and effectiveness of the proposed de-noising and evaluating process are proved.