Using Empirical Mode Decomposition to Process Marine Magnetotelluric Data
One of the most important steps in magnetotellurics (MT) studies is the derivation of frequency-based impedances from the measured time-varying electromagnetic fields. Accurate estimations of impedances, which depends on the quality of the collected data sets, can greatly improve the reliability of the subsurface resistivity structure model. Most current MT data processing methods use Fourier transform based procedures to estimate power spectral densities and, therefore, assume that the signals are stationary over the analyzed time segments. However, stationarity in geomagnetic data is not always ensured given the variety of source mechanisms causing the geomagnetic variations at different time and spatial scales. Additional complication and bias may arise from the presence of noise in the recorded electric and magnetic fields, which is particularly evident in marine MT measurements. I explore a new heuristic method for dealing with the non-stationarity of MT time series based on Empirical Mode Decomposition (EMD). It is a dynamic time series analysis method, in which time series containing stationary and / or non-stationary components can be decomposed into a finite and small number of Intrinsic Mode Functions (IMF). Physical meaningful instantaneous information (e.g. frequencies and amplitudes) can be derived from each IMFs. In this thesis it is the first time that the EMD method is used in combination with instantaneous spectra to determine impedance tensor estimates. The estimation is performed in the time-frequency domain using instantaneous spectra rather than in pure frequency domain as in traditional processing procedures. The procedure is tested on synthetic and field MT data. In synthetic tests the reliability of impedance estimates from EMD is compared to the synthetic responses of a 1D layered model. While the derived apparent resistivities and phases appear to be well recovered, a small systematic downward bias relative to the synthetic response values is observed. Through an analysis of the complete EMD procedure, I conclude that the bias is associated with numerical noise that is introduced by the decomposition used in EMD. Furthermore I find that this bias can be strongly reduced by either applying a second EMD algorithm to create a numerical reference time series of the magnetic field or by using a reference magnetic field time series measurements. To examine how impedance estimates are affected by noise, stochastic stationary and non-stationary noise are added on the time series. Comparisons reveal that estimates by EMD are generally more stable than those by simple Fourier analysis. At present stage, no robust estimate procedures are implemented in the EMD approach. However, I also compare the results derived from EMD to those derived by a commonly used data processing software (BIRRP), which incorporates additional sophisticated robust estimations to deal with noise issues. It is revealed that the results from both methods are already comparable. The processing scheme is then also applied to marine MT field data, which were measured at the Costa Rican subduction zone under the framework of collaborative research center SFB 574. Firstly, the non-stationary characteristics of motion induced noise is analyzed. Through analyzing the instantaneous spectra of the noisy section it can be shown that the motion induced noise is present over the whole frequency range. However, the effect of this noise decreases with the decreasing frequency. Further testing is performed on short, relatively quiet segments of several data sets, which exhibit different noise levels. Compared to a regular processing algorithm (BIRRP), the new method gives similar impedance estimates, but the impedance estimates are extended to lower frequencies and less noise biased estimates with smaller error bars are obtained at high frequencies. Finally, the EMD method is applied to long segments of data with many non-stationary noise packages. The estimates results derived from EMD are generally stable and less biased at all frequencies. In the low frequency range, results are comparable to those derived from BIRRP, and at high frequencies the results have smaller error bars. As a conclusion, non-stationary noise can heavily affect Fourier-based MT data processing. I show that by deriving impedance estimates based on the EMD method, a new methodology especially designed to handle non-stationary data, comparable or better impedance estimates over a larger frequency range can be derived without employing any sophisticated estimation procedures, which usually need to be invoked in FT based processing. Especially for marine applications, where compared to land data non-stationary noise is more pronounced and where the signal to noise ratio is reduced at high frequencies due to absorption by the overlying ocean layer, the new processing methodology I developed represents an important step towards deriving a better resolved Earth model to greater depth underneath the seafloor.
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