The Application Of Empirical Mode Decomposition In The Inversion Of NMRL Echo Signal

The echo signal of Nuclear Magnetic Resonance Logging （NMRL） has the characterof weak and wide bandwidth. Traditional filtering method from the frequency domain hasthe the conflict between de-noising and keeping the integrality of the signal. TheEmpirical Mode Decomposition（EMD） provides a new idea to the solution of the problemabove-mentioned.This thesis firstly introduces the NMR theory. explain the process of the detection ofthe echo signal under the interaction of strongly inhomogeneous static and radio frequencymagnetic fields. Use the Inversion Algorithm to obtain a series of single-exponentialtransverse-relaxation echo strings. Describes two common inversion methods of singularvalue decomposition （SVD） and the non-negative Least square（NNLS） method. Theinversion results influence by many factors including the number of distribution, the echonumber, and signal to noise ratio and so on.EMD is suitable for process non-lineary the non-stationary. The method candecompose the signal to several layers of intrinsic mode functions（IMF） adaptivelywithout any prior knowledge according to characteristics of signals themselves the timescale. Applying the Hilbert transform of IMF can get the time-frequency-energydistribution. Decomposing the echo signal detected in the NMR logging to layers ofintrinsic mode functions. According to characteristic of the IMF that on the time scale ishigh frequency to the low frequency. Use the threshold de-noising method based on theabsolute median deviation of the high frequency IMF. the echo signal can be obtained bythe reconstruction of the intrinsic mode functions after de-noising. Comparing thesignal-to-noise ratio （SNR） of the echo signal before and after decomposition based on thethreshold de-noising method can effectively improve the T₂spectrum.