Evaluating EM waveforms by singular-value decomposition of exponential basis functions

Exponential basis functions preconvolved with the system waveform are used to convert measured transient decays to an ideal frequency-domain response that can be modeled more easily than arbitrary waveform data. Singular-value decomposition (SVD) of the basis functions are used to assess which specific EM waveform provides superior resolution of a range of exponential time constants that fan be related to earth conductivities. The pulse shape, pulse length, transient sampling scheme, noise levels, and primary field removal used in practical EM systems all affect the resolution of time constants. Step response systems are more diagnostic of long time constants, and hence good conductors, than impulse response systems. The limited bandwidth of airborne EM systems compared with ground systems is improved when the response is sampled during the transmitter on time and gives better resolution of short time constants or fast decays.