NONCAUSALITY OF THE DISCRETE-TIME MAGNETOTELLURIC IMPULSE-RESPONSE

For the most part, MT data processing and interpretation is best accomplished in the frequency domain. However, for some purposes estimates of the time-domain DTIR can be useful. When input signals are restricted to appropriately band-limited functions, there is always a well defined DTIR that produces the same outputs as the continuous time counterpart. However, causality of the DTIR does not follow from causality of the CTIR, and forcing a DTIR estimated from frequency-domain impedance measurements to be causal can lead to very poor results. In some circumstances (e.g., the 1-D MT problem), the CTIR is known to be causal. For computing smooth transfer functions which interpolate frequency-domain estimates, one would perhaps like to enforce this constraint. This can be done in a number of ways, but not by forcing zn = 0 for n < 0 in the expansion of equation (8). -from Author