Noncausality of the discrete‐time magnetotelluric impulse response

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Abstract
Under the assumption that the external source magnetic fields are uniform, the electric (E) and magnetic (H) fields observed at the surface of the conducting earth satisfy a time‐invariant linear relation, which may be expressed as multiplication in the frequency domain, [Formula: see text], Eq. (1), or as convolution in the time domain, [Formula: see text], Eq. (2). Here the tilde denotes quantities in the frequency domain; e.g., [Formula: see text] is the frequency‐domain magnetotelluric (MT) impedance, and Z the corresponding time‐domain impulse response. For simplicity in the following discussion, I treat all quantities as scalars, although the operations in equations (1) and (2) generally involve vectors and tensors.

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