Noncausality of the discrete-time magnetotelluric impulse response

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, (1)E¯(ω)=Z¯(ω)H¯(ω), or as convolution in the time domain, (2)E(t)=Z*H(t)=∫−∞∞Z(t−τ)H(τ)dτ. Here the tilde denotes quantities in the frequency domain; e.g., Z¯ 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.