Acoustic and Electromagnetic Souding of a Half-Space for a Continous Depth Variation of Density and Conductivity

A combined application of seismic and electromagnetic sounding methods improves the geophysical exploration of the earth's crust. We investigate both the acoustic and the electromagnetic fields at the surface of a crust model consisting of an inhomogeneous half-space, where respectively either the density or the conductivity varies as a rational power of a linear function of depth. The solutions of a class of wave equat'iona reducible to Bessel's equations allow to obtain the spectral variation of the pressure or of the magnetic field for this model. The result consists of the generalization of an equivalent approach applied to the magnetotelluric technique. Analysis of the spectrum for the reflection coefficients shows that: (1) for normalized wavenurnbers larger than 10 it is difficult to define the subsurface model, because the spectrum doesn't differ from the homogeneous case; (2) for normalized wavenumbers lower than 10 positive powers of the linear function yield better resolution; and (3) for po- sitive powers the phase changes sign and the modulus reaches a minimum value in the low frequency range of the spectrum. The results may be useful to estimate porosity and fluid content variation in the vertical direction of submarine sedimentary sequences.