Fj. Esparza et E. Gomeztrevino, 1-D INVERSION OF RESISTIVITY AND INDUCED POLARIZATION DATA FOR THE LEAST NUMBER OF LAYERS, Geophysics, 62(6), 1997, pp. 1724-1729
An automatic inverse method has been developed for generating layered
earth models from electrical sounding data. The models have the minimu
m number of layers required to fit a resistivity sounding curve or a c
ombined resistivity and induced polarization sounding. The ground is m
odeled using a very large number of thin layers to accommodate arbitra
ry variations. The properties of the layers are optimized using as a c
onstraint the L-1 norm of the vertical derivative of the resistivity d
istribution. The use of linear programming leads to piecewise smooth d
istributions that simulate traditional models made up of a few uniform
layers. The process considers from the simplest model of a uniform ha
lfspace to models of many layers, without fixing a priori the number o
f discontinuities. The solution is sought by iterating a new linear ap
proximation, similar to the classical process of linearization, except
that a reference model is not present in either the data vector or th
e unknown function. For induced polarization soundings, the problem is
linear and the solution is obtained in a single iteration, provided a
n adequate resistivity model is available. The performance of the meth
od is illustrated using numerical experiments and published deep resis
tivity data from Australia. The method also is applied to combined res
istivity and induced polarization soundings from a local groundwater p
rospect in Mexico.