RESIX IP2DI v4 is a finite
element forward and inverse modeling program that calculates the IP and resistivity
responses of two-dimensional earth models. Inversion can be one of two cell based
algorithms or true polygon inversion. The cell based algorithms are also commonly referred
to as SMOOTH Models. RESIX 2DI v4 has got the exact same algorithms
as RESIX IP2Di v4 but does not support induced polarization (IP) data.
Interpex Smooth Model Algorithm
The Interpex Smooth Model Algorithm calculates the forward
response of a homogeneous half-space using a finite element routine. It then performs a
rapid least squares inversion of apparent resistivity using non-linear optimization
The regularization methods used to stabilize the inversions
are of two types: the first is based on Occam's Principle, which optimizes smoothness in
the model; the other is based on a ridge regression algorithm, which minimizes the least
squares error. There is also an exact inversion method available which calculates the
partial derivatives of all the data and then performs the inversion.
Zonge Smooth Model Algorithm
This algorithm uses a two-dimensional finite element method
which incorporates topography in modeling
resistivity (and IP data). This is accomplished by
first constructing a rectangular finite element mesh in the
normal fashion (based on depth), and then deforming it so the surface nodes match the
supplied topography profile. Nodes at depth are adjusted
to a lesser degree than the surface nodes as the depth increases.
Otherwise, the method used is the same as the standard method
of Rijo. In the special case where the topography is flat, it produces equations which are the same as those used by
Rijo (1977) and Wannamaker (1992).
2D Polygon Forward and Inverse Calculations
The polygon algorithm calculates the theoretical response
using the isoparametric finite element method developed by Luiz Rijo (1977). This
PhD thesis (Modeling of Electric and Electromagnetic Data, 7-88,155) is available
through University Microfilms International of Ann Arbor, Michigan.
Models are constructed using an interactive graphics screen
that allows two user-selectable pseudosections to be displayed above model construct area.
The results from either Smooth Model algorithm may be displayed as a color filled
background section to aid in polygon model construction.
For the polygon finite element modeling the grid is
determined from the number of electrodes and the electrode spacing. The package
automatically defines a fine grid for models with a topographic relief and assigns a very
high resistivity value for air. Interactive finite element grid editing allows the use to
delete or insert vertical or horizontal elements.
This polygon inversion is different from other methods
currently being used in that it requires that the user construct a geological model. The
model is composed of closed bodies, layers, or both which are automatically mapped onto
the finite element mesh.
The polygon inversion is performed using Inman-style
ridge regression inversion of polygon-based 2-D models to best fit the 2-D pseudosection
data in a least squares sense. Up to 200 model parameters can be selected from body
resistivities and IP parameters and from the x- and z-position of each vertex. In
addition, groups of vertices can be locked together to form a single unit whose x- and/or
z-position can be used as an inversion parameter.
This inversion is a genuine 2-D inversion of
2-D pseudosection data which allows the user to choose the parameters that are set as free
and those set to be frozen. By default, all parameters are frozen; the user interactively
selects those parameters to be used in the inversion using the mouse during model