Interpex 2D Smooth Inversion for fast
results
Zonge 2D Smooth Inversion algorithm for
depth images including topography
Inmanstyle ridge regression inversion of
polygonbased 2D models to best fit the 2D pseudosection data in a least
squares sense
Supports Wenner, Gradient (not for Smooth
Model Algorithms), PoleDipole, PolePole, Schlumberger and DipoleDipole
arrays
Direct data import from Scintrex, Zonge,
Geosoft, ABEM, AGI Swift, Campus, Iris, OYO, Diapir and ASCII formats
High resolution graphics with 256 color
fill for both screen and hardcopy results
Interactive polygon model construction
using mouse
Smooth models can be used as background to
aid in polygon model construction
User defined color palettes
Interactive Zoom on data and model
displays
Convert and export the 2D data as 1D
Sounding data to RESIX 1D Family compatible files

PROGRAM DESCRIPTION
RESIX IP2DI v4 is a finite
element forward and inverse modeling program that calculates the IP and
resistivity responses of twodimensional 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 halfspace
using a finite element routine. It then performs a rapid least squares
inversion of apparent resistivity using nonlinear optimization techniques.
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
twodimensional 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 Ph.D thesis (Modeling of Electric
and Electromagnetic Data, 788,155) is available through University
Microfilms International of Ann Arbor, Michigan.
Models are constructed using an
interactive graphics screen that allows two userselectable pseudosections
to be displayed above model construct area. The results from either Smooth
Model algoritm 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
performedusing Inmanstyle ridge regression inversion of polygonbased 2D
models to best fit the 2D 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 zposition of each vertex. In addition,
groups of vertices can be locked together to form a single unit whose x
and/or zposition can be used as an inversion parameter.
This inversion is a genuine 2D
inversion of 2D 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 construction.
Interpex Smooth Inversion 
Screen capture shows 2D pseudosection of the resistivity data at the top,
the calculated smooth depth section at the bottom and the synthetic
pseudosection from the depth section in the middle.
Data courtesy of Zonge Engineering.

Zonge Smooth Model Inversion

Screen capture shows 2D pseudosection of the resistivity data at the top,
the calculated smooth depth section at the bottom and the synthetic
pseudosection from the depth section in the middle.
The model section presents a 'true'
topography section since the topography is incorporated in the model
calculation.
The model was calculated using the Zonge
Smooth model algorithm. Both the data and model sections are draped from
topography.

Polygon Model Construct Screen

Screen capture shows the polygon model construction screen using the Zonge
Smooth Model as a background to aid in model construction.
Polygon models are defined as layers and/or
bodies. Any of the vertices and/or body parameters can be set as a FREE
parameter in the polygon inversion.

Model Comparison

Screen capture shows the Interpex Smooth Model at the top, Zonge Smooth
Model in the middle and an example polygon model at the bottom.

Polygon Inversion Example

Slide show demonstrating the POLYGON inversion technique RESIX IP2DI v4 uses.
The picture shows the field data on top with the calculated data from the
model shown at the bottom the next pseudosection.
Synthetic data was generated using a box
with a resistivity of 10 ohmm in a halfspace of 100 ohmm. This data was
then transformed to be the field data.
To demonstrate the inversion a starting
model was assumed to be a box with a resistivity of 30 ohmm in a halfspace
of 30 ohmm. The box was set up to allow one corner to move freely but the
shape of the box was fixed.
All resistivity values were also allowed to
change in the inversion. It can clearly be seen that the inversion not only
changes the position of the box, but also the resistivity values. 
INVERSION EXAMPLE

This slide show is similar to the one above, except that the starting model
was a box with all corners free and all resistivity values free.
Again the inversion changes all corners of
the body and also the resistivity values to finally produce a model that not
only matches the shape of the initial model used to create the synthetic
data but also the resistivity values. 
