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RESIX 2DI v4 & IP2DI v4

2-D Resistivity and IP Forward and Inverse Modeling


    Three 2D algorithms

    Interpex 2D Smooth Inversion for fast results

    Zonge 2D Smooth Inversion algorithm for depth images including topography

    Inman-style ridge regression inversion of polygon-based 2-D models to best fit the 2-D pseudosection data in a least squares sense

    Supports Wenner, Gradient (not for Smooth Model Algorithms), Pole-Dipole, Pole-Pole, Schlumberger and Dipole-Dipole 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


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 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 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 Ph.D 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 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 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 construction. 

Interpex Smooth InversionSmooth Image Model Screen capture shows 2-D 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 InversionZonge Smooth Model


Screen capture shows 2-D 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

Polygon Model Construction


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

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 ohm-m in a halfspace of 100 ohm-m. 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 ohm-m in a halfspace of 30 ohm-m. 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. 


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.



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