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We have just uploaded a new demonstration program (concept)
to invert 2-D magnetotelluric geophysical data.
The above is performed via a 2-D Niblett-Bostick approach.
Try inverting COPROD2 data (in 15 minutes) from within your smartphone.
The program is free and on-line (see tutorial below).
Web-Inverse_Tutorial MT 2-D Niblett-Bostick
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About us:
Versamedium Web Services is a startup company that provides on-line solutions to linearized inverse problems with discrete data. It is well known that inverse problems could be ill-conditioned or ill-posed in nature. Although by using a local regularization scheme we can tackle these problems, and find meaningful solutions in diverse areas such as: Tomography, Optical Imaging, Particle Sizing, Geophysical Prospecting, Exponential Analysis in Magnetic Resonance (NMR) or Diffusion ordered spectroscopy.
Take for instance the example of the Diffusion Partial Differential equation whose forward solution represents a measurable observable. In our case we aim to find a set of interaction coefficients or properties of the medium, knowing the incident source and the observable. Traditionally, one way to solve for such intricate problems is by solving in terms of Green's function formalism and by further expressing a solution for the forward problem as a linearized approximation in terms of the Fréchet derivative (alternatively, the sensitivity matrix) within first order approximation, then by expressing the integral of the Fréchet derivative together with the data and the model unknowns as a Linear System of Equations (LSE). At this point among other inversion schemes is Versamedium Web Services which solves the inverse problem represented by the numerical LSE. This might be done in a recursive iterative procedure, obtaining this way the desired solution.
Our current product is a web based service which delivers fast solutions on site.
How:
With Versamedium's Web Services you can solve complex optimization problems on-line, and you can try it for FREE:
Example I:
Vertical Electric Soundings (1-D Nonlinear):
Vertical electric soundings constitutes a valuable tool in determining the electric properties of the subsoil. Electric currents are injected in the subsoil through punctual electrodes and then, voltage is measured usually in the center of the electrode array.
Figure 1. Data (red dots) and Versamedium's response obtained after 10 nonlinear times 10 linear iterations (green) rms = 0.6 %, Synthetic Data (red). For Model in Figure. 2.
Figure 2. Versamedium's model (1000 layers) obtained after 10 nonlinear times 10 linear iterations (green). Synthetic Model (red) and Occam's Reference Model (yellow).
Example II:
Magnetotelluric Soundings (2-D Linearized):
The Versamedium Web Service can also solve problems in 2 or 3 dimensions. Consider a real case, in which a complex nonlinear problem in 2-D has been linearized. Fig. 3 shows the results obtained by applying the Versamedium web service to a 2-D real data set COPROD2 (Jones, 1993a).
Figure 3. We can see that when using the smallest window, allows to identify the two main anomalies found in other works. The strongest conductive anomaly in Figure 3 corresponds to the North American Central Plains (NACP) conductivity anomaly, which has been well discussed in the literature Jones1993a. The smaller lobular anomalies towards the right end of the profile corresponds in turn to the known Thomson Nickel Belt (TOBE) anomaly.
E-mail: info@versamedium.com
REFERENCES:For more details see Versamedium Web Service: White Paper
Sebastiáo Rita, Pacheco C.N. , Braga J.P. and Piló-Veloso Dorila , (2006), ``Diffusion coefficient distribution from NMR-DOSY experiments using Hopfield neural network'', Journal of Magnetic Resonance Volume 182, Issue 1, September 2006, Pages 22-28.
Ye J. C., Webb K. J., Millane R. P., Downar T. J.. (1999), ``Modified distorted Born iterative method with an approximate Fréchet derivative for optical diffusion tomography'', J. Opt. Soc. Am. A Vol. 16, No. 7/July 1999 pp. 1814-1826.
McGillivray P. R. and Oldenburg D. W. , (1990), ``Methods for Calculating Fréchet derivatives and sensitivities for the non-linear inverse problem: A comparative study '', Geophysical Prospecting, 38,499-524.
Esparza, F.J. y Gómez-Treviño, E. (1996), ``Inversion of magnetotelluric soundings using a new integral form of the induction equation'', Geophys. J. Int., 127 : 452-460.
Oldenburg D.W. (1978), The Interpretation of direct current resistivity measurements, Geophysics , 43 (3) : 610-625.
Jones, A. G. (1993a), The COPROD2 dataset: Tectonic setting, recorded MT data, and comparison of models, J. Geomag. Geoelectr., 45 : 933-955.
Rodríguez J., Esparza F.J. and Gómez-Treviño E., (2010), `` 2-D Niblett-Bostick magnetotelluric inversion '', Geologica Acta (Vol. 8, 1). http://www.geologica-acta.com/pdf/vol0801a03.pdf
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