A novel algorithm called Isometric Method (IM) for solving smooth real-valued non-linear inverse problems has been developed. Model and data spaces are represented by using m+1 corresponding vectors at a time (m is the dimension of model space). Relations among vectors in the data space are set up and then transferred into the model space thus generating a new model. If the problem is truly linear, this new model is the exact solution of the inverse problem. If the problem is non-linear, the whole procedure has to be repeated iteratively. The basic underlying idea of IM is to postulate the distance in the model space in such a way that the model and data spaces are isometric, i.e. distances in both spaces have the same measure. As all model-data vector pairs are used many times in successive iterations, the number of the forward problem computations is minimized. There is no necessity to deal with derivatives. The requirement for the computer memory is low. IM is suitable especially for solving smooth medium non-linear problems when forward modelling is time-consuming and minimizing the number of function evaluations is topical.
The code on this page is available in MATLAB. Please, do not hesitate to contact us for more information: malek [at] irsm.cas.cz.
Program for 3D seismic refraction data processing using the modified time-term method.
download current version 0.2 |
source code |
article Valenta and Dohnal (2007)
Matlab code for dispersive waveform calculation of the surface wave. Calculation is based on summation the particular frequency components with the introduction of phase shifts, corresponding to velocity dispersion and given distance from a seismic source.
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