SMTIP as ill-posed inverse problem

The results of the kinematic stage of the inverse problem solution are  four parameters: three coordinates of the events and its beginning time. Estimation of the velocity is carried out too. It is supposed that initial value of the velocity  is known.
Determination of the beginning time of events  is based on automatic cross-correlation data.
The results of the dynamic  stage of the inverse problem solution are  six functions 

555

777

The method of minimization. Regularized solution

sm2

Control solution. Creating the optimal algorithm for the inverse problem

sm3

sm4

Control of  solution accuracy during data processing

Key of   control  is  to follow   the roadmap of the  optimal inverse problem solutions, which has four steps:

  1. Mathematical simulation of  seismic wave propagation for  the fixed event and for the specific sensor array;
  2. The perturbation of  simulated data by noise with pre-fixed variance  (usually 25-30%);
  3. Search the optimal algorithm of inverse problem for  preset noise, event parameters and sensor array  in the fixed stability interval (so called correctness  of domain for the inverse operator  -  ill-posed problems theory);
  4. Apply the optimal algorithm to real microseismic data