Velocity inversion in cross-hole seismic tomography by counter-propagation neural network, genetic algorithm and evolutionary programming techniques

The disadvantages of conventional seismic tomographic ray tracing and inversion by calculus-based techniques include the assumption of a single ray path for each source– receiver pair, the non-inclusion of head waves, long computation times, and the difficulty in finding ray paths in a complicated velocity distribution. A ray-tracing algorithm is therefore developed using the reciprocity principle and dynamic programming approach. This robust forward calculation routine is subsequently used for the cross-hole seismic velocity inversion. Seismic transmission tomography can be considered to be a function approximation problem; that is, of mapping the traveltime vector to the velocity vector. This falls under the purview of pattern classification problems, so we propose a forward-only counter-propagation neural network (CPNN) technique for the tomographic imaging of the subsurface. The limitation of neural networks, however, lies in the requirement of exhaustive training for its use in routine interpretation. Since finding the optimal solution, sometimes from poor initial models, is the ultimate goal, global optimization and search techniques such as simulated evolution are also implemented in the cross-well traveltime tomography. Genetic algorithms (GA), evolution strategies and evolutionary programming (EP) are the main avenues of research in simulated evolution. Part of this investigation therefore deals with GA and EP schemes for tomographic applications. In the present work on simulated evolution, a new genetic operator called ‘region-growing mutation’ is introduced to speed up the search process. The potential of the forward-only CPNN, GA and EP methods is demonstrated in three synthetic examples. Velocity tomograms of the first model present plausible images of a diagonally orientated velocity contrast bounding two constant-velocity areas by both the CPNN and GA schemes, but the EP scheme could not image the model completely. In the second case, while GA and EP schemes generated an accurate velocity distribution of a faulted layer in a homogeneous background, the CPNN scheme overestimated the vertical displacement of the fault. One can easily identify five voids in a coal seam from the GA-constructed tomogram of the third synthetic model, but the CPNN and EP schemes could not replicate the model. The performances of these methods are subsequently tested in a real field setting at Dhandadih Colliery, Raniganj Coalfields, West Bengal, India. First arrival traveltime inversion by these algorithms from 225 seismic traces revealed a P-wave velocity distribution from 1.0 to 2.5 km s−1. A low-velocity zone (1.0 km s−1 ), the position of a suspected gallery in the Jambad Top coal seam, could be successfully delineated by CPNN, GA and EP schemes.