This research is to develop and implement inversion methods based on neural networks for application to geophysical inversion problems, particularly, seismic inversion. The motivation for this approach is to improve the mapping of elastic parameters along a seismic line. This type of inversion for each point along a seismic line is currently computationally expensive. However, for a selected number of points along a line, it can be used to derive the elastic properties while training a neural network, that is, deriving the connection weights. After training, seismic gathers from the intermediate surface points can be input to the network to estimate depth-dependent elastic properties for those points resulting in a complete map. The most difficult part of the problem is to train the network. Global optimization methods such as simulated annealing and genetic algorithms will be used for the network training since the methods have proven successful in geophysical inversion.