Shallow high-resolution reflection data provide information about near-surface geology from 20 m to 300 m depth. Within a receiver-spread range of 10 m to 150 m, a layered-dipping earth model is a simple and valid model in most cases of shallow reflection surveying. We formulated an approach to quickly estimate parameters such as interval velocity, reflector depth, and dip by inverting reflected traveltime of a layered-dipping earth model. To reduce the ambiguity of inverted solutions, we apply constraints on dip directions and depth to reflectors. Accuracy of modifications to update the model is controlled by: 1) using an explicit expression of the Jacobian matrix; 2) inverting model parameters layer by layer from shallow to deep, which is equivalent to solving a diagonal matrix; 3) employing the Levenberg-Marquardt method that is simplified and numerically stabilized by the singular value decomposition technique. Root-mean-square error and maximum deviation were introduced to track iteration convergence, thereby reducing the possibility of rejecting an acceptably modified model. Error-free synthetic examples, tested on a PC computer, showed the stability and speed of this approach. Application of this approach to real shallow seismic reflection field data confirms its accuracy and applicability on inexpensive personal computers.
MethodIn this section, we briefly discuss an approach that performs fast estimations of parameters of a layered-