We address three areas of the problem of the stacking velocity determination: (1) the development of a new high‐resolution velocity determination technique, (2) the choice of an optimal velocity trial scenario, and (3) a unified approach to the comparison of time‐velocity spectra produced by various methods. We present a class of high‐resolution coherency measures providing five‐eight times better velocity resolution than conventional measures. The measure is based on the rigorous theory of statistical hypothesis testing and on the statistics of directional data. In its original form, our method analyzes only the phase distributions of the data, thus making unnecessary careful spherical divergence corrections and other normalization procedures. Besides the statistical one, we develop an “instantaneous” version of the conventional coherency measure. This measure is based on the concept of the trace envelope, thus eliminating the need for an averaging procedure. Finally, we design a hybrid high‐resolution coherency measure, incorporating the latter and the statistical one. Carrying out a systematic comparison of various measures of coherency, we present a simple estimate of an attainable velocity resolution. Based on this estimate, we define an optimal velocity grid, providing uniform coverage of all details of the time‐velocity spectrum. To facilitate quantitative comparisons of different coherency functions, we develop a unified normalization approach, based on techniques known in image processing. Described methods are tested on synthetic and field data. In both cases, we obtained a remarkable improvement in the time‐velocity resolution. The methods are general, very simple in implementation, and robust and reliable in application.
Efficient construction of high-resolution TVD conservative schemes for equations with source terms: application to shallow water flows
