Seminar Details

Seminar Details


Feb 11

3:30 pm

Envelope Crossing Distributions for Gaussian Fields

Krzysztof Podgorski


Lund University

The envelope process is an analytical tool often used to study extremes and wave groups. In an approach to approximate the first passage probability for the underlying response the average number of envelope crossings is used to obtain an upper bound. The method of sampling distribution is applied to the envelope field that is a generalization of the envelope process. As oppose to the one dimensional version, the envelope field is not uniquely defined and its statistical properties depend on a chosen version. We utilize convenient envelope sampling distributions to decide for a version that has desired smoothing properties. The spatial-temporal Gaussian sea-surface model is used to illustrate this approach. One intrinsically multivariate problem is studying velocities of moving spatial records. Under the Gaussian model we derive sampling properties of the envelope velocity measured at the level contours. By associating the properties of envelope with the properties of group waves we present differences between statistical distributions of individual waves and waves groups.