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Envelope crossing distributions for Gaussian fields

Podgorski, Krzysztof LU and Rychlik, Igor LU (2008) In Probabilistic Engineering Mechanics 23(4). p.364-377
Abstract
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.

In the first part of the paper, we review the approach as well as give a brief account of the previous results with some focus on the contribution of Ove Ditlevsen.



In the main part of the paper, the method of sampling distribution is applied to the envelope field that is a generalization of the envelope process.

Here we notice that the envelope field is not uniquely defined and that its statistical properties depend on a chosen version.... (More)
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.

In the first part of the paper, we review the approach as well as give a brief account of the previous results with some focus on the contribution of Ove Ditlevsen.



In the main part of the paper, the method of sampling distribution is applied to the envelope field that is a generalization of the envelope process.

Here we notice that the envelope field is not uniquely defined and that 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. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
sea surface models, Rice's formula, Envelope field, Gaussian stochastic processes, velocity distributions
in
Probabilistic Engineering Mechanics
volume
23
issue
4
pages
364 - 377
publisher
Elsevier
external identifiers
  • wos:000259894400004
  • scopus:51049115725
ISSN
0266-8920
DOI
10.1016/j.probengmech.2007.10.010
language
English
LU publication?
yes
id
1f567279-d52a-47ea-ad63-73585c11ff03 (old id 932902)
date added to LUP
2009-07-09 09:14:59
date last changed
2017-01-01 04:51:31
@article{1f567279-d52a-47ea-ad63-73585c11ff03,
  abstract     = {The envelope process is an analytical tool often used to study extremes and wave groups. <br/><br>
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.<br/><br>
In the first part of the paper, we review the approach as well as give a brief account of the previous results with some focus on the contribution of Ove Ditlevsen.<br/><br>
<br/><br>
In the main part of the paper, the method of sampling distribution is applied to the envelope field that is a generalization of the envelope process.<br/><br>
Here we notice that the envelope field is not uniquely defined and that its statistical properties depend on a chosen version. <br/><br>
We utilize convenient envelope sampling distributions to decide for a version that has desired smoothing properties.<br/><br>
The spatial-temporal Gaussian sea-surface model is used to illustrate this approach.<br/><br>
<br/><br>
<br/><br>
One intrinsically multivariate problem is studying velocities of moving spatial records. <br/><br>
Under the Gaussian model we derive sampling properties of the envelope velocity measured at the level contours.<br/><br>
By associating the properties of envelope with the properties of group waves we present differences between statistical distributions of individual waves and waves groups.},
  author       = {Podgorski, Krzysztof and Rychlik, Igor},
  issn         = {0266-8920},
  keyword      = {sea surface models,Rice's formula,Envelope field,Gaussian stochastic processes,velocity distributions},
  language     = {eng},
  number       = {4},
  pages        = {364--377},
  publisher    = {Elsevier},
  series       = {Probabilistic Engineering Mechanics},
  title        = {Envelope crossing distributions for Gaussian fields},
  url          = {http://dx.doi.org/10.1016/j.probengmech.2007.10.010},
  volume       = {23},
  year         = {2008},
}