# The use of multiwavelets for uncertainty estimation in seismic surface wave dispersion.

## Abstract

This report describes a new single-station analysis method to estimate the dispersion and uncer- tainty of seismic surface waves using the multiwavelet transform. Typically, when estimating the dispersion of a surface wave using only a single seismic station, the seismogram is decomposed into a series of narrow-band realizations using a bank of narrow-band filters. By then enveloping and normalizing the filtered seismograms and identifying the maximum power as a function of frequency, the group velocity can be estimated if the source-receiver distance is known. However, using the filter bank method, there is no robust way to estimate uncertainty. In this report, I in- troduce a new method of estimating the group velocity that includes an estimate of uncertainty. The method is similar to the conventional filter bank method, but uses a class of functions, called Slepian wavelets, to compute a series of wavelet transforms of the data. Each wavelet transform is mathematically similar to a filter bank, however, the time-frequency tradeoff is optimized. By taking multiple wavelet transforms, I form a population of dispersion estimates from which stan- dard statistical methods can be used to estimate uncertainty. I demonstrate the utility of this new method by applying it to syntheticmore »

- Authors:

- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1413439

- Report Number(s):
- SAND-2017-13271

659371

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 58 GEOSCIENCES

### Citation Formats

```
Poppeliers, Christian.
```*The use of multiwavelets for uncertainty estimation in seismic surface wave dispersion.*. United States: N. p., 2017.
Web. doi:10.2172/1413439.

```
Poppeliers, Christian.
```*The use of multiwavelets for uncertainty estimation in seismic surface wave dispersion.*. United States. doi:10.2172/1413439.

```
Poppeliers, Christian. Fri .
"The use of multiwavelets for uncertainty estimation in seismic surface wave dispersion.". United States.
doi:10.2172/1413439. https://www.osti.gov/servlets/purl/1413439.
```

```
@article{osti_1413439,
```

title = {The use of multiwavelets for uncertainty estimation in seismic surface wave dispersion.},

author = {Poppeliers, Christian},

abstractNote = {This report describes a new single-station analysis method to estimate the dispersion and uncer- tainty of seismic surface waves using the multiwavelet transform. Typically, when estimating the dispersion of a surface wave using only a single seismic station, the seismogram is decomposed into a series of narrow-band realizations using a bank of narrow-band filters. By then enveloping and normalizing the filtered seismograms and identifying the maximum power as a function of frequency, the group velocity can be estimated if the source-receiver distance is known. However, using the filter bank method, there is no robust way to estimate uncertainty. In this report, I in- troduce a new method of estimating the group velocity that includes an estimate of uncertainty. The method is similar to the conventional filter bank method, but uses a class of functions, called Slepian wavelets, to compute a series of wavelet transforms of the data. Each wavelet transform is mathematically similar to a filter bank, however, the time-frequency tradeoff is optimized. By taking multiple wavelet transforms, I form a population of dispersion estimates from which stan- dard statistical methods can be used to estimate uncertainty. I demonstrate the utility of this new method by applying it to synthetic data as well as ambient-noise surface-wave cross-correlelograms recorded by the University of Nevada Seismic Network.},

doi = {10.2172/1413439},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Fri Dec 01 00:00:00 EST 2017},

month = {Fri Dec 01 00:00:00 EST 2017}

}