# Stochastic analysis of sonic logs from the upper crystalline crust: methodology

## Détails

ID Serval

serval:BIB_56F7A0A870F6

Type

**Article**: article d'un périodique ou d'un magazine.

Collection

Publications

Institution

Titre

Stochastic analysis of sonic logs from the upper crystalline crust: methodology

Périodique

Tectonophysics

ISSN-L

0040-1951

Statut éditorial

Publié

Date de publication

1996

Peer-reviewed

Oui

Volume

264

Pages

341-356

Langue

anglais

Résumé

To relate local fluctuations observed in sonic logs to small-scale

velocity fabric dong boreholes, both filtering effects and noise

introduced by the logging procedure must be taken into account. Sonic

log velocities are represented as a time series consisting of a large-scale

deterministic and a small-scale stochastic component. The deterministic

trend, approximated by a low-order polynomial best-fit, contains

information on the average velocity structure, whereas the small-scale

stochastic variations consist of noise plus in situ velocity variations

convolved with the logging system response. The velocity fluctuations

of the sonic data considered here are zero-mean and have quasi-Gaussian

probability density functions. Therefore, they are well characterised

by their second statistical moment, i.e. their autocovariance function.

Tests on synthetic data indicate that the autocovariance function

corresponding to this data model may be used to extract information

on the second-order statistics of the in situ velocity variations

along the borehole and to constrain the level of white noise in sonic

logs. Ignoring the presence of filtering effects and noise in sonic

logs may result in seriously flawed estimates of the second-order

statistics of the actual velocity structure. Assuming a von Karman

autocovariance function for the in situ velocity variations, this

model provides a good match to the autocovariance functions of sonic

log data from the Siljan Ring (Sweden) and Sudbury areas (Canada).

Although differing significantly in their noise content these two

data sets yield similar results for the small-scale velocity structure,

which is modelled as a bandlimited self-affine time series. For the

Siljan Ring borehole we found a close relation between small-scale

variations of the borehole diameter as determined from caliper logs

and the level of uncorrelated noise present in the sonic log data.

velocity fabric dong boreholes, both filtering effects and noise

introduced by the logging procedure must be taken into account. Sonic

log velocities are represented as a time series consisting of a large-scale

deterministic and a small-scale stochastic component. The deterministic

trend, approximated by a low-order polynomial best-fit, contains

information on the average velocity structure, whereas the small-scale

stochastic variations consist of noise plus in situ velocity variations

convolved with the logging system response. The velocity fluctuations

of the sonic data considered here are zero-mean and have quasi-Gaussian

probability density functions. Therefore, they are well characterised

by their second statistical moment, i.e. their autocovariance function.

Tests on synthetic data indicate that the autocovariance function

corresponding to this data model may be used to extract information

on the second-order statistics of the in situ velocity variations

along the borehole and to constrain the level of white noise in sonic

logs. Ignoring the presence of filtering effects and noise in sonic

logs may result in seriously flawed estimates of the second-order

statistics of the actual velocity structure. Assuming a von Karman

autocovariance function for the in situ velocity variations, this

model provides a good match to the autocovariance functions of sonic

log data from the Siljan Ring (Sweden) and Sudbury areas (Canada).

Although differing significantly in their noise content these two

data sets yield similar results for the small-scale velocity structure,

which is modelled as a bandlimited self-affine time series. For the

Siljan Ring borehole we found a close relation between small-scale

variations of the borehole diameter as determined from caliper logs

and the level of uncorrelated noise present in the sonic log data.

Mots-clé

acoustical logging, boreholes, caliper logging, noise, crystalline, rocks, statistical analysis

Création de la notice

25/11/2013 19:27

Dernière modification de la notice

20/08/2019 15:11