Stochastic analysis of sonic logs from the upper crystalline crust: Methodology
1996 (English)In: Tectonophysics, ISSN 0040-1951, E-ISSN 1879-3266, Vol. 264, no 1-4, 341-356 p.Article in journal (Refereed) Published
To relate local fluctuations observed in sonic logs to small-scale velocity fabric along 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 Kármán 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.
Place, publisher, year, edition, pages
Elsevier, 1996. Vol. 264, no 1-4, 341-356 p.
acoustical logging; boreholes; caliper logging; noise; crystalline rocks; statistical analysis; SUDBURY STRUCTURE; BOREHOLE; HETEROGENEITY; PROPAGATION; LITHOSPHERE; SCATTERING
IdentifiersURN: urn:nbn:se:uu:diva-28034DOI: 10.1016/S0040-1951(96)00135-7OAI: oai:DiVA.org:uu-28034DiVA: diva2:55930