Welcome to RokBites, your bi-weekly guide to brushing up on RokDoc techniques. 👩💻💡
This week, we're diving into Backus averaging and its implementation on RokDoc.
Hit play on the video below or jump to the summary below to start!
Understanding Seismic Wave Propagation with Backus Averaging
For geoscientists, understanding how geological layers interact with acoustic waves is crucial for accurate modelling. It is important to move from the log resolution scale to the seismic resolution one with confidence and accuracy.
Complexity at Smaller Scales
At finer scales, geological layers exhibit significant complexity. Sonic logging can achieve resolutions as fine as 0.15 inches, presenting challenges in modelling without introducing unnecessary details into synthetic seismograms. Simple averaging is insufficient, as it does not preserve the wavefield's features or anisotropy information.
The Contribution of George Edward Backus
George Edward Backus, a distinguished American geophysicist, made substantial contributions to modern geophysics. His seminal paper, "Long wave elastic anisotropy produced by horizontal layering" (1962) demonstrated that for long-distance seismic waves, a layered isotropic structure can mimic a single, consistent medium if its stiffness remains unchanged across layers.
Shales might appear isotropic at the log scale but are intrinsically anisotropic at the core scale due to their mineralogy. Conversely, sandstones may exhibit strong variations at the log scale while being isotropic at the core scale. Backus's theory elucidates variations in P-wave speeds as effects of these layers, particularly when contrasts are significant in well logs.
Application of Backus Theory
Backus theory, when applied to well-log data, allows for the separate computation of layer-induced and intrinsic anisotropy contributions. This understanding is essential for the upscaling required before modelling seismic wave propagation in such media. The theory formulation provides a comprehensive set of VTI parameters, including the upscaled vertical P and S wave velocity.
It allows the user to upscale Vp-Vs-Rho logs without losing the geophysical character of the logs themselves - it is not a simple smoothing filter!
Determining the Averaging Window
A critical consideration in Backus theory is the appropriate averaging window length. In their 2007 paper, 'The Backus number' Liner and Fei introduced the 'Backus number', which is a function of dominant frequency, averaging window size, and minimum velocity in the logging interval. They determined that when the Backus number is less than 1/3, the original and averaged wavefields are virtually identical. This is identified as 'scattering limit'.
Implementation in RokDoc
In RokDoc, the Backus number is set at 0.1, well below the scattering limit. Users must input the averaging length, determined from Liner and Fei's work, as a function of minimum P-wave velocity and dominant frequency.
To determine the length of the averaging window, simply use the following equation:
in which f: dominant frequency; V is the P-wave velocity; 0.1 is the set value for Backus number.
By analysing well log data and extracting a statistical wavelet from full stack data, these parameters can be defined. For example, with a dominant frequency of ~70Hz and the minimum velocity in the interval of interest set to 3000 m/s, the averaging length is set at 4 meters.
To perform Backus averaging in RokDoc, open the Well Viewer, navigate to well ops > synthetics and filters and select 'Backus averaging'. Watch the video above for a quick RokDoc demo!
Testing different Backus window sizes is advisable, particularly in challenging areas with strong reflectors. In cases of strong vertical anisotropy, testing the Backus averaging window is crucial to ensure accurate wavefield propagation modelling and, consequently, upscaling.
RokDoc will apply Backus averaging and produce the anisotropy logs for Epsilon, Gamma, Delta as output as well.
Conclusion
After performing Backus averaging for P-wave velocity, S-wave velocity, and density logs, the user can proceed to synthetic seismogram creation or any 2-D and 3-D modelling in RokDoc.
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