My PhD Thesis, PDF 3MB - Stanford University

For this test, I use the forward modeling method described in Chapter 3. Since this
method is a semi-analytical approach, there is no grid dispersion in the computing.
4.4.3 Field data: one dimensional geological structure
For field data, I first choose a data set collected at BP's Devine test site where the
lithology is layer cake, and the geological structure is approximately one dimensional. A
linear sweep from 200Hz to 2000Hz was used as the source spectrum. Figure 4.8 shows
the travel time and centroid frequency picks from this field data set. It can be seen from
these picks that the high centroid frequency correlates to the fast travel time. This
correlation indicates that the high velocity formation in this area has low attenuation. I
first use travel time tomography to reconstruct the velocity structure and obtain ray paths.
Then, I use the ray paths and centroid frequencies to inverse the attenuation structure. A
1-D layered model is assumed for this inversion problem. Figure 4.9 shows the velocity
and attenuation reconstructions. For the attenuation tomography, the starting model is a
homogeneous model which is calculated using the average of centroid frequency shift
data. The initial source frequency f S is 1750 Hz. After inversion the final source
frequency fs is 1520 Hz. The attenuation coefficient o and velocity v are converted to
Q-values using equation (4.3). The lithology and the sonic log are also shown in Figure
4.9 for comparison. They exhibit an excellent geometric agreement with the inversion
results. As what we expect, Figure 4.9 shows that shale and sand have lower Q-value
and slower velocity, and limestone has higher Q-value and faster velocity.
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