My PhD Thesis, PDF 3MB - Stanford University
My PhD Thesis, PDF 3MB - Stanford University
My PhD Thesis, PDF 3MB - Stanford University
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The generalized reflection and transmission coefficients method is applied to<br />
numerically investigate seismic wave attenuation in the simple open borehole and<br />
complicated boreholes with invaded zones. In order to measure the intrinsic attenuation<br />
we need to remove the geometrical spreading effect which is complex and highly<br />
frequency-dependent. If we use the frequency shift method to estimate intrinsic<br />
attenuation for a simple open borehole, we can introduce a frequency-dependent<br />
geometrical spreading factor, exp(-gfz), to do the correction (but only for open hole).<br />
It is difficult to determine the details of the frequency-dependent geometrical<br />
spreading for the complicated boreholes. I introduce an apparent geometrical spreading<br />
factor expressed by 1 / z p<br />
, which may approximately include the effect of the frequency-<br />
dependent term exp(-gfz) if we select a proper power p. Simulation tests show that the<br />
power p=1 for a simple borehole, p1 for a flushed<br />
zone model. How large the power p deviates from 1 depends on the structure of the<br />
invaded zones, such as the velocity contrast and the invaded depth. For the specific<br />
borehole models investigated in this chapter, p=0.5 for the invaded zone model and<br />
p=1.21 for the flushed zone model.<br />
Chapter 6<br />
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