Figure 6-3 plots the value of a ("Intercept") and b ("slope of spec- 

 trum") as a function of azimuth. The resulting spectral estimates are 

 fitted with the above model. Approaching azimuths of 0" and 180°, the 

 profiles nearly parallel the linear trend and the results are unreli- 

 able, due to the small number of depths available for analysis resulting 

 In a very narrow frequency band width used In the model regression. 



The coefficients b(6) do not show any relationship to the trend, as 

 predicted by theory. This does not Imply that directional dependence In 

 b(6) Is never found In spectra from sea-floor profiles. If a surface 

 had two or more distinct signals (perhaps due to differing relief- 

 forming processes) superimposed, cyclical behavior In b(6) would be pos- 

 sible. For example, envision a hypothetical surface composed of an Iso- 

 tropic two-dimensional signal with spectra slope b^(e), overlain by a 

 simple linear trend (like the one described above) with spectral slope 

 ^^(6). Perpendicular to trend, b(9) would be some combination of b^(e) 

 and bQ(6) depending on their relative amplitudes. Parallel to trend, 

 b(6) would equal just b^(6), in this example, since the linear trend 

 with slope bg(6) is constant In the direction parallel to strike. The 

 example spectra from the Mendocino Fracture Zone presented In Chapter 4 

 Illustrate this effect. Appendix E examines a series of artificially 

 generated surfaces and their spectral characteristics. 



In the results shown In Figure 6-3, the parameter a(6) shows the 

 expected relationship to co8(e-9^),e^ . 90", as predicted by theory. 

 This model cosine function can be used to parameterize the surface 

 anlsotropy. The model sinusoid Is generated by an Iterative regression 

 technique (see Appendix C.2) which determines the following equation 



84 



