Amplitude-variation-with-angle (AVA) analysis is generally based on the ass
umption that the medium parameters behave as step functions of the depth co
ordinate z, at least in a finite region around the interface. However, outl
iers observed in well logs often behave quite differently from step functio
ns. In this paper, outliers in the acoustic propagation velocity are pa ram
eterized by functions of the form c(z)= c(1) \ z/z(1)\(alpha). The wavelet
transform of this function reveals properties similar to those of several o
utliers in real well logs. Moreover, this function is self-similar, accordi
ng to c(beta z)= beta(alpha)c(z), for beta > 0. Analytical expressions are
derived for the acoustic normal incidence reflection and transmission coeff
icients for this type of velocity function. For oblique incidence, no expli
cit solutions are available. However, by exploiting the self-similarity pro
perty of the velocity function, it turns out that the acoustic angle-depend
ent and frequency-dependent reflection and transmission coefficients are se
lf-similar as well. To be more specific. these coefficients appear to be co
nstant along curves described by p(1-alpha)omega(-alpha) = constant, where
p is the raypath parameter and omega the angular frequency. The singularity
exponent alpha that is reflected in these curves may prove to be a useful
indicator in seismic characterization.