EFFECTS OF ATTENUATION ON REFLECTIONS

A well-known effect of attenuation is the change in frequency content and amplitude of a pulse propagating through an attenuating medium. Another aspect of wave propagation in viscoelastic media is the presence of frequency dependent reflection coefficients. This phenomenon is studied here in three different ways.;In the second part of this study, a new method of generating laterally homogeneous synthetic seismograms by using wave equation extrapolation is derived. It takes into account attenuation in the different media but is applicable only for layered media. The attenuation model used is the so-called constant-Q model. The results of this computer simulation show that the effect of attenuation contrast is noticeable only in cases of a large Q-contrast relative to the change of elastic properties. In those situations one can observe a relative increase in the amplitude of post-critical reflections and a decrease in the amplitude of the head-waves. No phase effects is observed except near the critical angles.;The third section deals with the experimental verification of this effect. The results prove that attenuation contrast does have an important effect on reflections when the acoustic impedances of the two considered media are very close. While it is a very common property in the upper crust of the earth, this condition of very low acoustic impedance contrast is difficult to simulate in the laboratory and results in a high degree of inaccuracy in the data. Nevertheless by using samples of polymer and silicon rubber we have shown that with low acoustic impedance contrast and high attenuation an increase in the amplitude of reflections due to Q-contrast is observable. We have also simulated the recorded experimental signals at different angles of incidence by using a model of attenuation for which the Q quality factor is independent of frequency. Finally we have shown that for a large angle of incidence ((GREATERTHEQ) 20 - 30 degrees) the Q-contrast effect dies out when the elastic reflection coefficient is very low. We always used angles lower than the critical angle to avoid problems due to the singularity of this zone. Theoretically according to the results of Part II, when the critical angle is low, the effects of attenuation occur at post-critical reflection angles and are observable in head-wave amplitudes.;The first way is theoretical. Relative effects of different viscoelastic models of attenuation on reflections are studied, and it is shown that all of the models verify the same conclusions. Then a review of the theory of wave propagation in laterally homogeneous viscoelastic media emphasizing the role of the quality factor Q is presented. The possibility of a quality factor Q independent of frequency in two dimensions is examined in detail.