On: “Stratigraphic filter theory: Combined effects of parallel bedding and random inhomogeneities” by I. Lerche (GEOPHYSICS, 51, 1531–1537, August 1986).

Abstract

In the paper by Lerche (hereafter referred to as Lerche 86), the author compared his formula of effective attenuation (42) based on the mean field attenuation with formula (41), attributed to Wu (1982a), and claimed that Wu’s formula “explicitly assumed that the Born approximation is valid (i.e., that the scattering by the randomly sited centers is from the unperturbed incident wave with no modification to the wave from previous scattering),” while in his result “the modification to the incident wave is taken into account through the statistically sharp mean field” and therefore is “more correct.” However, neither the statement about the validity condition of Wu’s formula not the author’s formula (42) from the mean field approach is correct. In fact, the mean field formalism, when improperly applied to amplitude attenuation, can generate physically meaningless results. The impotence and fallacy of the mean field formalism in dealing with amplitude attenuation in 3-D random media have been recognized since the early 1980s (Wu, 1980, 1982a, b; Sato, 1982a, b). This recognition and the developments thereafter can be considered as one of the major advances in the field of scattering attenuation of seismic waves (Herraiz and Espinosa, 1987; Wu, 1987). Retreat from this advance seems injudicious and illogical. Therefore, I would like to take this opportunity to clarify some basic problems of scattering attenuation.