Pseudo-Depth/Intercept-Time Monotonicity Requirements in the Inverse Scattering Algorithm for Predicting Internal Multiple Reflections (Communications in Computational Physics, 2018)
In this paper we discuss the inverse scattering algorithm for predicting internal multiple reflections (reverberation artefacts), focusing our attention on the construction mechanisms. Roughly speaking, the algorithm combines amplitude andphase information of three different arrivals (sub-events) in the data set to predict onemultiple reflection. The three events are conditioned by a certain relation which requires that their pseudo-depths, defined as the depths of their turning points relativeto the constant background velocity, satisfy a lower-higher-lower relationship. Thisimplicitly assumes a pseudo-depth monotonicity condition, i.e., the relation betweenthe actual depths and the pseudo-depths of any two sub-events is the same. We studythis relation in pseudo-depth and show that it is directly connected with a similar relation between the vertical or intercept times of the sub-events. The paper also providesthe first multidimensional analysis of the algorithm (for a vertically varying acousticmodel) with analytical data. We show that the construction of internal multiples is performed in the plane waves domain and, as a consequence, the internal multiples withheadwaves sub-events are also predicted by the algorithm. Furthermore we analyzethe differences between the time monotonicity condition in vertical or intercept timeand total travel time and show a 2D example which satisfies the former but not the latter. Finally we discuss one case in which the monotonicity condition is not satisfied bythe sub-events of an internal multiple and discuss ways of lowering these restrictionsand of expanding the algorithm to address these types of multiples.