Spatial Resolution for Processing Seismic Data: Type-2 Methods for Finding the Relevant Granular Structure

One of the main methods of determining the Earth structure is the analysis of the seismic data. Based on the seismic data, we produce a 3-D map describing the density at different locations on different depths. Due to incomplete coverage and measurement uncertainty, this map provides only an approximate description of the actual density distribution. For example, based on the seismic data, it is impossible to distinguish between the densities at two nearby points. In other words, what we actually reconstruct is not a function of 3 variables, but rather values determined on the appropriate spatial granules. Because of this granularity, it is necessary to find the spatial resolution at different locations and at different depths, i.e., in other words, it is necessary to determine the corresponding granules. In this paper, we show how Type-2 methods can help in determining these granules.