The Best Manifold Theory in the Frequency Domain of Time Dependent Functions an Application to: Seismic Engineering

Abstract The paper presents a novel civil engineering interpretation of the Fourier spectrum and phase of a seismic record. When the concept of linear manifolds is accounted for, we can generate clear interpretations of the maximum projections of a seismic event. Choosing the greatest ordinates of a given spectrum is equivalent to the selection of the frequency space where the maximal projections are recorded. The use of these maximum ordinates generates the original seismic record with great accuracy and with a minimum of data. This fact clearly indicates that most of the information about a time dependent signal is encoded in this best manifold. This fact is relevant, as it will clearly reduce the processing time, (depending on every record) up to 90%.