Estimation of the cyclostationary dependence in geophysical data fields

Geophysical multivariate data fields are frequently analyzed using linear inverse modelling. A cyclostationary dependence, whether annual, semiannual or diurnal, is usually present in these data. The dependence can be introduced in the inverse linear model in two different ways, known as the ''fixed phase'' and the ''phase smoothed'' approaches. When either of them is set to the analysis of real data, the interpretation of some of the diagnostics parameters is not straightforward. From statistical considerations, both methods are expected to perform rather loosely at some points. It is then hard to decide if those values of the parameters correspond to characteristics present in the observed field or to failures of the method. To settle this matter, we proceed in this work to analyze the same synthetic geophysical fields with both methods. The fields consist basically of geophysical waves of known frequency, upon which a cyclostationary dependence is imposed, that are embedded in noise. Different fields were generated by changing the phase of the cyclostationary dependence and the characteristics of the noise, and analyzed using both methods. Through this systematic procedure we assess the real meaning of the diagnostic parameters. Because the true signals and phase of the cyclostationary dependence are known, the performances of both approaches can be compared.