AN ANALYSIS OF 3-D ANALYTIC SIGNAL

The mathematical and physical basis of defining the 3-D analytic funct ion and the corresponding analytic signal is critically examined, and it is proved that 3-D analytic signals based on (1) scalar and (2) vec tor additions of the horizontal derivatives of the total magnetic fiel ds are completely identical. Two sets of simulated gridded data are co nsidered, and 3-D analytic signals are computed using both scalar and vector additions and are found to be identical. The equality of scalar and vector additions of 3-D analytic signals is further demonstrated with the help of gridded-surface vertical magnetic field data from the Krishna-Godavari Basin, Andhra Pradesh, India.