We have developed a 2D isotropic continuous wavelet-like transform for a spherical surface. The transform is simply defined as the surface convolution between the original field and a kernel, based on the zeroth-order Bessel function with a spherical correction. This spherical correction violates the geometric similarity for the various scales of the kernels, which becomes more apparent at longer wavelengths. We found numerically that this transform is practically equivalent to a Gaussian bandpass filter in the spherical harmonic domain. We have applied this wavelet-like transform on the recently acquired Martian gravity and topography fields. Using a ratio constructed locally from these two fields, we have constructed a map describing the lateral variations of the localized admittance function on Mars.
Bibliographical noteFunding Information:
We thank discussions with Stephen Y. Bergeron, Ludek Vecsey, and T.K.B. Yanagawa. We acknowledge very helpful comments from an anonymous reviewer and suggestions from the editor David Gubbins. This research was supported by geophysics program of the National Science Foundation and a travel grant to M. Kido by the University Minnesota Supercomputing Institute.
Copyright 2004 Elsevier Science B.V., Amsterdam. All rights reserved.
- Bandpass filter
- Martian gravity data