Continuous wavelet-like filter for a spherical surface and its application to localized admittance function on Mars

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.