THE 2-DIMENSIONAL RESOLUTION KERNEL ASSOCIATED WITH RETRIEVAL OF IONOSPHERIC AND ATMOSPHERIC REFRACTIVITY PROFILES BY ABELIAN INVERSION OF RADIO OCCULTATION PHASE DATA

Errors in radio occultation experiments associated with departures fro m sphericity can be analyzed on the basis of straight-ray tomography i n which (1) only one parallel projection of the object is available, ( 2) diffraction is neglected, and (3) inversion is achieved by assuming the object to be circularly symmetric. The straight-line tomographic case and the actual curved ray paths in a spherically symmetric atmosp here are related by an analytic transformation. A previously unknown k ernel function transforms the two-dimensional (2-D) atmospheric refrac tivity map from the plane of propagation to a 1-D radial profile along the locus of ray periapsides. This function consists of a discrete, p ositive singularity plus an extended negative branch; the negative bra nch rises smoothly from negative infinity in the neighborhood of the p ositive singularity toward zero. Knowledge of the resolving kernel all ows study of horizontal and vertical resolution in a rigorous manner. Spherically symmetric structures are reproduced exactly with the kerne l; processing of band-limited projection data results in a modified ke rnel of finite vertical resolving power. In general, the horizontal ex tent of significant contributions, including levels of 10% of the peak , is of the order 2 root 4.6rH centered on the locus of periapsides, w here r is the radius of the point in consideration and H is the refrac tivity scale height; the vertical extent of significant contributions extends from approximately one sampling distance below r to a few samp ling distances above it. We confirm the expected result that a refract ivity structure of radial thickness Delta r will be retrieved properly only if its circumferential extent is approximately 2 root 2r Delta r or greater centered on the periapsis point. In addition, a positive r efractivity structure limited in circumferential extent introduces art ifacts of negative refractivity in the retrieved profile. The artifact s first appear at the projected altitude onto the vertical of the stru cture's circumferential edges and continue downward. The error represe nted by such negative refractivity artifacts is diminished somewhat by the general exponential increase in refractivity with decreasing alti tude of a real atmosphere. Thus the relative error depends on the loca l scale height and the circumferential extent of the refractivity stru cture.