Spherical shells are used for a variety of applications ranging from fundamental gas properties measurement in large resonators to studies involving millimeter-size prototype intertial-confinement-fusion (ICF) targets. Most applications demand that either or both shell surfaces have a high degree of sphericity. Fabrication from hemishells inevitably leads to geometric imperfections and leaves the interior surface unavailable to metrological inspection. However, many common asphericities are predicted to break the degeneracy of resonator modes to first order in a boundary perturbation expansion [J. B. Mehl, J. Acoust. Soc. Am. 79, 278--285 (1985)]. Various centimeter size aluminum and beryllium shells were manufactured with artificially enhanced common fabrication errors. The resonant modes of a completely closed shell are excited and detected using a swept-sine heterodyne technique [A. Migliori et al., Physica B 183, 1--24 (1993)] with four pinducers in contact with the exterior at the tetrahedral angles. Both shell and interior gas resonances are distinguishable, are nearly uncoupled, and display measurable mode splitting. While various gases, pressures, and temperatures are examined, primary research involves materials and conditions relevant to the manufacture of ICF targets. Experimental results are compared with the perturbation theory, and the utility of the technique is examined.