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This paper presents a variety of results. First, it examines propagation for the multiple-layer range-independent test case (Na) of Workshop97. Results indicate that, for 200 Hz, only one sediment layer plus a half-space are needed to describe that highly depth-variable bottom (originally consisting of 34 sediment layers over a half-space). Additionally, at 100 Hz, only two sediment layers plus a half-space give excellent accuracy while, at 25 Hz, at most three sediment layers plus a half-space are needed for high accuracy. These results point the way to the inversion method (SUB-RIGS) developed here and are applied to the workshop data. Second, this paper briefly examines model accuracy for our range-dependent field predictions. When an older and problematic propagation model code was used in the context of the Stennis Geoacoustic Inversion Techniques (GAIT) Workshop '01 calibration case (CAL), we found that the propagation predictions were off. These errors cause major problems for the TC1 inversion. Thus, SUB-RIGS was updated to use a more accurate-and far more efficient-propagation model (RAMGEO). A key point illustrated here is that it is not always clear when an embedded propagation code may need updating. Additionally, the CAL data are examined in terms of the sensitivity of various frequencies to various bottom parameters. These sensitivities also point the way toward the development of the SUB-RIGS method in which frequency/range behaviors are decoupled for various bottom parameters. Finally, this paper presents inversion estimates for the bottom parameters of the test case TC1 and of the calibration case CAL (both sloping bottoms) from the GAIT Workshop '01. The SUB-RIGS inversion method (not automated) is described and applied where frequency subspacing (as a function of range) plus reduced iterated grid searches determine layer properties. The method usually (but not necessarily) assumes: a linear bottom slope; up to three sediment layers over a half-space; segmented sound-speed profiles (assumed to be linear within a layer); densities (assumed to be constant within a layer); and sediment attenuation (assumed to be constant throughout except at the very low depths to eliminate false returns). This method does find- rather accurate sound-speed profiles for the layers. The sediment densities and attenuation (which have less effect on the propagation) are less accurately estimated.