The rate of decay with distance of shear-wave amplitude, computed from 20-sec S-wave spectra, is determined from TERRAscope records of small earthquakes in the greater Los Angeles area. Piecewise log-linear interpolation functions and traditional diminution functions are used to fit spectral decay to a maximum distance of 150 km. Simultaneously, isotropic source and receiver terms are determined. Separate branches of the spectral decay function are found for two categories of source depth: greater than 10 km and less than 10 km. In the hypocentral distance range of 20 to 150 km and in the frequency range of 0.5 to 8.0 Hz, an important result of the investigation is that the horizontal-component decay rate associated with deeper-crustal sources is generally greater than that associated with shallower sources and is greater than that which is estimated using more traditional models of spectral decay with distance. The same behavior generally holds for vertical-component spectra. The variation in apparent attenuation rate with source depth should affect seismic-hazard estimates associated with the rupture of blind thrust faults in the Los Angeles basin and vicinity. The results of the inversions suggest that interpolation function representations of spectral decay are sensitive to perturbations of S-wave amplitude due to crustal reflectors, such as post-critical S-wave arrivals from mid-crustal to deep-crustal velocity interfaces.