A spectral decomposition method has been adapted to identify and quantify isotopic source terms in high resolution gamma-ray spectroscopy in scenarios with static geometry and shielding. Monte-Carlo simulations were used to build the response matrix of a shielded high purity germanium detector monitoring an effluent stream with a Marinelli configuration. The decomposition technique was applied to a series of calibration spectra taken with the detector using a multi-nuclide standard. These results are compared to decay corrected values from the calibration certificate. For most nuclei in the standard ($^{241}$Am, $^{109}$Cd, $^{137}$Cs, and $^{60}$Co) the deviations from the certificate values were generally no more than $6$% with a few outliers as high as $12$%. For $^{57}$Co the deviations from the standard reached as high as $25$%, driven by the very low statistics of the sources presence in the calibration spectra. Additionally, a full treatment of error propagation for the technique is presented.
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