Several active and passive techniques have been developed to detect, localize, and quantify cavitation activity during therapeutic ultrasound procedures. Much of the prior cavitation monitoring research has been conducted using lossless in vitro systems or small animal models in which path attenuation effects were minimal. However, the performance of these techniques may be substantially degraded by attenuation between the internal therapeutic target and the external monitoring system. As a further step toward clinical application of passive acoustic mapping (PAM), this paper presents methods for attenuation estimation and compensation based on broadband cavitation data measured with a linear ultrasound array. Soft tissue phantom experiment results are used to illustrate: 1) the impact of realistic attenuation on PAM; 2) the possibility of estimating attenuation from cavitation data; 3) cavitation source energy estimation following attenuation compensation; and 4) the impact of sound speed uncertainty on PAM-related processing. Cavitation-based estimates of attenuation were within 1.5%-6.2% of the values found from conventional through-transmission measurements. Tissue phantom attenuation reduced the PAM energy estimate by an order of magnitude, but array data compensation using the cavitation-based attenuation spectrum enabled recovery of the PAM energy estimate to within 2.9%-5.9% of the values computed in the absence of the phantom. Sound speed uncertainties were found to modestly impact attenuation-compensated PAM energies, inducing errors no larger than 28% for a 40-m/s path-averaged speed error. Together, the results indicate the potential to significantly enhance the quantitative capabilities of PAM for ensuring therapeutic safety and efficacy.