When an explosive charge is detonated under water, the explosion produces a shock wave and an oscillating gaseous bubble whose behavior is intimately related to the physical properties of the explosive itself and of its environment. Many of these properties can be calculated from detailed measurements of the shock wave and of the bubble and its oscillations, but such measurements are seldom available for large explosions. We show an iterative inversion procedure for making band‐limited estimates of the shock wave and bubble oscillation pressure waveforms from power spectra of farfield hydroacoustic recordings of large underwater explosions. We also show the ensemble averaging procedure that is needed to produce spectral estimates of sufficient stability and resolution to support the inversion procedure.