I used seismic waveforms recorded within 2 km from the epicenter of the first four Source Physics Experiments (SPE) explosions to invert for the moment tensor spectra of these explosions. I employed a 1D Earth model for Green’s function calculations. The model was developed from P‐ and Rg‐wave travel times and amplitudes. I selected data for the inversion based on the criterion that they had consistent travel times and amplitude behavior as those predicted by the 1D model. Because of limited azimuthal coverage of the sources and the mostly vertical‐component‐only nature of the dataset, only long‐period, volumetric components of the moment tensor spectra were well constrained. The source spectra, particularly their long‐period levels and corner frequencies, could not be fit by traditional explosion source models. To achieve a better fit, I used a model with parameters derived from regressing observed values against source yield and depth. These values were calculated from measured source moments and corner frequencies. Although the number of data points used in the regression is small, the approach suggests a potential way to develop a source model for chemical explosions when more data with wider coverage of yield, depth of burial, and material property are collected.