Estimation of source time functions and yields of explosions directly from seismograms using the cube-root scaling law

I estimate the source time functions and yields of explosions directly from seismograms. The method requires seismograms at a single receiver for two events of different size at the same source location and eliminates the path effect between source and receiver by finding a ratio filter that shapes the seismogram of the smaller event to the seismogram of the larger. If the noise is small, the convolution of the filter with the source time function of the smaller event yields the source time function of the larger event. The two source time functions are also related by the well-known scaling law in which the injected volume is proportional to the yield and the time constant is proportional to the cube-root of the yield. These two independent equations are solved for the two source time functions by a trial-and-error method that gives the ratio of the yields. The two seismograms are then deconvolved to recover two estimates of the Green’s function. Applying the method to seismograms from the 2009 and 2013 North Korean underground nuclear tests gives yields of 6 and 16 kt, respectively. This method has applications in seismic exploration on land using a dynamite source.