Seismic moments and volume changes

For many situations of practical interest, the seismicity that results from ground deformation associated with a change in volume, Δ V, is related to the volume change by ΣM0 = Kμ∣ΔV∣, where ΣM0 is the sum of the seismic moments of the earthquake population, μ is the modulus of rigidity, and K is a factor close to 1. A necessary condition for this relationship is that the change in volume is accommodated only by seismic failure. The relationship between seismic moment and volume change was used to analyze earthquake sequences resulting from ground deformation that could most easily be described as volume changes. First, in the East Rand Proprietary Gold Mine, South Africa, total seismic moments of mine tremors were found to be in good agreement with total moments inferred from the volume of rock mined. Second, annual sums of seismic moments for the Denver earthquakes were compared with yearly total moments estimated from the volume of fluid injected at the Rocky Mountain arsenal well. There was good agreement between calculated and observed moments from 1962 to 1965 when annual rates of fluid injection were high. Nearly all of the Denver earthquakes in these years correspond to the accommodation of injected fluid at depth. The association between earthquakes that occurred after February 1966, when the fluid injection was stopped, and the Rocky Mountain arsenal well is not clear. Finally, the total seismic moment for earthquakes near Matsushiro, Japan, that occurred from March to September 1966 was found to be in good agreement with the moment calculated from the expansion of the seismic source region determined from measurements of horizontal and vertical ground movement. Energy changes were calculated for the volumetric changes considered here and compared with the total energy radiated in the seismic waves. The seismic energies ranged from 0.2% to 3% of the total energy changes.