Global patterns of radiated seismic energy and apparent stress

Radiated energies from shallow earthquakes with magnitudes ≥5.8 that occurred between 1986 and 1991 are used to examine global patterns of energy release and apparent stress. In contrast to traditional methods which have relied upon empirical formulas, these energies are computed through direct spectral analysis of broadband seismic waveforms. Velocity-squared spectra of body waves are integrated after they have been corrected for effects arising from depth phases, frequency-dependent attenuation, and focal mechanism. The least squares regression fit of energy E_s to surface wave magnitude M_s for a global set of 397 earthquakes yields log E_s = 4.4 + 1.5M_s, which implies that the Gutenberg-Richter relationship overestimates the energies of earthquakes. The least squares fit between E_s and seismic moment M₀ is given by the relationship E_s = 1.6 × 10^-5 M₀, which yields 0.47 MPa as the average global value of apparent stress. However, the regression lines of both E_s-M_s and E_s-M₀ yield poor empirical predictors for the actual energy radiated by any given earthquake; the scatter of data is more than an order of magnitude about each of the regression lines. On the other hand, global variations between E_s and M_o, while large, are not random. When subsets of E_s-M₀ are plotted as a function of seismic region and faulting type, the scatter in data is substantially reduced. The E_s-M₀ fits for many seismic regions and tectonic environments are very distinctive, and a characteristic apparent stress τ_c can be derived. The lowest apparent stresses (<1.5 MPa) are associated with thrust earthquakes at subduction zones. The highest apparent stresses (>3.0 MPa) are associated with strike-slip earthquakes that occur at oceanic ridge-ridge transforms and in intraplate environments seaward of island arcs. Intermediate values of apparent stress (1.5 < τ_a < 3.0 MPa) are associated with strike-slip earthquakes at incipient or transitional plate boundaries. In general, the dominant mode of failure for a tectonic environment is associated with the faulting type that has the lowest apparent stress. An energy magnitude M_E can complement moment magnitude M_w in describing the size of an earthquake. M_E, being derived from velocity power spectra, is a measure of seismic potential for damage. M_w, being derived from the low-frequency asymptote of displacement spectra, is more physically related to the final static displacement of an earthquake. When earthquake size is ranked by moment, a list of the largest events is dominated by earthquakes with thrust mechanisms. When earthquake size is ranked by energy, the list of the largest events is dominated by strike-slip earthquakes.