The effect of bandwidth limitations on the inference of earthquake slip-weakening distance from seismograms

Numerous researchers have obtained estimates of slip-weakening distance, Dc, and fracture energy for recent earthquakes. Dc, is often observed to be a significant fraction of the total slip and tends to correlate with total slip. Although these observations may well be true of real earthquakes, we show that low-pass filtering of strong-motion seismograms can also produce some of these effects in inverted rupture models. We test the accuracy of Dc, estimates by calculating them in low-pass-filtered versions of models A and B of Guatteri and Spudich (2000). Models A and B are two different rupture models for a hypothetical M 6.5 earthquake, and they have nearly identical rupture time, slip, and stress-drop distributions, and nearly identical predicted seismograms, but Dc, for model B is about twice that for model A. By low-pass filtering slip models A and B at 1.0 Hz, we simulate the blurring effects of band-limited waveform inversions on these slip models. At each point on a fault, D???c is defined to be the slip at the time of the peak slip speed at that point. Low-pass filtering the slip models causes an upward bias in Dc inferred from stress-slip curves, and it causes an artificial correlation between D???c and the total slip. Low-pass filtering might also bias fracture energy high and radiated energy low. These biases should be considered when interpreting Dc derived from band-limited slip models of real earthquakes.