Fig. 1.

The ‘swimming’ artifact of a 1D array in a 2D Earth. (a) ‘Swimming’ effect at a lower frequency (0.125 Hz) with respect to a teleseismic (75°–90°) linear array of 16 stations (1° spacing). Upper left figure shows the artifact: at t = 10 s, maximum array response drifted from the true location A (0°, as solid-edged star) to the apparent location B (0.9°, dash-edged star), a difference of about 100 km. Upper right figure shows the traveling time curve sampling envelopes of stations #1,6, 11 and 16 (distance 75°, 80°, 85°, 90°, respectively, plotted as yellow triangles). The solid and dashed abscissas denote the travel time curve of a hypothetical source occurring at a certain location and origin time. At t = 10 s, the blue dashed line is the traveling time curve that yields the overall maximum of the array response, taking into account the signal decay. Instead of the true source location A, it introduces an apparent location B closer to the array. On the other hand, the array response of the travel of B′ (reference window strategy) is smaller than that of A, therefore no swimming artifact is created. (b) ‘Swimming’ effect in a different frequency band, with solid curves showing t = 0 s, and dashed curves showing t = 10 s, respectively. Note that, at all the frequencies, the maximum of array response shifts towards the array direction, this effect is reduced at a higher frequency. (c) Exponential-fitting estimation of the frequency-dependent time-decay function. Envelopes of the stacked signals are smoothed with a time window 2.5 times the upper period bound of the bandpass filter. Each envelope is aligned to t = 0 and normalized with respect to its maximum. Due to the contamination of the signals by the micro-seisms, only signals higher than 0.25 Hz are analyzed. An attenuation decay function e^−0.1ft is estimated and used for all frequencies in this paper.