FIR filter effects and nucleation phases

The symmetric impulse response of linear phase Finite Impulse Response (FIR) filters most commonly used in modern seismic recording systems produces precursory signals to impulsive arrivals. These acausal filter-generated artefacts may result in misinterpretations of various onset properties. Prior to any onset interpretation, these effects have to be removed from the seismic record. This can be achieved without loss of bandwidth by post-filtration of this digital seismograms if the filter coefficients and the decimation ratios are known. We have analysed numerous signals from different instruments and sampling rates for precursory phases and found that-in contrast to commonly held beliefs-FIR-filter-related precursory signals are not always easy to recognize visually from their waveform signature. Furthermore, they can exhibit surprisingly similar properties to those reported for nucleation phases, although the majority of nucleation phases reported in the past have been obtained on instruments with a causal response. We demonstrate examples of filter-related precursory signals for events scanning nine orders of moment, from 10(10) N m to 10(19) N m. Surprisingly, the lower bound of the artefact durations as a function of seismic moment scales close to the cube root of the seismic moment. We interpret this as being caused by the fact that above a certain seismic moment, the attenuated source signal acts as a causal lowpass filter of a smaller bandwidth than the FIR filter. Assuming an omega(-2) source model, constant stress drop and an empirical relationship between the maximum artefact duration and the cut-off frequency of the FIR filter, the artefact durations are expected to scale proportional to the 1/2.5 power of the seismic moment, in comparison to 1/3 as proposed for nucleation phases.