The Picking Procedure

The majority of automatic phase pickers are designed for on-line detection and timing of P [for review see, Allen, 1982], and occasionally S arrivals [e.g., Cichowicz, 1993]. Our goal is to identify weak, marginal arrivals as well as the primary seismic phases. For this reason, we designed our autopicker to identify as many phase arrivals as possible, at the risk of also including a number of ``false" picks. Our algorithm can be categorized as a short-term-average (STA) long-term-average (LTA) picker. STAs are sensitive to rapid increases in the amplitude of a time series and LTAs measure the local background amplitude. Thus the ratio of the STA to the preceding LTA is a measure of the local signal-to-noise. If the ratio is higher than a threshold value a phase arrival is declared and a corresponding arrival time is calculated.

Our picker requires four main input parameters (Table 1): an STA and an LTA window length, the length of a Hanning filter, and a threshold value. The picker outputs arrival times with corresponding confidences. The algorithm proceeds in the following way:

1. An envelope function is generated from the seismogram (Figure 1b). The envelope function can be thought of as a positive outline of the seismogram and is defined: [e.g., Kanasewich, 1981] where E is the envelope function, s is the seismogram, and is the Hilbert transform of the seismogram.
2. We apply an STA/LTA filter to the envelope function to obtain what we refer to as the ratio function. Two moving averages are taken along the envelope function, an LTA followed directly by an STA. The ratio of the STA to the LTA is taken at every digitization point; these STA/LTA values define the ratio function. The STA-LTA ratios are not taken along the raw seismogram because positive and negative amplitudes would produce meaningless long- and short-term averages. Other pickers generate their ratio functions from the absolute values [e.g., McEvilly and Major, 1982] or the squares [e.g., Swindell and Snell, 1977] of the seismogram's amplitudes. While this is computationally efficient, the envelope function has the advantage of remaining positive at zero crossings during phase arrivals. Thus an STA taken from an envelope function is a better measure of the instantaneous signal strength. Baer and Kradolfer (1987) utilize the square of the envelope function in their automatic picking algorithm.

   Optimum lengths for the STA and LTA windows depend on the frequency content of the seismogram. For example, long-period records require larger averaging windows than do short-period records (Table 1 ). The STA should be short enough to resolve a phase arrival but not so short that it produces meaningless fluctuations in the ratio function. The LTA window must be long enough to give an average value of the local noise; however, excessively long LTAs are to be avoided because they extend the time period following strong arrivals in which weak arrivals are obscured due to the ``loading up'' of the LTA.

3. The ratio function is smoothed by convolution with a Hanning filter (Figure 1c). We found this necessary to prevent rapid fluctuations in the ratio function which can produce inaccurate arrival times.
4. Arrival times and confidences are extracted from the smoothed ratio function (SRF). An arrival is declared when the SRF exceeds the threshold value. We define the time at which this occurs as the trigger point. The time of the arrival is defined by the inflection point that precedes the local maximum immediately following the trigger point (Figure 1c). For short-period seismograms this produces arrival times which are generally close (see travel-time residual section) to what a human operator might pick (Figure 1a). Other possibilities for defining the arrival time such as, local minimums in the SRF, produced a larger residual spread than did picks defined by the inflection point. Strong impulsive arrivals will generally produce accurate picks and large local maximums in the SRF. Thus, the amplitude of the local maximum following the trigger point is a good measure of pick confidence. The arrival times and pick confidences are stored for later processing.

 

 
Table 1:   Optimum picking parameters for the NEIC short- and long-period seismograms