Adaptive Event Process - Depth

Ronald Warren Cook
Maxwell Technologies
2000 June

Abstract - (Page under construction, but gist is there.)
An adaptive event depth processor is proposed (2000 Jan) which in theory would absolutely determine seismic event depths by utilizing automatic detections from existing processors at the Prototype International Data Center. In reality, however, it is primarily dependent on the success of these detectors to detect discriminatory depth phases. Using the existing IASPEI travel time tables for the most prominent depth phases pP and sP, the initial capabilities and feasibility of the proposed method is examined for quite a number of events in various regions.
   The process adapts to the event depth by using unidentified detections not only for stacking purposes, but also for noise elimination. Using the simple idea that, the detections following the initial P of the stations observing an event, when transformed to a depth window and aligned as if each were a depth phase, will stack only if a detection really is a depth phase. It is therefore possible to make certain depth-stack enhancing predictions. It is further demonstrated that those detections that are not depth phases can also be utilized to enhance those that are.

Background
It was Jack Murphy's idea (2) to get the "tx" detections from the existing detection tuples at the Prototype International Data Center (PIDC). Associated to an event, a network of stations having the initial P detection, with known travel times, are used as locaters of that event. The tx phases, those having teleseismic characteristics in period, slowness or propagation speed, are obtained from detection records that include and follow a seismic station's P phase detection. At the PIDC, they typically undergo more extensive processing that associates them as identified phases such as PP, PcP, ScP, S, et al. Event depth processing at the PIDC and elsewhere has had to rely on location solutions often requiring regionally distributed stations or seismic analyst depth phase analysis to confidently discriminate between natural and manmade events. This assuming events below several kilometers depth are not manmade. Several signal processing techniques have been tried to varying degrees of success as by Roy(6), Woodgold(5).


Figure 1. Some IASPEI 91 Travel Time Curves.






   Figure 1, shows a typical difference in travel time curves of the geoseismic pP - P phase and sP - P for the depths at which they are tabulated in the IASPEI 1991 Seismological Tables.

Stacking the Unidentified Detections (tx phases)
   The stacking process stems from Anne Henson & Hans Israelsson (2). All the tx phases are treated as if each were a pP phase arrival plus or minus a time window, then transformed to a depth window based on each station's distance, the tx-P phase time and the IASPEI 91 tables. Next, a stack is created of the entire observing network station's transformed windows. If there is a pP amongst the multiple tx on multiple stations, it aligns and will sum on the event depth as a peak in the depth window 0-700 km as in Figure 2. There are fifteen stations contributing to the pP stack for this event retrieved from the PIDC and having a Reviewed Event Bulletin (REB) depth of 198 km located beneath the Hindu Kush area of Asia. That is, there are fifteen that agree with the depth cited in the REB. The stack of pP phases is denoted pP_r meaning pP raw.
   The process produces nice peaks, but often imbedded in the tx summations of other phases, whatever they may be, and tx probability of interference greatly increases as the depth of the event decreases to the surface and the P-coda increases. Initially, the first tx phases were ignored when they produced a depth window below 50 kilometers thereby removing the large peaks that can preceed those that are pP. That will not be done in this paper as such a procedure must ultimately be dealt with analytically. Anne, Hans and others suggested the removal of known phases such as PcP when the tx-P time is coincident with their arrival. That is also not done at present.





  Figure 2. Stack of tx aligned to pP travel time for event
            1997/08/06 15:00:12 36.4N 70.8E 198km mb 4.71.






An unidentified stack of fifteen station's tx transformed depth windows follows the pP stack that is in agreement with the REB as do numerous small stacks of ten or less windows fall between and on the sides of the one in agreement.
If the tx phase can be processed as pP, then it can also be processed as sP, that is, aligned according to the IASPEI 91 sP travel time table relative to P. Comparing the two stacks, both have a significant peak aligned at the dashed line indicating the REB depth. Figure 3 shows a good sP stack with fifteen stations, and as is often the case the depth indication does again match that of the pP_r stack; but in this case the primary stack does not match the REB. The stack of sP phases is denoted sP_r meaning sP raw.













Figure 3. Stack of tx aligned to sP travel time for event    
1997/08/06 15:00:12 36.4N 70.8E 198km mb 4.71.;      

Noting that both phases are supposed to align at the REB depth, it seems reasonable to assume these two stacks are themselves stackable and doing that produces Figure 4. Quite obviously by these examples, tx stacking of depth phases can work. However there are some examples where the process thus far, would have produced a nice fairly solitary peak of considerable sharpness. There are some that would remain indeterminate. Having rushed through these initial figures, of note are the unidentified stack of equal station count trailing the pP_r stack which we now recognize as an interfering sP alignment. Preceeding the sP_r stack is an even larger stack and that, too, is noticed as pP. What has happened.



Figure 4. Stack sum of tx aligned to
pP travel time and to sP travel time.



The sum of the areas under a constant number of tx windows in the depth domain is nearly a constant and those between the interfering sP of the pP_r stack at about 322 km and the sP_r stack at 202 km have been forced into a narrower depth window. So, while the pP may not be aligned as well, the amplitude of the unwanted pP stack in the sP_r has increased to a larger value than the sP_r sum. Variations occur because the +/- time window does not transform to a constant depth window due to the everchanging slopes of the depth curves indicated in Figure 1. We can compensate for this with derivatives; however, it is much simpler just to assume a constant depth window centered on the transformed tx arrival time. The inverse transform to obtain the then varying time window may be done for statistical analyses should it be necessary. The next obvious choice is to sum the pP_r and sP_r, since only the correct depth indicating stacks will reinforce. The most prominent peak in this combined stack is the true depth indicator for the event. That is not always so. How can we rid ourselves of those prominent secondary peaks?

The Prediction Filters - two self-determined masks

If we want to look at a pP stack, we want the most enhancement of the pP/tx summation that we can get, so for each suspect tx/pP we predict a corresponding sP for that depth and create the respective sP binary window that correspond to the tx in case it really is pP on each station see Figure 5. For each of the these event's windows, scale is maintained to show relative effects.

Having the mask to remove the sP/tx, we very simply subtract the predicted sP/tx binary window scan for each station. Who says we can do that. What justification? Suppose we had a synthetic trace with only binary pP and sP depth windows. If we fed this into the aforedescribed process, the pP binary pulse would come out all by itself. The predicted sP would have been removed see Figure 5. Note that prediction will also occur for the real sP/tx wherever it is, but as a mask, it will not detract from the real pP we seek. Additional enhancement may be possible with this consideration.









Figure 5. Stack sums or pP_r (raw),                                               Figure 6. Stack sums or sP_r (raw),
sP_p (predicted), pP_i (intermediate).                                               pP_p (predicted), sP_i (intermediate).

Of course, in the real, non-synthetic situation there is some probability that one of the other tx phases preceeding the real pP is, as a predicted sP, deleterious to the actual pP binary window corresponding to the tx seen at a particular station. We note this as a reduced sum in the corrected graph.In the sum of the binary station depth windows, however, we do not expect it to be as deleterious to the pP as to the other "noise" tx phases since only the real pP is properly aligned for the observing network and the chances of other phases aligning is reduced. In fact,it tends to counter the prevalence of tx phases that are often detected in the noisy coda of the initial P arrival. When subtracting the predicted sP from the pP, if the result is negative, we simply substitute zero. The relation between the synthetic and realdata is that the processing is equivalent. The data is different.

    Calling:

                     pP_i = pP_r - sP_p;  pP_r-sP_p >= 0

                          = 0          ;  pP_r-sP_p <  0
By analogy, were we to be in the frequency domain rather than that of depth, we might be looking at a low-pass filter being the sP_p prediction. The resulting stretching of the binary depth window, both in width and separation, increases the misalignments of such and reduces their sum. This expected result may be compensable. Window factors affecting this "stretch" are Poisson's ratio given by: and by the simple fact that the area under the sum is distrubed over a greater total depth window. Often, sP phase waveforms portray the depth of an event and no pP phases may be evident or maybe just a few that provide a reference to where the sP actually is. By analog, we can do for sP_i just as we do for pP_i. Asuming each tx to be an sP, we create a predicted pP and subtract it from the sP to get the best isolation of an aligned peak indicating the event depth, sP_c.
                     sP_i = sP_r - pP_p;  sP_r-pP_p >= 0

                          = 0          ;  sP_r-pP_p < 0
By analogy, were we to be in the frequency domain rather than that of depth, we might be looking at a high-pass filter.













Figure 7. Composite of the pP_i and sP_i stacks
using an intermediate or partial correction.

Notching the Depth - the total mask

Further consideration of the mask implies that the sP_p and pP_p may be used on the sP_r and pP_r stacks, respectively. That is, we can add the two predicted masks together, the low-pass and high-pass filters, to obtain one mask like a notched filter thus yielding a balanced operation on either side of these individual raw stacks. This nearly doubles the correct depth stack enhanceability by these methods.
The time transformed depth window should be a function of the distance and phase, since it increases with sP relative to pP and with distance.
Often, sP phases waveforms portray the depth of an event and no pP phases may be evident or maybe just a few that provide a reference to where the sP actually is. By analog, we can do for sP just as we do for pP. Asuming each tx to be an sP, we create a predicted pP and subtract it from the sP to get the best isolation of an aligned peak indicating the event depth, sP_c.
The new:

                 pP_c = pP_r - sP_p - pP_p;  pP_r -sP_p -pP_p >= 0.

                      = 0;    pP_r -sP_p -pP_p <  0.


                 sP_c = sP_r - pP_p - sP_p;  sP_r -pP_p -sP_p >= 0.

                      = 0;    sP_r -pP_p -sP_p <  0.

While it may be advantageous to modify the predicted sP_p and pP_p based on many factors, initial results of summing the the two stacks, pP_c and sP_c show promise as a method of automatically detecting the depth of an event, at least at depths greater than 50 km. Referring again to the synthetic, the sum would be normalized by dividing by 1/(2N), where N is the number of stations, the two comes from adding two phases. The real situation is quite different as only a fraction have real pP and sP observations. However, using N gives relevance as a reliability factor since fewer stations would certainly produce a less reliable result. Quite a few examples show the promise of this technique.



Figure 10. Composite of the pP_c and sP_c stacks.



The Synthetic Proof Using the Above Event Depth Processing Model

In the following Figure 11, the above event 1101528 is used as a model to generate synthetic tx arrivals that are then input to the process for validation of its operation. As one can see, there is a resulting solitary depth indicator; however, optimality of the process is not demonstrated. Constant depth windows (CDW) are used, and that implies that the input time window is variable. At 20 degrees the window may be +/- 1.2 seconds while for a station at 90 degrees it mah have a somewhat narrower +/- .8 seconds. It may be desireable to modify the depth window as a function of depth and of distance.





Use of the depth signal the fourth mask

Sometimes there is no pP and more often no sP. In the latter case the pP_c can be used to mask the sP_c trace to create a fourth mask. However, the pP_c by itself may be a sufficient indicator because add the two corrected stacks when there is no sP serves only to increase the noise in the composite or sum of the two. So, methods to decide when and when not to perform these operations are critical to this last process.

Additional examples

Time and the resultant depth windows are tuneable. While errors relate to stations, paths, travel time curves, perhaps a 3-D presentation of various window widths can help determine the true depth. It seems the initial windows relate directly to the timing parameters of phases set by the PIDC during event analysis. P is typically +/- 2 seconds to be defining in an event.

Conclusions

The process does not work miracles. Mixed events, especially those having an associated tremor within pP or sP time of the initial event can make analysis difficult.

Since the phases under consideration are often of larger amplitude than other tx phases, we may wish to consider the effect of their amplitudes on a stack. The zero or one binary state may be usefully replaced by the rms amplitude of each tx depth window. Since the reflected depth phases are often of lower frequency content, additional stack enhancement might be obtainable by filter selection. Some items remaining to investigate:
1. How often is the pP sum sufficient?
2. Is the pP corrected for sP sufficient or better? How often
3. Ditto sP.
4. Is the composite of phases best.
5. What improvements are gained by putting other phases in the composite.
6. What improvements are gained by removing tx corresponding to other phases
7. By what percentage can one expect a reduction in peak amplitude caused by prediction?
8. The whole works (all phases) put into a Simplex reduction scheme?
9. Widening the depth transformed window increases the peak amplitude until the maximum is equal all stations having a tx. Show the example 1101528 narrow, medium, wide.
10. Increasing amplitude of the predicted pulse offers some enhancement.
11. What optimum width can be used for prediction phases.
12. Can edge effects (not +/- but 0/+ sP_P, and 0/- pP_p of predicted phases for shallow events and -/++ sP_p, and --/+ pP_p for deeper events offer improvement? How much?
13. Accuracy of the IASPEI tables is critical.
14. Plot some Poisson ratio curves for a few depths & distance ranges.
15. Use the improvement factor of pP_c/pP_r areas to determine if sP should be used.
16. Use predicted sP mask from pP_c to mask sP_r and derive sP_c.

Reference:

1. Kennett, B. L. N. (1991). IASPEI 1991 Seismological Tables, Research School of Earth Sciences, Australian National University.

2. Murphy, J. R. and R. W. Cook (2000 Apr). Improved Focal Depth Determination for use in CTBT Monitoring. Presented at the 95th Annual Meeting of the Seismological Society of America, San Diego, CA by Jeff Stevens

3. Henson, Anne and Hans Israelsson (1993). Center for Seismic Studies, Final Technical Report, 1992 Oct - 1993 Oct.

4. Israelsson, H. (1994). Stacking of Waveforms for Depth Estimation," Center for Seismic Studies, Final Report C95-02

5. Woodgold, R. D. (1999 Feb). Wide-Aperture Beamforming of Depth Phases by Timescale Contraction, BSSA V_89 N1 P168-177

6. Roy, Falguni (1989). Depth phase identification by prediction error filtering: analysis of synthetic explosion signals, Phys. Earth Planet. Interiors 54, 210-230.

7. Robinson, E. A. and S. Trietel (1980). Geophysical Signal Analysis, Prentice-Hall, Englewood Cliffs, New Jersey.

8. Kanesewich, E. R. (1975). Time Sequence Analysis in Geophysics, 2nd Ed.; The University of Alberta Press, Edmonton, Alberta, CAN


Acknowledgement:

Thanks to Maxwell Technologies for the use of their equipment and to Jack Murphy for asking me to make a tx transformed pP and sP depth stack.
Thanks to Paul Wessel & Walter Smith for GMT - integrally involved in the graphics.
Thanks to John Coyne for the waveform processing system Geotool.

Author:

Cook, R W; rwc@cowaro.com

Maxwell Technologies - Systems Division Reston Geophysics Office
11800 Sunrise Valley Dr., Suite 1212
Reston, VA 20191-5309 United States


2000 Dec 01 - http://cowaro.com/2000Adaptive/Adaptive_Event_Process.html