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107 nips-2010-Global seismic monitoring as probabilistic inference

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Author: Nimar Arora, Stuart Russell, Paul Kidwell, Erik B. Sudderth

Abstract: The International Monitoring System (IMS) is a global network of sensors whose purpose is to identify potential violations of the Comprehensive Nuclear-Test-Ban Treaty (CTBT), primarily through detection and localization of seismic events. We report on the ﬁrst stage of a project to improve on the current automated software system with a Bayesian inference system that computes the most likely global event history given the record of local sensor data. The new system, VISA (Vertically Integrated Seismological Analysis), is based on empirically calibrated, generative models of event occurrence, signal propagation, and signal detection. VISA exhibits signiﬁcantly improved precision and recall compared to the current operational system and is able to detect events that are missed even by the human analysts who post-process the IMS output. 1

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 Global seismic monitoring as probabilistic inference Nimar S. [sent-1, score-0.436]

2 edu Abstract The International Monitoring System (IMS) is a global network of sensors whose purpose is to identify potential violations of the Comprehensive Nuclear-Test-Ban Treaty (CTBT), primarily through detection and localization of seismic events. [sent-9, score-0.581]

3 We report on the ﬁrst stage of a project to improve on the current automated software system with a Bayesian inference system that computes the most likely global event history given the record of local sensor data. [sent-10, score-0.479]

4 The new system, VISA (Vertically Integrated Seismological Analysis), is based on empirically calibrated, generative models of event occurrence, signal propagation, and signal detection. [sent-11, score-0.436]

5 VISA exhibits signiﬁcantly improved precision and recall compared to the current operational system and is able to detect events that are missed even by the human analysts who post-process the IMS output. [sent-12, score-0.363]

6 The IMS is the world’s primary global-scale, continuous, real-time system for seismic event monitoring. [sent-15, score-0.773]

7 Perfect performance remains well beyond the reach of current technology: the IDC’s automated system, a highly complex and welltuned piece of software, misses nearly one third of all seismic events in the magnitude range of interest, and about half of the reported events are spurious. [sent-17, score-0.867]

8 Like most current systems, the IDC operates by detection of arriving signals at each sensor station (the station processing stage) and then grouping multiple detections together to form events (the network processing stage). [sent-19, score-1.209]

9 1 The time and location of each event are found by various search methods including grid search [2], the double-difference algorithm [3], and the intersection method [4]. [sent-20, score-0.446]

10 In the words of [5], “Seismic event location is—at its core—a minimization of the difference between observed and predicted arrival times. [sent-21, score-0.584]

11 ” Although the mathematics of seismic event detection and 1 Network processing is thus a data association problem similar to those arising in multitarget tracking [1]. [sent-22, score-0.924]

12 In simple terms, let X be a random variable ranging over all possible collections of events, with each event deﬁned by time, location, magnitude, and type (natural or man-made). [sent-27, score-0.388]

13 ) NET-VISA computes a single most-likely explanation: a set of hypothesized events with their associated detections, marking all other detections as noise. [sent-39, score-0.529]

14 All such waves occur in a variety of types [7]—body waves that travel through the earth’s interior and surface waves that travel on the surface. [sent-51, score-0.61]

15 Each particular wave type generated by a given event is called a phase. [sent-55, score-0.423]

16 These waves are picked up in seismic stations as ground vibrations. [sent-56, score-0.622]

17 Typically, seismic stations have either a single 3-axis detector or an array of vertical-axis detectors spread over a scale of many kilometers. [sent-57, score-0.448]

18 Various parameters of the detection are measured—onset time, azimuth (direction from the station to the source of the wave), slowness (related to the angle of declination of the signal path), amplitude, etc. [sent-61, score-0.634]

19 2 Based on these parameters, a phase label may be assigned to the detection based on the standard IASPEI phase catalog [7]. [sent-62, score-0.411]

20 The parameters of an event are its longitude, latitude, depth, time, and magnitude (mb or body-wave magnitude). [sent-65, score-0.433]

21 We compute the accuracy of an event history hypothesis by comparison to a chosen ground-truth history. [sent-68, score-0.41]

22 An edge is added between a predicted and a true event that are at most 5 degrees in distance2 and 50 seconds in time apart. [sent-70, score-0.419]

23 We report 3 quantities from this matching— precision (percentage of predicted events that are matched), recall (percentage of true events that are matched), and average error (average distance in kilometers between matched events). [sent-73, score-0.558]

24 3 Generative Probabilistic Model Our generative model for seismic events and detections follows along the lines of the aircraft detection model in [8, Figure 3]. [sent-74, score-1.029]

25 In our model, there is an unknown number of seismic events with unknown parameters (location, time, etc. [sent-75, score-0.588]

26 These events produce 14 different types of seismic waves or phases. [sent-77, score-0.726]

27 A phase from an event may or may not be detected by a station. [sent-78, score-0.547]

28 If a phase is detected at a station, a corresponding detection is generated. [sent-79, score-0.31]

29 Additionally, an unknown number of noise detections are generated at each station. [sent-81, score-0.29]

30 For NET-VISA, the evidence Y = y consists only of each station’s set of detections and their parameters. [sent-82, score-0.29]

31 If e is the set of events (of size |e|), λe is the rate of event generation, and T is the time period under consideration, we have Pθ (|e|) = (λe · T )|e| exp (−λe · T ) . [sent-85, score-0.617]

32 (1) The longitude and latitude of the ith event, ei are drawn from an event location density, pl (el ) l on the surface of the earth. [sent-87, score-0.816]

33 The depth of the event, ei is uniformly distributed up to a maximum d depth D (700 km in our experiments). [sent-88, score-0.37]

34 Similarly, the time of the event ei is uniformly distributed t between 0 and T . [sent-89, score-0.608]

35 The magnitude of the event, ei , is drawn from what seismologists refer to as the m Gutenberg-Richter distribution, which is in fact an exponential distribution with rate λm : Pθ (ei ) = pl (ei ) l 1 1 λm exp −λm ei . [sent-90, score-0.594]

36 · |e| i i=1 Pθ (e ) = exp (−λe · T ) pl (ei ) l i=1 1 λe λm exp −λm ei . [sent-92, score-0.326]

37 m D (3) Maximum likelihood estimates of λe and λm may be easily determined from historical event frequencies and magnitudes. [sent-93, score-0.388]

38 3 Figure 1: Heat map (large values in red, small in blue) of the prior event location density log pl (el ). [sent-97, score-0.5]

39 2 Correct Detections The probability that an event’s j th phase, 1 ≤ j ≤ J, is detected by a station k, 1 ≤ k ≤ K, depends on the wave type or phase, the station, and the event’s magnitude, depth, and distance to the station. [sent-104, score-0.369]

40 Let dijk be a binary indicator variable for such a detection of event i, and ∆ik the distance between event i and station k. [sent-105, score-1.434]

41 Then we have Pφ (dijk = 1 | ei ) = pjk (ei , ei , ∆ik ). [sent-106, score-0.503]

42 m d d (5) If an event phase is detected at a station, i. [sent-107, score-0.547]

43 dijk = 1, our model speciﬁes probability distribution for the attributes of that detection, aijk . [sent-109, score-0.499]

44 The arrival time, aijk , is assigned a Laplacian distribut tion whose mean consists of two parts. [sent-110, score-0.417]

45 The ﬁrst is the IASPEI travel time prediction for that phase, which depends only on the event depth and the distance between the event and station. [sent-111, score-0.945]

46 The second is a learned station-speciﬁc correction which accounts for inhomogeneities in the earth’s crust, which allow seismic waves to travel faster or slower than the IASPEI prediction. [sent-112, score-0.605]

47 The station-speciﬁc correction also accounts for any systematic biases in picking seismic onsets from waveforms. [sent-113, score-0.385]

48 Let µjk t be the location of this Laplacian (a function of the event time, depth, and distance to the station) and let bjk be its scale. [sent-114, score-0.532]

49 Truncating this Laplacian to the range of possible arrival times produces a t jk normalization constant Zt , so that Pφ (aijk | dijk = 1, ei ) = t 1 jk Zt exp − |aijk − µjk (ei , ei , ∆ik )| t t t d bjk t . [sent-115, score-1.038]

50 (6) Similarly, the arrival azimuth and slowness follow a Laplacian distribution. [sent-116, score-0.332]

51 The location aijk of the z arrival azimuth depends only on the location of the event, while the location aijk of the arrival slows ness depends only on the event depth and distance to the station. [sent-117, score-1.564]

53 (8) The arrival amplitud aijk is similar to the detection probability in that it depends only on the event a magnitude, depth, and distance to the station. [sent-119, score-0.963]

54 We model the log of the amplitude via a linear regression model with Gaussian noise: Pφ (aijk | dijk = 1, ei ) = √ a 1 jk 2πσa exp − (log(aijk ) − µjk (ei , ei , ∆ik ))2 a a m d jk 2σa . [sent-120, score-0.87]

55 2 (9) Finally, the phase label aijk automatically assigned to the detection follows a multinomial distribuh tion whose parameters depends on the true phase, j: Pφ (aijk | dijk = 1, ei ) = pjk (aijk ). [sent-121, score-1.045]

56 Because phase labels indicate among other things the general physical path taken from an event to a station, a distinct set of features were learned from the event characteristics for each phase. [sent-123, score-0.895]

57 To estimate the individual station weights αwjk for each phase j and feature w, a hierarchical model was speciﬁed in which each station-speciﬁc weight is independently drawn from a feature-dependent global Normal 2 distribution, so that αwjk ∼ N (µwj , σwj ). [sent-124, score-0.384]

58 Detection probability at station 6 for P phase, surface event 1. [sent-129, score-0.685]

59 10 Time Residuals around IASPEI prediction for P phase at station 6 model 3. [sent-131, score-0.384]

60 00 180 −6 −4 −2 0 Time 2 4 6 Figure 2: Conditional detection probabilities and arrival time distributions (relative to the IASPEI prediction) for the P phase at Station 6. [sent-142, score-0.408]

61 3 False Detections Each station, k, also generates a set of false detections f k through a time-homogeneous Poisson process with rate λk : f k k Pφ (|f |) = (λk · T )|f | exp −λk · T f f . [sent-144, score-0.408]

62 (11) kl kl The time ftkl , azimuth fz , and slowness fs of these false detections are generated uniformly over kl their respective ranges. [sent-146, score-0.858]

63 The amplitude fa of the false detection is generated from a mixture of two kl kl Gaussians, pk (fa ). [sent-147, score-0.518]

64 Finally, the phase label fh assigned to the false detection follows a multinomial a k kl distribution, ph (fh ). [sent-148, score-0.515]

65 If the azimuth and slowness take values on ranges of length Mz and Ms , respectively, then the probability of the lth false detection is given by 1 1 1 k kl k kl Pφ (f kl ) = p (f )p (f ) . [sent-149, score-0.719]

66 (12) T M z Ms a a h h Since the false detections at a station are exchangeable, we have l=|f k | l=|f k | k k k Pφ (f ) = Pφ (|f |) · |f |! [sent-150, score-0.647]

67 kl Pφ (f ) = exp l=1 5 −λk f ·T l=1 λk f pk (f kl )pk (f kl ) . [sent-151, score-0.341]

68 Since detections from real seismic sensors are observed incrementally and roughly in time-ascending order, our inference algorithm also produces an incremental hypothesis which advances with time. [sent-155, score-0.742]

69 Our starting hypothesis is that all detections in our detection-window are false detections and there are no events. [sent-159, score-0.694]

70 Any new detections added to the detection window are again assumed to be false detections. [sent-161, score-0.557]

71 As the windows move forward the events older than t0 − MT become stable: none of the moves modify either the event or detections associated with them. [sent-162, score-0.913]

72 We deﬁne the score Se of an event as the probability ratio of two hypotheses: one in which the event exists, and another in which the event doesn’t exist and all of its associated detections are noise. [sent-167, score-1.503]

73 If an event has score less than 1, an alternative hypothesis in which the event is deleted clearly has higher probability. [sent-168, score-0.847]

74 Critically, this event score is unaffected by other events in the current hypothesis. [sent-169, score-0.64]

75 (3) and (13) we have pl (ei )λe λm l Se (ei ) = exp −λm ei m D  Pφ (dijk j,k  Pφ (aijk | dijk , ei )  | ei ) δ(dijk, 0) + δ(dijk, 1) k . [sent-171, score-0.953]

76 λf kl pk (f kl )pk (fh ) h Mz Ms a a Note that the ﬁnal fraction is a likelihood ratio comparing interpretations of the same detection as either the detection of event i’s j th phase at station k, or the lth false detection at station k. [sent-172, score-1.803]

77 (15) By deﬁnition, any detection with score less than 1 is more likely to be a false detection. [sent-175, score-0.292]

78 Also, the score of an individual detection is independent of other detections and unassociated events in the hypothesis. [sent-176, score-0.693]

79 Birth Move We randomly pick a detection, invert it into an event location (using the detection’s time, azimuth, and slowness), and sample an event in a 10 degree by 100 second ball around this inverted location. [sent-178, score-0.834]

80 The depth of the event is ﬁxed at 0, and the magnitude is uniformly sampled. [sent-179, score-0.491]

81 Improve Detections Move For each detection in the detection window, we consider all possible phases j of all events i up to MT seconds earlier. [sent-180, score-0.533]

82 We then associate the best event-phase for this detection that is not already assigned to a detection with higher score at the same station k. [sent-181, score-0.638]

83 If this best event-phase has score Sd (dijk ) < 1, the detection is changed to a false detection. [sent-182, score-0.292]

84 Improve Events Move For each event ei , we consider 10 points chosen uniformly at random in a small ball around the event (2 degrees in longitude and latitude, 100 km in depth, 5 seconds in time, and 2 units of magnitude), and choose those attributes with the highest score Se (ei ). [sent-183, score-1.171]

85 Death Move Any event ei with score Se (ei ) < 1 is deleted, and all of its currently associated detections are marked as false alarms. [sent-199, score-1.039]

86 Final Pruning Before outputting event hypotheses, we perform a ﬁnal round of pruning to remove some duplicate events. [sent-200, score-0.388]

87 In particular, we delete any event for which there is another higher-scoring event within 5 degrees distance and 50 seconds time. [sent-201, score-0.836]

88 Such spurious, or shadow, event hypotheses arise because real seismic events generate many more phases than we currently model. [sent-202, score-1.028]

89 In addition, a single phase may sometimes generate multiple detections due to waveform processing, or “pick”, errors. [sent-203, score-0.458]

90 These additional unmodeled detections, when taken together, often suggest an additional event at about the same location and time as the original event. [sent-204, score-0.446]

91 Note that the birth move is not a greedy move: the proposed event will almost always have a score Se (ei ) < 1 until some number of detections are assigned in subsequent moves. [sent-205, score-0.819]

92 Also in this ﬁgure, we show a precision-recall curve for SEL3 using scores from an SVM trained to classify true and false SEL3 events [10] (SEL3 extrapolation). [sent-211, score-0.295]

93 Since the NEIC has many more sensors in the United States than the IMS, it is considered a more reliable summary of seismic activity in this region. [sent-215, score-0.43]

94 The table on the left shows a break-down by LEB event magnitude. [sent-218, score-0.388]

95 3 103 Figure 4: Recall and error (km) broken down by LEB event magnitude and azimuth gap (degrees). [sent-240, score-0.558]

96 Large gaps indicate that the event location is under-constrained. [sent-242, score-0.446]

97 For example, if all stations are to the southwest of an event, the gap is greater than 270 degrees and the event will be poorly localized along a line running from southwest to northeast. [sent-243, score-0.54]

98 By using evidence about missed detections ignored by SEL3, NET-VISA reduces this uncertainty and performs much better. [sent-244, score-0.318]

99 6 Conclusions and Further Work Our results demonstrate that a Bayesian approach to seismic monitoring can improve signiﬁcantly on the performance of classical systems. [sent-253, score-0.436]

100 Given that the difﬁculty of seismic monitoring was cited as one of the principal reasons for non-ratiﬁcation of the CTBT by the United States Senate in 1999, one hopes that improvements in monitoring may increase the chances of ﬁnal ratiﬁcation and entry into force. [sent-255, score-0.487]

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