org.opensha.sha.earthquake.calc.recurInterval
Class BPT_DistCalc
java.lang.Object
org.opensha.sha.earthquake.calc.recurInterval.EqkProbDistCalc
org.opensha.sha.earthquake.calc.recurInterval.BPT_DistCalc
 All Implemented Interfaces:
 EventListener, ParameterChangeListener
public final class BPT_DistCalc
 extends EqkProbDistCalc
 implements ParameterChangeListener
Title: BPT_DistCalc.java
Description:
.
This represents the Brownian Passage Time renewal model as described by Matthews et al. (2002, BSSA, vol 92, pp. 22232250).
This adds several "Safe" methods are also supplied to avoid numerical artifacts; see description for each method for more details
 Version:
 1.0
 Author:
 Edward Field
Fields inherited from class org.opensha.sha.earthquake.calc.recurInterval.EqkProbDistCalc 
adjustableParams, aperiodicity, APERIODICITY_PARAM_INFO, APERIODICITY_PARAM_NAME, aperiodicityParam, cdf, commonInfoString, DEFAULT_APERIODICITY_PARAM_VAL, DEFAULT_DELTAX_PARAM_VAL, DEFAULT_DURATION_PARAM_VAL, DEFAULT_HIST_OPEN_INTERVAL_PARAM_VAL, DEFAULT_MEAN_PARAM_VAL, DEFAULT_NUMPOINTS_PARAM_VAL, DELTA_X_DEFAULT, DELTA_X_PARAM_INFO, DELTA_X_PARAM_NAME, deltaX, deltaX_Param, duration, DURATION_PARAM_INFO, DURATION_PARAM_NAME, durationParam, HIST_OPEN_INTERVAL_PARAM_INFO, HIST_OPEN_INTERVAL_PARAM_NAME, histOpenInterval, histOpenIntParam, integratedCDF, integratedOneMinusCDF, mean, MEAN_PARAM_INFO, MEAN_PARAM_NAME, meanParam, NAME, NUM_POINTS_PARAM_INFO, NUM_POINTS_PARAM_NAME, numPoints, numPointsParam, pdf, upToDate 
Method Summary 
protected void 
computeDistributions()

double 
getCondProb(double timeSinceLast,
double duration)
This is a version of the parent method getCondProb(*) that avoids numerical artifacts
at high timeSinceLast (where 1cdf gets too close to 0, and we therefore have division by
zero). 
static double 
getCondProb(double mean,
double aperiodicity,
double timeSinceLast,
double duration)
This computed the conditional probability using Trapezoidal integration (slightly more
accurrate that the WGCEP2002 code, which this method is modeled after). 
double 
getCondProbForUnknownTimeSinceLastEvent()
This computes the probability of an event over the specified duration for the case where the
date of last event is unknown (looping over all possible values), but where the historic open
interval is applied (the latter defaults to zero if never set). 
EvenlyDiscretizedFunc 
getCondProbFunc()
Overrides name and info assigned in parent 
double 
getSafeTimeSinceLastCutoff()
This returns the maximum value of timeSinceLast (as discretized in the xaxis of the cdf) that is
numerically safe (to avoid division by zero in the conditional probability calculations, where the
denominator is 1cdf). 
static void 
main(String[] args)
Main method for running tests. 
void 
testSafeCalcs()
This tests the difference between values obtained using the local and parent
getCondProbFunc(*) methods for cases within safeTimeSinceLast, where the fix
for small normalized durations is applied in the local method. 
Methods inherited from class org.opensha.sha.earthquake.calc.recurInterval.EqkProbDistCalc 
computeMeanFromPDF, fitToThisFunction, getAdjParams, getAperiodicity, getCDF, getCondProbFunc, getCondProbGainFunc, getHazFunc, getMean, getMeanTimeSinceLastEventPDF, getName, getPDF, getTimeSinceLastEventPDF, initAdjParams, makeIntegratedCDFs, parameterChange, setAll, setAll, setAll, setAll, setAllParameters, setDuration, setDurationAndHistOpenInterval 
Methods inherited from class java.lang.Object 
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
BPT_DistCalc
public BPT_DistCalc()
computeDistributions
protected void computeDistributions()
getCondProb
public static double getCondProb(double mean,
double aperiodicity,
double timeSinceLast,
double duration)
 This computed the conditional probability using Trapezoidal integration (slightly more
accurrate that the WGCEP2002 code, which this method is modeled after). Although this method
is static (doesn't require instantiation), it is less efficient than the nonstatic version
here (it is also very slightly less accurate because the other interpolates the cdf).
Note also that if timeSinceLast/mean > aperiodicity*10, timeSinceLast is changed to equal
mean*aperiodicity*10 (to avoid numerical problems at high timeSinceLast).
 Parameters:
timeSinceLast
  time since last eventrate
  average rate of eventsalpha
  coefficient of variation (technically corrrect??)duration
  forecast duration
 Returns:
getCondProb
public double getCondProb(double timeSinceLast,
double duration)
 This is a version of the parent method getCondProb(*) that avoids numerical artifacts
at high timeSinceLast (where 1cdf gets too close to 0, and we therefore have division by
zero).
We know that at infinite time the mean residual life (expected time to next earthquake) for BPT
approaches the following asymptotically:
mrl = 2*mean*aperiodicity*aperiodicity
(Equation 24 of Matthews et al. (2002, BSSA, vol 92, pp. 22232250)), so the conditional probability
becomes 1exp(duration/mrl) at large timeSinceLast. We also define a safeTimeSinceLast as that where
1cdf becomes close to zero (<= SAFE_ONE_MINUS_CDF). Beyond this point we assume the conditional
probability varies linearly between the value at safeTimeSinceLast and 1exp(duration/mrl), where
"infinite time" is taken as timeSinceLast/mean = 10. While this choice of 10 is somewhat arbitrary,
differences are only slight, and mostly only for low aperiodicity (<0.15). Also keep in mind that
the probability of getting beyond safeTimeSinceLast is SAFE_ONE_MINUS_CDF (e.g., 1e13), so we are
way out on the tail, where application of the model will always be speculative anyway.
The above does not solve all numerical problems, as we can get instability before safeTimeSinceLast
where p2p1 in the parent method becomes too small (e.g., 1e14), which occurs when duration/mean is
<= 1e3 (and again, only for aperiodicities <= 0.2). To avoid this problem, the smallest duration/mean
for which conditional probability is computed is MIN_NORM_DURATION, with values below this simply being
the value for MIN_NORM_DURATION scaled by (duration/mean)/MIN_NORM_DURATION. The testSafeCalcs show that
this produces conditional probabilities within 0.1% of true values where these numerical artifacts are
lacking, and shows that discrepancies elsewhere are for very unprobable states (e.g., just below
safeTimeSinceLast); nonetheless, this fixes these other numerical artifacts.
 Overrides:
getCondProb
in class EqkProbDistCalc
 Parameters:
timeSinceLast
 duration

 Returns:
getCondProbFunc
public EvenlyDiscretizedFunc getCondProbFunc()
 Overrides name and info assigned in parent
 Overrides:
getCondProbFunc
in class EqkProbDistCalc
 Returns:
getCondProbForUnknownTimeSinceLastEvent
public double getCondProbForUnknownTimeSinceLastEvent()
 This computes the probability of an event over the specified duration for the case where the
date of last event is unknown (looping over all possible values), but where the historic open
interval is applied (the latter defaults to zero if never set).
This avoids numerical artifacts in the parent method a couple ways.
First, if histOpenInterval>=safeTimeSinceLast, we simply return the conditional probability at
safeTimeSinceLast (technically we should weight average the values beyond, but they are
nearly constant, the weights are decaying beyond (so that at safeTimeSinceLast is highest),
and the likelihood of histOpenInterval ever getting to safeTimeSinceLast is vanishingly
small (as noted in the doc for the getCondProb method here)).
A less efficient way of calculating this cond probability is also used if unstable results are
expected (see details regarding "numer" and "denom" below).
 Overrides:
getCondProbForUnknownTimeSinceLastEvent
in class EqkProbDistCalc
 Returns:
getSafeTimeSinceLastCutoff
public double getSafeTimeSinceLastCutoff()
 This returns the maximum value of timeSinceLast (as discretized in the xaxis of the cdf) that is
numerically safe (to avoid division by zero in the conditional probability calculations, where the
denominator is 1cdf). This returns Double.Nan if no xaxis values are safe (not even the first ones).
The threshold for safe values was found by trial and error and checked for aperiodicity values between
0.1 and 1.0 (using the GUI).
 Returns:
testSafeCalcs
public void testSafeCalcs()
 This tests the difference between values obtained using the local and parent
getCondProbFunc(*) methods for cases within safeTimeSinceLast, where the fix
for small normalized durations is applied in the local method. This prints all
cases that differ by more than 0.1%. All those printed are indeed the problems
we sought to avoid, and are very rare circumstances anyway.
main
public static void main(String[] args)
 Main method for running tests.
Test1 compares the static getCondProb(*) method against values obtained directly from the WGCEP2002
code; all are within 0.3%.
Test2 campares the non static getCondProb(*) method against the static; all are within 0.5%. The
differences is that the nonstatic is slightly more accurate due to interpolation of the CDF
(exact same values are obtained otherwise; see commented out code).
Test3 is the nonstatic used more efficiently (exact same values as from nonstatic above); this
is about a factor of two faster.
Test4 examines what happens if delta is changed to 0.01 in the nonstatic method (also about
a factor of two faster).