Earthquake catalogues and preparation of input data for PSHA science or art?

Transcription

1 Earthquake catalogues and preparation of input data for PSHA science or art? Marijan Herak Department of Geophysics, Faculty of Science University of Zagreb, Zagreb, Croatia

2 EARTHQUAKE CATALOGUES All catalogues list for each earthquake at least (if available): 1.Origin time 2.Epicentral coordinates 3.Magnitude and/or intensity All other aspects vary from catalogue to catalogue. In particular: 1.Geographical coverage 2.Temporal coverage 3.Magnitude coverage 4.Resolution and precision of parameters 5.Additional parameters listed (hypocentral depth, other magnitudes, references for parameters, fault plane solutions i.e. best double couple, number of read phases used in location, quality indices, uncertainties of parameters, macroseismic data...) 6...

3 EARTHQUAKE CATALOGUES Catalogues are the basic prerequisite and fundamental data source for the PSHA! PROBLEMS: 1.As a rule, national catalogues need to be MERGED with other catalogues in order to obtain coverage of seismic sources well outside the borders of respective countries. Catalogues often need to be merged also to increase temporal coverage (mostly for historical earthquakes). 2.Resulting master catalogue is always quite INHOMOGENEOUS regarding: the type of magnitude the resolution of parameters (e.g. magnitudes to one or two decimals, epicentral coordinates to one, two, three... decimal places, etc.) 3.The catalogue always contains a large (unknown) number of aftershocks and foreshocks. Therefore, it needs to be DECLUSTERED. 4.Resulting master catalogue is always INCOMPLETE regarding magnitude for various periods of reporting, and different geographical areas. There is no universal recipe to deal with MERGING, INHOMOGENEITIES, CLUSTERING and INCOMPLETENESS...

4 EARTHQUAKE CATALOGUES MERGING TWO OR MORE CATALOGUES To compile the working catalogue for the research area a number of regional and/or national catalogues need to be merged together. Typically we have: 1.National catalogues 2.Regional catalogues (EMSC, Balkan UNESCO...) 3.Global catalogues (ISC, NEIC, ANSS...) 4.Historical catalogues (Karnik, Shebalin & Leydecker...) Criteria must be established beforehand for: I.Declaring an earthquake listed in more than one catalog to be one and the same; II.Giving preference to the record from one catalogue when two or more catalogues list the same event. Duplicate events in two or more catalogues Usually spatial temporalmagnitude windows are defined, within which all events are declared to be the same. E.g. period BC 1750: ( M < 0.5 or I < 1 MCS) & T < 1 day & X< 1000 km... period : ( M < 0.2 or I < 0.5 MCS) & T < 5 s & X< 2 km Now, all we have to do is choose the right one...

5 EARTHQUAKE CATALOGUES MERGING TWO OR MORE CATALOGUES Choosing the preferred solution HINTS: 1. Case A National catalog is in principle preferred to others if event is far from its borders (define far!). 2. Case B event is not listed in a national catalog (B1 missing from a, exists in c ), or is close to the border (B2, B3). Of all available solutions choose the one obtained with more data (or better referenced, or the one that has depth reported, or the one that lists more than one magnitude, or the one with more precise location, or the one instrumentally located,...). Or should we just take average coordinates and magnitude? Or weighted average? Or Case C (C not in a ) Use regional or global database with caution if no local solution exists. 4. Case D Use regional or global database well outside the borders, but check if this event is listed also in national catalogues. 5. Always keep track of the originating catalogue! D a C Researc h area B2 B1 b A1 B3 A2 c Earthquake Coverage by national and/or regional catalogues r Political borders

6 EARTHQUAKE CATALOGUES HOMOGENIZATION Homogenizing magnitudes All magnitudes used for PSHA should be of the same kind in these parts of the world M L seems to be most widely used. If other magnitudes are reported, they need to be converted using one of the published conversion formulas (e.g. M S M L ). This is tricky! Beware of extrapolations! If more than one magnitude is reported in the contributing catalogue consistently use either: average median maximum... Other things to do... For events with no depth reported assign default depth for the respective epicentral region. Convert intensities into magnitudes (when no instrumental magnitude exists) using empirical regional formulas. Add flags indicating, e.g.: assigned (fixed) depths epicentral or maximal felt intensity reference for the originating catalogue macroseismic magnitudes...

7 EARTHQUAKE CATALOGUES DECLUSTERING One of the key assumptions earthquakes are independent of each other. They are distributed randomly in time according to the Poisson distribution. Hence, inter event times are distributed exponentially. This is NOT TRUE, unless foreshocks and aftershocks are removed from the catalogue! This is MANDATORY before any analysis is done with catalogue data (for the PSHA). In particular, completeness analyses and determination of the recurrence parameters (Gutenberg Richter relation) must be done on declustered catalogues! DECLUSTERING identify and remove all dependent events Methods: simple space time magnitude dependent windows more sofisticated algorithm for detection of clusters

8 EARTHQUAKE CATALOGUES DECLUSTERING For an earthquake M = M o, X = X o, T = T o : all events with: M < M o, X X o <DX(M o ), T T o < DTa(M o ) are declared aftershocks, and all events with: M < M o, X X o <DX(M o ), T o T < DTf(M o ) are declared foreshocks DX, DTa, DTf are functions of the mainshock magnitude, M o. E.g.: Space time windows STON-SLANO (1996), M = 6.0 M o DX(km) DTa (days) DTa (years) Minimal radius : 15.0 km Minimal time: 15.0 days DTa/DTf = 5

9 EARTHQUAKE CATALOGUES DECLUSTERING Cluster detection Problem with space time windows: Clouds of epicentres are rarely circular Thresholds are defined arbitrarily (at best using statistics and the Omori law) Epicentres ALTERNATIVE: Define cluster in a different way, e.g.: 1.Form initial cluster from aftershocks near the mainshock within the first 2 3 days; 2.Include into the cluster all events that occur closer than D to any of the members of the cluster 3.Stop the cluster formation if T days have passed without any addition to the cluster, but not before T min. 4.Repeat 2 3 if necessary to include missed events in the first run Maximal inter-cluster distance Outside the cluster Initial cluster Clusters defined in this way have no prescribed shape or duration. However, D and T are again arbitrarily defined... Many other algorithms also exist, e. g. the one published by Raesenberg (1985).

10 EARTHQUAKE CATALOGUES DECLUSTERING Testing When declustering is complete, it is recommended to test if the origin times in the resulting mainshock catalogue are distributed according to the Poissonian distribution. Failing the test may be due to: Bad choice of the windowing parameters, or INCOMPLETENESS of the catalogue in the inspected period and for the magnitudes considered. RESIST temptation to shrink windows too much, even if it passes the test! CROATIA: M >= 4.0, Probability of non-exceedance 90% 95% 99% Chi-squared : < Anderson-Darling: < Days No. of earthquakes from to Observed Theor. Ratio CROATIA: M >= 3.5, Probability of non-exceedance 90% 95% 99% Chi-squared : < Anderson-Darling: < Days No. of earthquakes from to Observed Theor. Ratio

11 EARTHQUAKE CATALOGUES DECLUSTERING Croatian Earthquake Catalogue (BC-2006) AFTER BEFORE Assign equivalent magnitude to the main-shock?

12 EARTHQUAKE CATALOGUES COMPLETENESS Gutenberg-Richter relation log n = a bm or log N = A BM log N = log Nref B(M Mref) Croatia, , mainshocks only log n / log N b ML = 0.90 B = 0.85 b = 0.65 log n log N M It is one of the simplest relations in seismology It expresses the most fundamental features of earthquake recurrence (self-similarity, fractal properties...) It is the basis of all probabilistic hazard studies

13 BUT... G R relation does not hold near or beyond M max (where it matters the most!) Use alternative forms, i.e. B b b ML Use maximum likelihood estimate (?). At low magnitudes catalogs are not complete and have different completeness thresholds for different periods of time Conservatively estimate completeness threshold(s), and use appropriate algorithms (but how?) / log n log N a and b values are not constant they vary with time (this is even considered an earthquake precursor!) ALEATORY UNCERTAINTY? (BTW, does M max have aleatory uncertainty?) Seismogenic zones (and especially single fault zones) are often too small to provide enough data to deduce a and b values from observations EPISTEMIC UNCERTAINTY... Consider a number of alternative, arbitrarily weighted, (a,b) value models (logic trees!). But which values to choose and how to weight them? a and b values are not statistically independent!?, see above! What about the uncertainties of estimated a and b?

14 EARTHQUAKE CATALOGUES Methods to estimate completeness I. Inspection of the magnitude frequency graphs a) visual inspection b) testing of slope change (nonparametric algorithms) Croatia, , mainshocks only log n / log N b ML = 0.90 B = 0.85 b = 0.65 log n log N M

15 EARTHQUAKE CATALOGUES Methods to estimate completeness II. Stability of the maximum likelihood b value estimate a) visual inspection b) testing of slope change (nonparametric algorithms) b Time1 Time2 b = log e / (M mean M c M) M c magnitude completeness threshold M c M c, assumed for large M c and for short time periods b becomes unstable

16 EARTHQUAKE CATALOGUES Methods to estimate completeness III.Stability of the activity rate, N ref N ref = (number of earthquakes with M M ref ) / year 1. Compute N ref for a series of sliding time windows 2. Plot against the left window edge 3. Choose the time after which N ref stabilizes Much easier said than done due to aleatory variability of N ref!

17 EARTHQUAKE CATALOGUES Methods to estimate completeness Automatic procedure: 1. Decluster the revised catalogue 2. Divide the territorry into square cells of sides L 3. Exstract subcatalog of mainshocks for each of cells 4. Choose temporal window width, W, and window shift 5. Choose threshold magnitude, M min 6. Choose the year (Y o ) after which the catalogue is certainly complete for M M min and minimum required number of earthquakes (n min ) after Y o 7. Check if there are at least n min events with M M min after Y o if not increase L and start over at point 3 8. Choose initial year, and compute seismicity rate (normalized to 1 year and e.g km 2 ) for each of the temporal windows 9. Find minimum (N 1 ) and maximum (N 2 ) rate after Y o ; Define reference activity N ref as average of N 1 and N Find the first window in which N ref is exceeded. Take the year of the left window edge (Y c ) and declare it as the year when complete reporting begins for M M min for that cell 11. Repeat for all cells, and plot N, Y c and L on maps

18 EARTHQUAKE CATALOGUES Completeness results

19 ZONATION This is the most controversial part of PSHA (personal opinion N seismologists or geologists will produce N significally different zonations... ) This is the art part? Basic guidelines for zonation: 1.Keep the zones large enough to hold statistically significant amount of earthquakes. 2.Keep the zones small enough to keep seismicity homogeneous (with respect to the recurrence law: a, b, M max should be spatially stationary within a zone). 3.The epicentres should be distributed as uniformly as possible (no large aseismic areas within a zone). 4.Do not draw borders along the faults (keep major fault systems within a zone). Seismic source zones DO NOT coincide with geological zones! 5.Borders of zones should not cross the clouds of aftershocks. 6.The style of faulting and geometry of faults should not vary significantly within a zone (e.g. do not mix strike slip with reverse faults). Ideally, each zone should encompass just one fault system. A posteriori... Check if the earthquakes within each zone obey the recurrence law that is inherent in the PSHA procedure adopted. If not, check the catalogue and/or the zoning (enlarge zones?)! Or change the PSHA algorithm...

20 ZONATION All earthquakes Example: B Ad hoc zonation of SE Croatia and adjacent regions: Are the zones F, J, K too large? Does the zone I extend too far to the south? Does the zone F extend too far to the NE? Should the zone I be united with H? Is E a zone at all? Should it be shrunk? What about L? A C K L E D J G F I H

21 ZONATION Or is this better? Mainshocks, M 3.0

22 ESTIMATION OF EARTHQUAKE RECURRENCE PARAMETERS One has to estimate at least 3 parameters for each of the seismogenic zones: 1. a value (or N ref, or λ activity rate for M M ref ) 2. b value (the slope) 3. M max Everything must be done on a declustered catalogue! 1. a value (or N ref, or λ activity rate for M M ref ) 2. b value a and b values are usually estimated using the maximum likelihood (ML) approach For catalogues with completeness varying in time use Weichert s (1980) MLalgorithm, or Kijko and Sellewol (1989, 1992) approach when gaps are present. For fault sources quaternary slip rates are used (when known...). M ref is arbitrarily defined, either as M ref = 0, or as the lowest magnitude of engineering importance (often M ref = 3.5, or even as M ref = 4.0). Drawbacks of ML: 1.No truncation for M max 2.The variances computed do not depend on the quality of fit!

23 ESTIMATION OF EARTHQUAKE RECURRENCE PARAMETERS 3. Maximum magnitude in a zone M max VERY important parameter and most difficult to estimate! 1.Take the largest observed magnitude and increase it by M (e.g. M max = M max,obs + 0.3) Problem: Is observed maximum close enough to maximum possible M? 2.Take the largest observed M in similar tectonic regions around the world Problem: Define similar! 3.Estimate M max from empirical regression relations (e.g. Wells & Coppersmith, 1994) between the observed magnitude and : length of ruptured fault segment rupture area surface rupture... Problem: How to estimate the length of maximal possible future rupture, etc. 4.Use statistics on observed set of magnitudes to estimate the extreme value (e.g. Kijko, 2004) Problem: often diverges, representativeness of observations for the long term behaviour...

24 ESTIMATION OF EARTHQUAKE RECURRENCE PARAMETERS 1. a value (or N ref, or λ activity rate for M M ref ) 2. b value 3. M max 4. Uncertainites Alternative: Use forward modelling! Best parameters are the ones that maximize the probability that the observed sample is drawn from the theoretical distribution described by them... Generate a large number of synthetic catalogues, use e.g. the Kolmogorov Smirnov test to decide if observed catalogue is significantly different from the synthetic one... Advantages: Sets of parameters (N ref, b, c, M max...) are given probability of being the right ones (objectively determined weights in logic trees!) Any kind of recurrence relationship can be used All kinds of uncertainties can easily be handled

25 UNCERTAINTIES 1. Aleatory variability intrinsic variability, inherent to the respective phenomenon Example: variability of observed acceleration or intensity (same magnitude, same distance). It can not be reduced with accumulating more observations. (Or can it?) 2. Epistemic uncertainties uncertainties due to lack of knowledge Example: choice of attenuation relationship, estimated b values for small datasets, locations of epicentres... Aleatory variability is dealt with within the hazard algorithm, e.g. by considering distributions instead of single values. Epistemic uncertainties are handled through a logic tree approach that considers a large number of weighted plausible scenarios (e.g. different attenuation relations, style of faulting, recurrence laws,...). Great care must be exercised to ensure that scenarios are (as much as posssible): mutually exclusive collectivelly exhaustive (these two imply that one of the scenarios is the true one!) the branches of the tree must be independent as a value is correlated with the b value they can not represent separate branches!

26 UNCERTAINTIES recurrence parameters (a, b, M max,...) 1. Aleatory variability is usually neglected! In the case of recurrence parameters this is the same as their temporal variation (which arguably exists)! Example: b N(b o, σ b ) Consequences are quite serious: If b is described by a distribution, than seismicity is characterized by a family of magnitude frequency curves, each of which has its own probability (weight) to become the controlling one at any time...

27 UNCERTAINTIES recurrence parameters (a, b, M max,...) It may be shown that if aleatory variability exist, the number of parameters needed to describe the recurrence relation increases to 10! Gutenberg Richter: 2 parameters Truncated G R: 3 (4) parameters Truncated G R with aleatory variation of parameters: 10 parameters [a o, σ a ] [b o, σ b, c, M max1, M max2, M a1, M a2 ] M ref = 3.5 N ref = The shape of the curve changes! o

28 UNCERTAINTIES recurrence parameters (a, b, M max,...) 2. Epistemic uncertainties represent our lack of knowledge Deal with it by logic-trees assign viable recurrence models to a number of branches! Besides recurrence parameters, consider also alternative models (branches) for: zonation attenuation laws recurrence law (characteristic earthquake, G-R,...) soil amplification... The number of branches may become very large bootstraping methods may help, but strictly speaking they violate the logic of logic-trees... Zone A Along with their aleatory variabilities! a 1, b 1, M max1 w = 0.3 a 2, b 2, M max2 w = 0.4 a 3, b 3, M max3 w = 0.3 Att-1,w = 0.5 Att-2,w = 0.5 Att-1,w = 0.5 Att-2,w = 0.5 Att-1,w = 0.5 Att-2,w = 0.5 Att-1,w = 0.5 Att-2,w = 0.5 Att-1,w = 0.5 Att-2,w = 0.5 Att-1,w = 0.5 Att-2,w = 0.5

29 SCIENCE or art? for pesimists: Ars cum grano scientiae or for optimists: Scientia cum grano artis!