Research topic 7 (RT7) - Creation of a new PSHA input model for South America and calculation of results

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• Julio Garcia - GEM Hazard Team, GEM Foundation, Pavia, Italy
• Marco Pagani - GEM Hazard Team, GEM Foundation, Pavia, Italy
• Luis Rodriguez - UME School, IUSS, Pavia, Italy
• Graeme Weatherill-GEM Hazard Team, GEM Foundation, Pavia, Italy

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The creation of a new seismic hazard model and the computation of the hazard in South America were the two milestones of this research topic and the SARA hazard component. The hazard model covering the whole continent is the synthesis of the information gathered and the results produced by the topics from 1 until 6. The required input data included:

• A database of active faults from RT2,
• A database of focal mechanism solutions from RT3,
• Seismological, geological and geophysical information characterising the subduction and deeper regions from RT3,
• A harmonised earthquake catalogue from RT4,
• A selection of GMPEs (and weights) from RT6
  

The construction of the earthquake source model [ESM] and the calculations were performed by the GEM hazard team in collaboration with scientists from the South American region. All the software used is open source and developed by GEM Hazard Team, GEM Foundation. To manage the basic information and for the ESM preparation, the OpenQuake Hazard Modeller's Toolkit - HMTK was used. Some functionalities were extended (or created ad-hoc) to support the construction of the model. The calculations were performed using the hazard component of the OpenQuake engine. Tutorial and documentation are available at HMTK documentation, OQ-engine documentation.

The seismic hazard modelling was performed according to the well-known probabilistic seismic hazard analysis (PSHA) proposed by (Cornell, 1968; McGuire 2004) and nowadays widely used in seismic design, providing the basis for building codes around the world.
The SARA hazard model [v.1.0] can be considered innovative in many respects, since it is a model developed within a community-based effort which contains advanced and original methods for earthquake modelling:

• The shallow seismicity is modelled using an integrated model of distributed seismicity (area-source for both, active shallow crust and stable continental regions) and crustal fault sources,
• The subduction interface seismicity is modelled as large fault sources with a 3D geometry, and,
• The subduction in-slab seismicity is modelled as 3D volumes of ruptures describing the spatial distribution of events within this area.
  

In the following sections, we briefly describe how these models were built, which are newest, innovative and controversial aspects in each case in order to encourage and promote open discussion within the South America scientist community.

The pre-processing of the harmonised catalogue provided by the topic 4, was the first step. Prior to being used in the seismic hazard modelling, two crucial analysis were performed: the declustering (i.e. dependent earthquakes are removed from the catalogue) and the completeness of the catalogue, where magnitude-time windows in which the catalogue can be considered “complete” are defined.

In the declustering analysis we attempt to identify and to remove earthquakes which occur in clusters such as foreshocks/aftershocks sequences and swarms. This is a statistical analysis were earthquake clusters are usually defined by their proximity in time and space. For declustering, several approaches can be used (e.g. stochastic, deterministic = linking and windowing methods). Even when windowing methods as the Gardner and Knopoff (1974) are capable to identify in a straightforward way the foreshock/mainshock/aftershock sequences, simply by applying the windows forward and backward in time from the mainshock, they do not distinguish between different generation of aftershocks (i.e. 1st-generation resulting from the mainshock and those associated to previous aftershocks) and it is assumed that all dependent events would occur within the window. Also, they assumed a circular spatial window searching not full consistent with fault extension for larger magnitude earthquakes.
In SARA, we use the most widely applied deterministic approach (Gardner and Knopoff, 1974), which is based on a windowing algorithm originally conceived for Southern California, but later adopted/modified to be used across the world (Stiphout et al., 2012; Uhrhammer, 1986, Grünthal, unpublished). In order to decluster the catalogue, taking into account the tectonic context and related seismicity present in the region (active shallow, stable and interface/inslab subduction) we test the performance of the method using different time-windows (Grünthal, Gardner and Knopoff and Uhrhammer, see HMTK documentation).
For the active shallow and the subduction region we used a Garder and Knopoff window, whilst for the stable continental region using an Uhrhammer window a better performance was found. The distribution of events through time and latitude showing the foreshock/mainshock/aftershock sequences after applying the declustering for the subduction region is presented below, together with window sizes(distance and time) with respect to the magnitude used by declustering methods.

Distribution of events through time and latitude [foreshock/mainshock/aftershock sequences]	Scaling of distance with magnitude
	Scaling of time with magnitude

The completeness analysis is an essential and compulsory step for any seismicity analysis and crucial for estimating reliable seismicity rates. The main goal is to determine a reliable estimate of the earliest time at which all events for different magnitudes classes are included in the catalogue in a given region.
The completeness of the earthquake catalogue can be analysed using different statistical techniques (e.g. Stepp, 1971; Albarello et al., 2001 and Woessner and Weimer, 2005). In the current version of the Modeller’s Toolkit the Stepp (1971) methodology for analysis of catalogue completeness is implemented. Supposing that earthquake occurrences follow a Poisson distribution, the Stepp Test evaluates the stability of the mean rate of occurrences (λ) of events which fall in a predefined magnitude range in a series of time windows (T). The test provides as a result the minimum observations length (in time/years) needed for establishing reliable average recurrence intervals for events of a certain magnitude class. Information from topic 4 regarding the contributing data sets to the harmonised catalogue assisted in the interpretation of the statistical estimators, to converge toward a spatio-temporal model of completeness for whole period covered by the SARA catalogue (historical and instrumental). In a first phase, the region was divided into large scale zones, in order to identify regional variations on completeness and possible common-b areas within the region. In this analysis, we distinguished between crustal/shallow earthquakes and earthquakes in the subduction or deeper regions. For each zone, the temporal variation in catalogue completeness was explored (see below the results for shallow events in Peru). The algorithm of Stepp was run with a one-year time interval and two different magnitude intervals (0.25 and 0.5). A “preferred” solutions was selected after an inspection (and modifications if it were needed) of the results obtained running automatically the Stepp method.

Distribution of crustal events (red dots) in Peru	Stepp plot	Completeness Table
		Year	Magnitude
		1999	3.75
		1995	4.00
		1995	4.25
		1995	4.50
		1985	4.75
		1971	5.00
		1965	5.25
	Mag.-time density with completeness (dashed line)	1963	5.50
		1963	5.75
		1963	6.00
		1930	6.25
		1930	6.50
		1882	6.75
		1882	7.00
		1882	7.25
		1882	7.50

The magnitude-time completeness table computed for each large scale zone was used as default for all the area sources located within its boundaries, depending on their tectonic region type (crustal/subduction). However, further minor modifications on this table were made if sub-regional variations of the completeness were found during the magnitude-frequency distribution of a single source zone.

As mentioned before, the SARA distributed seismicity model was defined by a harmonised areal source based model, however, a smoothed seismicity model representing the shallow seismicity was included in a previous version (see more details here). The seismic source zones (SSZ) were defined as geographic polygons (or volumes) that delineate regions with homogeneous characteristics of seismicity and/or tectonic and geodynamic setting. Then, the characterisation of distributed seismicity is based mainly on information contained in the catalogue, on general tectonic/geophysical information [Meijde et al., 2013; Lloyd et al., 2010; Assumpcao et al., 2013] and on general information about the geodynamic setting [GEM GSRM v2.1, Kreemer et al., 2014] across the South American continent.
For each source zone, the parameters characterising the seismicity are:

• The maximum magnitude [Mmax]: For this release we adopted the approach of deriving this value by adding an increment of 0.3 to the magnitude of the largest observed earthquake in a SSZ. If the maximum observed magnitude was lower than 6.0, Mmax was set to 6.0. For Brazil background source zone the observed maximum magnitude was set as Mmax.
• The seismogenic thickness: In order to differentiate the crustal seismicity from mid-depth events from subduction and deeper seismcity (e.g. Bucaramanga nest in Colombia), the Gravity based Moho for South America (GMSA12, hereafter) proposed by van der Meijde et al. [2013] was used. The crustal thickness proposed in GMSA12 was used as a boundary/limit [lower seismogenic depth] to classify the events present on the catalogue (and/or sub-catalogues) as crustal or subduction/deeper related events. The upper seismogenic depth was defined by the distribution of the seismicity at depth.
• The focal depth: Histograms of the earthquakes at depth inside each SSZ were computed in order to assess the hypocentral depth distribution and their probabilities.
• Orientation and faulting styles of rupture planes: Because all sources typologies supported by the OQ-engine generate ruptures as extended surfaces, the definition of the possible nodal plane distribution is crucial. Here, we used the information associated with the faults located within the SSZ boundaries and the focal mechanism solutions provided by the Topic 3, to assess in the most robust way the most probably orientation of the ruptures planes.
• The activity rate: A magnitude frequency distribution [MFD] for each SSZ was computed using the declustered catalogue and the estimated completeness table [see previous sub-sections]. The seismicity occurrence is represented by a truncated Gutenberg-Ricther distribution (with a-value, b-value, Mmin and Mmax characterisation) assuming a magnitude binning interval of 0.1, a minimum magnitude of 4.5, a maximum magnitude as described before and the b and a values computed using the maximum likelihood estimator proposed by Weichert[1980]. The b-values are in the range from 0.7 to 1.3. The highest b-values are observed in Ecuador and in the boundary between Argentina and Bolivia.
  

In the next figures the spatial variations of the b-value and the Mmax are shown. A more detailed description of the SSZ characterisation is presented here.

b-values	Maximum magnitude [Mmax]

The procedures to define a fault source from geologic information (fault traces, fault dimension, slip rates) have been explored in the past [e.g. Kagan (2002); Bungum (2007)]. Usually, the occurrence rates on the faults are modeled following a characteristic or a truncated Gutenberg Richter model (e.g. Petersen et al., 2008; 2010). The characteristic model, where “characteristic” ruptures (same magnitude and slip distribution every time) on the fault are assumed, is easy to implement, however, it requires a wide knowledge about the fault (i.e. segmentation, characteristic magnitude, recurrence times) and for most of the faults this information is not always available or it is very uncertain. Here, we model the seismicity on the fault following a double truncated Gutenberg Richter model (TGR, Youngs and Coppersmith, 1985) using slip rates and fault dimensions. Some “a priori” assumptions constrained the method:

• The occurrence of the events on the fault follow a TGR, and the total seismic moment rate from the MFD equals the geological moment rate derived from the fault dimension and slip rate,
• The b-value on the fault is the same as the b-value of the SSZ where the faults is located,
• For each fault a lower and upper-bound magnitudes should be assigned.

The database of South American active faults [SAAF], compiled in the framework of the Topic 2, is the major input for the construction of SARA fault based seismicity model. Unfortunately, a large group of faults do not fulfil the minimum requirements (poor or incomplete definition of fault characteristics or slip rate assigned to the fault) to be modeled as a fault source following the methodology described above and were not considered on this release of the model. In addition, if the fault dimension was very short and the calculated Mmax was less than Mw6.0, the fault was not included. The fault model (see figure below) contained 497 crustal faults that we assumed to have generated surface-faulting earthquakes in the geologically recent past (with Mw>6.0) and that may be capable of producing future, potentially damaging earthquakes across the South American region.

Fault Model [by country]	North Andean 3D fault representation

As mentioned before, the characterisation of the South American subduction zones for PSHA was built around the work of a PhD student (UME School). The methodology used to define and characterise the source zones is based on the best available data in the region, including seismological, geological, tectonic, geophysics and geodinamic information. The method proposed by Heuret et al.(2011) was applied to defined the interplate source zones along the margin, trying to accomplish three main points:

• To create a geometry the most simple and generalised to represent the seismogenic areas,
• That such area agrees with the complexity of the region and tectonic environment, and,
• The source must be suitable to be used for hazard estimations.

The final geometry of the model captures the spatial variability of the subduction in the region and its complexity was represented using a three-dimensional surface, from which ruptures can be modelled according to the tectonic regime. A newest way of modelling was applied for the inslab and deeper sources, which were modelled as a collection of point sources, that follows the shape and extension of the slab at depths, and where finite ruptures are modelled. A new set of tools, developed by the Hazard group of the GEM Foundation was used. The subduction and deeper source model was consistent with other models developed for the South America region and the Caribbean (e.g. Petersen et al. 2010).

Geometry definition	Interface model	In-slab model
	Characterisation of the sources and segmentation

The GMPEs we used for this initial analysis following the Topic 6 results are presented below:

*Ground Motion Prediction Equations included within version 1.0.0 of the SARA hazard model*

• Abrahamson N., N. Gregor and K. Addo (2015). BC Hydro Ground Motion Prediction Equations For Subduction Earthquakes Earthquake Spectra, in press.
• Albarello, D., R. Camassi, and A. Rebez (2001). Detection of space and time heterogeneity in the completeness level of a seismic catalogue by a statistical approach: An application to the Italian area, Bull. Seismol. Soc. Am. 91, no. 6, 1694–1703.
• Akkar S., M. A. Sandikkaya, and J. J. Bommer (2014). Empirical Ground-Motion Models for Point- and Extended- Source Crustal Earthquake Scenarios in Europe and the Middle East, Bulletin of Earthquake Engineering (2014), 12(1): 359 - 387
• Assumpcao, M., Feng, M., Tassara, A., and Julia, J. (2013). Models of crustal thickness for south america from seismic refraction, receiver functions and surface wave tomography. Tectonophysics, 609:82–96,
• Atkinson Gail M. and David M. Boore (2006). Earthquake Ground-Motion Prediction Equations for Eastern North America; Bulletin of the Seismological Society of America, Volume 96, No. 6, pages 2181-2205
• Bindi D., M. Massa, L.Luzi, G. Ameri, F. Pacor, R.Puglia and P. Augliera (2014). Pan-European ground motion prediction equations for the average horizontal component of PGA, PGV and 5 %-damped PSA at spectral periods of up to 3.0 s using the RESORCE dataset, Bulletin of Earthquake Engineering, 12(1), 391 - 340
• Boore David M., Jonathan P. Stewart, Emel Seyhan and Gail Atkinson (2014). NGA-West2 Equations for Predicting PGA, PGV, nd 5 % Damped PGA for Shallow Crustal Earthquakes; Earthquake Spectra, Volume 30, No. 3, pages 1057 - 1085.
• Boore, D.M., Azari Sisi, A. and Akkar, S. (2012). Using Pad-Stripped Acausally Filtered Strong-Motion Data, BSSA 102(2), 751-760.
• Cornell, C. A. (1968). Engineering Seismic Risk Analysis. Bulletin of the Seismological Society of America, 58(5), 1583-1606.
• Drouet S. (2015). Unpublished for Brazil based on the method described in Douet & Cotton (2015)
• Drouet, S., Cotton, F. (2015): Regional Stochastic GMPEs in Low‐Seismicity Areas: Scaling and Aleatory Variability Analysis—Application to the French Alps. - Bulletin of the Seismological Society of America, 105, 4, pp. 1883—1902. DOI: http://doi.org/10.1785/0120140240
• Gardner, J. and Knopoff, L. (1974). Is the sequence of earthquakes in southern california, with aftershocks removed, poissonian. Bull. Seismol. Soc. Am, 64(5):1363–1367, 1974.
• Heuret, A., Lallemand, S., Funiciello, F., Piromallo, C., and Faccenna, C. (2011). Physical characteristics of subduction interface type seismogenic zones revisited. Geochemistry, Geophysics, Geosystems, 12(1):n/a–n/a, Jan. ISSN 15252027. doi: 10.1029/ 2010GC003230. URL http://doi.wiley.com/10.1029/2010GC003230.
• Kreemer, C., Blewitt, G., and Klein, E. C. (2014). A geodetic plate motion and global strain rate model. Geochemistry, Geophysics, Geosystems. 15(10): 3,849-3,889.
• Lloyd, S., van der Lee, S., Franc ̧a, G. S., Assumpcao, M., and Feng, M. (2010). Moho map of south america from receiver functions and surface waves. Journal of Geophysical Research: Solid Earth, 115(B11)
• McGuire, R. K., (2004). Seismic Hazard and Risk Analysis: Earthquake Engineering Research Institute Report MNO-10, 240 p.
• Montalva et al. (2015). Unpublished, adaptation of the Abrahamson et al. (2015) BC Hydro GMPE, calibrated to Chilean strong motion data.
• Petersen, M., Harmsen, S., Haller, K., Mueller, C., Luco, N., Hayes, G., and Rukstales, K. (2010). Preliminary Seismic Hazard Model for South America. In Proceedings of Confer- encia Internacional. Homenaje a Alberto Giesecke Matto.
• Petersen, M. D., Frankel, A. D., Harmsen, S. C., Mueller, C. S., Haller, K. M., Wheeler, R. L., Wesson, R. L., Zeng, Y., Boyd, O. S., Perkins, D. M., Luco, N., Field, E. H., Wills, C. J., and Rukstales, K. S. (2008). Documentation for the 2008 Update of the United States National Seismic Hazard Maps. Unites States Geological Survey Open File Report, 2008-1128 (version 1.1), page 128.
• Stepp, J. C. (1972). Analysis of the completeness of the earthquake sample in the Puget Sound area and its effect on statistical estimates of earth- quake hazard, Proc. of the International Conf. on Microzonation for Safer Construction: Research and Application, Seattle, Washington 64, 1189–1207.
• Stiphout, T. van, J. Zhuang, and D. Marsan (2012). Theme V -Models and Techniques for Analysing Seismicity. Technical report. Community Online Resource for Statistical Seismicity Analysis. URL: http://www.corssa.org.
• Tavakoli B. and S. Pezeshk in 2005 and published as “Empirical-Stochastic Ground-Motion Prediction for Eastern North America” (2005, Bull. Seism. Soc. Am., Volume 95, No. 6, pages 2283-2296).
• Uhrhammer, R. (1986). Characteristics of Northern and Central California Seismicity. In: Earthquake Notes 57.1, page 21.
• van der Meijde, M., Juli, J., and Assumpcao, M. (2013). Gravity derived moho for south america. Tectonophysics, 609:456 – 467. ISSN 0040-1951. doi: http://dx.doi.org/10.1016/ j.tecto.2013.03.023. URL http://www.sciencedirect.com/science/article/pii/ S0040195113001972. Moho: 100 years after Andrija Mohorovicic.
• Weatherill, G. A. (2014). OpenQuake Ground Motion Toolkit - User Guide. Global EarthquakeModel (GEM). Technical Report
• Weichert, D. H. (1980). Estimation of the Earthquake Recurrance Parameters for Unequal Observation Periods for Different Magnitudes. In: Bulletin of the Seismological Society of America 70.4, pages 1337 –1346
• Wells, D. L. and K. J. Coppersmith (1994). New Empirical Relationships among Magnitude, Rupture Length, Rupture Width, Rupture Area, and Surface Displacement. In: Bull. Seism. Soc. Am. 84.4, pages 974–1002
• Woessner, J., and S. Wiemer (2005). Assessing the quality of earthquake catalogues: Estimating the magnitude of completeness and its uncertainty, Bull. Seismol. Soc. Am. 95, no. 2, 684–698.
• Zhao, J. X., Zhang, J., Asano, A., Ohno, Y., Oouchi, T., Takahashi, T., Ogawa, H., Irikura, K., Thio, H. K., Somerville, P. G., Fukushima, Y., & Fukushima, Y. (2006). Attenuation relations of strong ground motion in Japan using site classification based on predominant period. Bulletin of the Seismological Society of America, 96(3), 898–913.

The OpenQuake-engine input model (NRML format) can be obtained at this Link

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