Malawi probabilistic seismic hazard analysis (PSHA) using the Malawi Seismogenic Source Model (MSSM)
Last Edited by Jack Williams 06/03/23 (jack.williams@otago.ac.nz)
Please note the accompanying manuscript that describes the use of these codes has now been published open-access in Geophysical Journal International:
J N Williams, M J Werner, K Goda, L N J Wedmore, R De Risi, J Biggs, H Mdala, Z Dulanya, Å Fagereng, F Mphepo, P Chindandali, Fault-based probabilistic seismic hazard analysis in regions with low strain rates and a thick seismogenic layer: a case study from Malawi, Geophysical Journal International, Volume 233, Issue 3, June 2023, Pages 2172–2206, https://doi.org/10.1093/gji/ggad060
If using these codes, we ask that you please cite this manuscript as well
Comments by Jack Williams 31/10/22
Very minor updates have been made to PSHA codes since October 2022 releases:
PSHAmap_MSSD_em_figures.m: option added to: (1) change colour axis levels for PSHA maps and (2) show area under Lake Malawi in sensitivity analysis maps.
hodge_psha_comparison.m: option added to compare new PSHA maps with Hodge et al (2015) at a 500 year return period.
gem_psha_comparison.m: option added to plot histogram to show distribution of hazard level differences between new PSHA maps and Poggi et al (2017) and Hodge et al (2015) for each site in Malawi grid.
PSHA_MSSM_site_figures_em.m: option added to find proportion of probability mass in deaggregation plots which were generated when epislon in ground motion model sampling was >3.
MSSM_source_aspectratio.m: new plot to show aspect ratio of all MSSM sources. Equivalent to Fig. A7 in the manuscript.
Comments by Jack Williams 31/10/22
The following describes the necessary files and steps to (1) generate the MSSM (Williams et al 2022a), and (2) use these data to perform a PSHA for Malawi (Williams et al 2023).
Codes are written in MATLAB and require the following toolboxes:
Image Processing
Mapping Toolbox
The following supplementary input files (v1.1) are stored on Zenodo at https://doi.org/10.5281/zenodo.6350792 and must be downloaded and stored in path as shown
misc_functions/malawi_Vs30_active.txt: USGS slope-based Vs30 values for Malawi (Wald and Allen 2007)
syncat_MSSM/EQCAT_comb.mat: Matab file for MSSM Direct catalog for all possible rupture weightings
psha_map_em/GM_MSSM_20221021: Ground motions needed to plot PSHA maps
psha_site_em/GM_MSSM_em_20221027.mat: Ground motions needed to plot PSHA-site analysis figures
mssm_comb.mat: Matlab file for combined MSSM Direct and Adapted MSSM catalogs
syncat_adaptedMSSM/MSSM_Catalog_Adapted_em.mat: Matlab file for Adapated MSSM event catalog
syncat_bg/syncat_bg.mat: Areal source stochastic event catalog
syncat_PSHA_MSSM_input.xls: Main spreadsheet for editing MSSM and PSHA inputs. Any updates must be saved to the Matlab variable ‘syncat_PSHA_MSSM_input.mat’
MSSM_sourcecalcs/MSSM.xls: Spreadsheet with data for each source in the Malawi Seismogenic Source Model. Contains 7 tabs:
#1 ‘Leonard 2010’: list of sections, faults, and multi-faults where geometric data is stored to perform slip rate, earthquake magnitude, and recurrence interval calculations using the Leonard 2010 scaling relationships as described in Williams et al (2021a). Uncertainties from extreme ends of logic tree
#2-4 ‘Section Geometry,’ ‘Fault Geometry,’ ‘MultiFaultGeometry’: list of sections with information on the geometry and source properties of each rupture type identified in the MSSM.
#5‘MSSM_AdaptedSources’: list of information necessary for PSHA using Youngs & Coppersmith 1985 approach. Each ‘section,’ ‘fault,’ or ‘multifault’ is contained within the largest system it is part of (i.e. fault or multi fault.’
#6‘BasinSpecificValues’: The plate motion vector (and 1 sigma error) for each basin in Malawi, calculated from the geodetic model described in Wedmore et al (2021). Used in slip rate calculations
#7‘FaultObliquity’: Spreadsheet to compare source moment rates in catalogs and their 'analytical' moment rate. Can also calculate their moment rate if they were optimally oriented to the regional extension azimuth and extended through the 35 km seismogenic layer in Malawi (see appendix A3 in Williams et al 2022).
The spreadsheets ‘Section Geometry,’ ‘Fault Geometry,’ ‘MultiFaultGeometry,’ and ‘MSSM_ApdatedSources’ are linked to ‘Leonard2010’ through VLOOKUP functions, and linked to Matlab through the generation of the ‘MSSM_sources’ .mat file using the ‘Generate_MATfile.m’ script
SZ_final.m: Source information for areal PSHA sources in East Africa as developed by the Global Earthquake Model (GEM; Poggi et al 2017). Additional sources for areas not covered by GEM are also included, where seismicity rates are defined by Fenton et al (2006).
Malawi Vs30_active.txt: vs30 values for Malawi as derived from topographic slope analysis (Wald and Allen 2007)
gis_files: Various GIS files to aid plotting maps such as national borders and Lake Malawi. Also includes the Malawi Active Fault Database (MAFD; Williams et al 2021c&2022b) and Malawi Seismogenic Source Models (MSSM) GIS files (Williams et al 2022a&2022c).
misc_functions: Various Matlab functions to support scripts as described below
MSSM_sourcecalcs/HangingWallFlexureInputs: Parameters for hanging-wall flexural calculations for intrarift sources in Lake Malawi basins (see Williams et al 2021b). Includes cross check with values for the Kenya Rift from Muirhead et al (2016).
MSSM_sourcecalcs/nbasin_fautdata/nb_slipratetable_id.csv: Slip rate values from offset seismic reflector for intrarrift faults in Lake Malawi (Shillington et al 2020).
GMPE/GMPE_Malawi: Function to apply GMPE to events in stochastic event catalogs during PSHA
GMPE/GMPEcoef_Malawi: Coefficients for GMPE used in PSHA
ISC_GEM_EAcatalog.mat: ISC catalog since for East Africa Seismicity (Poggi et al 2017).
MSSM_sourcegeom/fault_geom_1.m: Script for constructing 3D geometrical models of sources, where they are defined by 2D planes and/or grid points with an average spacing of 1 km. Points created using polygrid function (Sattari 2022) and p_poly_dist and p_poly_dist1 functions (Yoshpe 2022). The width of each source is defined by which ever value is lower out of: (1) its width as defined by an empirical scaling relation with source length (Leonard 2010) or (2) if it is intersected and cut by another source. Analysis of the latter performed using the function ‘fault intersect,’ which requires Surface Intersection function (Tuszynski 2022). The revised area of a source that is intersected is input into the MSSM.xls spreadsheet to revise source geometry. Returns variable ‘fault_geom_1,’ where grid points are sorted by fault or multifault, ‘sec_geom_1’ where grid points are sorted by section, 'and ‘fault_geometry_points_1’ where sources are defined by planes. Planes also stored as csv file MSSM_source_geometry'
MSSM_sourcegeom/fault_geom_2.m: Same as for fault_geom_1, but width of source is defined as the lower value out of: (1) extrapolation to the base of the seismogenic crust (35 km) (2) if it is intersected and cut by another source. Returns variable ‘fault_geom_2,’ where grid points are sorted by fault or multifault, and ‘fault_geometry_points_2’ where sources are defined by planes.
MSSM_sourcegeom/PlotMSSMgeom: Option to plot basic 3D geometric model of MSSM sources using 'MSSM_source_geometry.csv.' as contained in the MSSM release: https://doi.org/10.5281/zenodo.5599616.
MSSM_sourcegeom/Plot_MSSMpolygons.m: Option to plot basic 3D geometric model of MSSM sources using 'fault_geom_1'
MSSM_sourcegeom/source_map_figure.m: Option to plot 3D geometrical model of MSSM sources with section sources shown, SRTM-30 m Digital Elevation Model for Malawi (Sandwell 2011), Lake Malawi, and international boundaries. Requires Hillshade function (Hebeler 2022)
MSSM_sourcegeom/fault_intersect_figure.m: Option to plot 3D geometrical model of two faults intersecting
MSSM_sourcegeom/floating_rupture_figure.m: Option to plot 3D geometrical model of the distribution of a source’s events in the stochastic event catalogs once they have been randomly floated on the source. Figure plotted for source defined by 'source_id' in code. Requires source2site functions.
MSSM_sourcecalcs/MSSM_sourcecalcs.m: Takes fault geometry, geodetic extension rates, hanging-wall flexure calculations, and Leonard (2010) scaling relationships, and uses them to calculate fault slip rates and recurrence intervals through 10000 Monte Carlo simulations through MSSM logic tree (Williams et al 2022a). Results in terms of mean and 1 standard deviation can be saved as ‘MSSM sources_Calc’ and written into MSSM spreadsheet. For faults with slip rates estimated from the offset seismic reflector, slip rates are initially estimated from the systems-based approach, preserved in variable slip_rate_nb.sr, and then replaced with offset reflector values.
MSSM_sourcecalcs/MSSM_sourcecalcplots.m: Plots various figures to analyse MSSM_souces_calcs, such as prob density of fault slip rates, comparison between slip rates from geodesy and offset seismic reflector, histograms, and comparisons to Zomba Graben sources with the SMSSD (SMSSD.xlsx; Williams et al 2021a).
MSSM_sourcecalcs/nBasinFaultSlipRateCalc: Provides slip rate estimates for intrarift fault sources in the North Basin of Lake Malawi, with uncertainty incorporated using probabilistic workflow and Matlab codes provided by Zechar and Frankel (2009)
MSSM_sourcecalcs/MSSM_sourcecalcplots_nbasincomparison.m: Compares the slip rate probability distributions of intrarift faults in Lake Malawi when estimated from the offset reflector and when estimated from the systems-based approach. Requires: calc_overlap_twonormal (Kowerko 2022)
MSSM_sourcecalcs/hw_flexure_analysis/HangingWallFlexureCalculations.m: Performs hanging-wall flexural calculations for basins in Malawi as described in Appendix of Williams et al (2022a). Requires estimates for the rheological properties of Malawi's crust and border fault offset, as contained in HangingWallFlexureInputs.xlsx. Stores outputs as 'hangingwallfelxcalcs.mat'
MSSM_sourcecalcs/hw_flexure_analysis/HangingWallFlexurePlots.m: Plots hanging-wall flexure strain and crustal profiles as shown in Figure 4 and A3 in Williams et al (2022a). Also plots topographic profiles through basin using digital elevation models and Topotoolbox (Schwanghart and Scherler, 2014) as described in code.
Generate_MATfile.m: With MSSM source geometry and calculations complete, store data in variable MSSM_sources
!Any changes to MSSM files should be saved to MSSM.xlsx and relevant .csv files so it can be updated for the MSSM shape files!
syncat_bg/new_SZ_GR_Relation.xlsx: Derive a- and b-values of the G-R relationship for new areal source zones in areas not covered by Poggi et al (2017) based on their area and G-R parameters of stable carton seismicity from Fenton and Boomer (2006).
syncat_bg/new_SZ.m: Using a- and b- values from new_SZ_GR_Relation.xlsx, add new areal source zones to SZ_final.mat (Poggi et al 2017) using areal extents defined by 'GEM_SourceZones_WGS.shp'. Save in new Matlab structure 'new_SZ'
syncat_bg/syncat_bg.m: Script for simulating stochastic catalog of earthquakes as defined by the areal sources in the Matlab structure new_SZ. Returns variable ‘syncat_bg.’ Earthquakes treated as point sources, and considered to represent background/off fault seismicity in PSHA. Events >200 km from Malawi are filtered out using p_poly_distance function (Yoshpe 2022).
syncat_bg/syncat_bg_tmp.mat: 1000 year long bg event catalog for showing event distributions
syncat_bg/syncat_bg_analysis.m: Optional script to assess simulated syncat_bg: (1) find moment rate of all sources within Malawi, (2) plot mag-freq diagram for all sources and compared to theoretical rate, (3) plot distribution of events in a 1000 year long record (using syncat_bg_tmp)
syncat_bg/inMalawi-GR.xlsx: Spreadsheet for a-values of areal sources, scaled for their overlap area in Malawi
syncat_bg/GR_EastAfrica_GEM.m: Option to plot the SSA-GEM catalog for recorded seismicity in Malawi (Poggi et al 2017), and saves to variable ‘ISC_GEM_EAcatalog_Malawi’. Also to plot various event location maps and 95% confidence intervals for Gutenberg-Richter (G-R) relationship in Malawi using approach described in Tinti & Malaria (1987) and function 'GRrelation_MLEWeichert_EQMATca'. The 'GR_TintiMulargia' results are also saved here for plotting with MSSM_comb.
syncat_bg/GR_EastAfrica_GEM_filtered.m: Compares the SSA-GEM catalog for the Rukwa-Malawi source zone (Poggi et al 2017) for cases when the 2009 Karonga Earthquakes are and are not included. Analysis described further in Appendix A4 in the PSHA manuscript.
syncat_MSSM/rupture_weighting.m: Script for simulating stochastic catalog of earthquakes as defined by a direct interpretation of the earthquake magnitudes and recurrence intervals in the MSSM and Poission interevent times. Runs for all source combinations of 'section', 'fault', and 'multi fault sources' to determine best-fit w combination to regional b-value. This combination should be updated in syncat_PSHA_MSSM_input.xlsx. Outputs can be saved in 'EQCAT_comb.mat' and'r_weighting_results.csv' and results plotted in figures.
syncat_MSSM/syncat_MSSM.m: Runs as above for selected source combination. Returns variable ‘eqcat_test’ where the earthquake catalog is stored under ‘EQCAT’ and to be used for future PSHA
syncat_MSSM/syncat_MSSM_analysis.m: Optional. For plotting results of EQCAT such as magnitude-frequency distribution of record and comparison of sources moment rates. Also calculates and compares analytical and event-catalog moment rate of each source and plots. Saves in variable 'syncat_comparsion.mat' which can be used on file 'MSSM_comb.'
syncat_MSSM_adapted/syncat_AdaptedMSSM_em.m: Script for simulating stochastic catalog of earthquakes as defined by slip rate and area of sources in ‘MSSM_AdaptedSources,’ and the methods described in Youngs and Coppersmith (1985) and Goda and Sharipov, A.(2021). Uses function ‘characteristic_magnitude_YC1985’ and returns variable ‘MSSM_Catalog_Adapated_em’ where the event catalog is stored under ‘StochasticEventCatalog.’ G-R or char behaviour or length or crust limited fault widths are considered separately in distinct catalogs
syncat_MSSM_adapted/syncat_AdaptedMSSM_analysis_em.m: Optional. As above but for plotting analysis of StochasticEventCatalog_em. Includes plotting theoretical and catalog Y&C85 mfd curves for a single source.
mssm_comb: Optional. For combining Direct MSSM, all AdaptedMSSM_em, and bg catalog together into one 10 million year long catalog for analysis. Includes plotting MFD of all catalogs and checking respective moment rates. Also for sampling MSSM-combined in 50 year intervals in terms of moment rate and MFD ('sampleAnnualRate.mat') and and comparing it to the SSA-GEM catalog (using syncat_bg.mat and GR_TintiMulargia.mat created in syncat_bg folder) and geodetic models (as stored in misc_functions/geo_mo_rate).
This folder stores GMPE functions that are assessed during the PSHA. Note, these codes DO NOT need to be run before PSHA. GMPE selection is made in syncat_PSHA_MSSM_input.xlsx
GMPE/GMPE_Malawi: Function to run events simulated in event catalogs through Ground Motion Models (GMM) or Ground Motion Prediction Equations (GMPE) selected in 'syncat_PSHA_MSSM_input.' Uses coefficients in MATLAB function GMPEcoef_Malawi.m and variable GMPEcoef_Malawi.m. Output is median ground motion intensity and log standard deviation.
GMPE/GMPE_figure: Create figure to compare selected GMPE for a single hypothetical event
GMPE/seismicVelocityComparisonPlot: Plot 1D seismic velocity models for Malawi from Ebinger et al 2019 and Stevens et al 2021. Also compares to Boore et al 2016 curve for active stable crust. Uses data stored in vp.csv and MalawiSeismicVelocityComparison.xlsx
*** Require evaluating background catalog and all 5 MSSM catalogs through 4 GMPE. As a result, analysis is performed by equally dividing the catalog into 16 sub catalogs, and then evaluating these subcatalogs simultaneously on a cluster. These codes are currently set up for use on the Blue Crystal cluster at the University of Bristol (http://www.bris.ac.uk/acrc/). These codes may therefore require adaption for use elsewhere. ***
*** Each script is identical apart from the ‘num_par’ parameter which specifies which catalog interval it assesses. Use ‘par_opts’ variable to change how catalog is assessed ***
psha_site_em/PSHA_MSSM_sitexx.m: Site specific PSHA for Malawi. Returns ground motions at site for interval of stochastic event catalogs as denoted by xx. Each event in catalog is assessed using all ground motion prediction equations selected, vs30 =300 m/s or USGS value, and vs30=760 m/s and run using functions Source2Site, Source2Site3, GMPE Malawi. Runs first for background catalog, then for MSSM-based catalogs. Ground motions for each catalog are assessed over multiple spectral accelerations, and multiple sites can be assessed. Only 'num_need' ground motions are stored, with num_need determined by the length of the catalog and minimum return period assessed (currently set to 100 years, can be altered in syncat_PSHA_MSSM_input.xlsx). The num_need ground motions that are stored are iteratively updated as the catalog is assessed to stop file sizes becoming too large. They are then stored as 'AMAX_GM_xx' and AMAX_GM_bg_xx' for further analysis. In addition, the magnitude, GMPE, and source2site distances for the num_need largest ground motions are stored for use during disaggregation analysis.
psha_site_em/PSHA_MSSM_site_figures.m: Combines ground motions from all parallelisations, and then samples only num_need. Uses data for site-specific PSHA plots: (1) seismic hazard curves, (2) uniform spectra, (3) disagg plots. Since an ensemble modelling approach used, seismic hazard curves can be plotted for all event-catalogs-GMPE selection, and for a given PoE (currently 2% and 10% PoE in 50 years) the distribution of ground motions plotted using a beta distribution). Option to plot data from previously run PSHA codes by loading GM_20220221 Otherwise new results from subcatalogs should be combined by uncommenting relevant text. Dissagg plots require functions disagg_MSSM_JW and voxel (Joel, 2022).
psha_map/PSHAmap_MSSM_xx.m: PSHA code for generating Malawi PSHA Maps. Analysis only performed for one spectral acceleration (currently set as PGA). Maps created by performing site specific for multiple sites with grid spacing as defined in syncat_PSHA_MSSM_input.xls, USGS vs30 value and 760 m/s, and for PGA only. Code run over background and MSSM-based catalog interval as defined by xx and considers each GMPE. As with site-specific PSHA, only num_need ground motions are stored to prevent excessive file sizes.
psha_map/PSHAmap_MSSM_figures_em.m: PSHA Maps for Malawi using results from PSHAmap_MSSM_xx.m. Maps plotted in terms of contribution from aerial (background) and MSSM sources. Also option too plot comparison for different on-fault magnitude-frequency distribution comparison (by comparing G-R to MSSM-Direct and characteristic), different fault widths, and PSHA uncertainty maps (in terms of CoV and interquartile range of 20 ground motion values calculated for each site) Option to plot data from previously run PSHA codes by loading GM_20220302 Otherwise new results from subcatalogs should be combined by uncommenting relevant text. Also option to saves ground motions in txt files so can be compared to Poggi et al (2017) maps and Hodge et al (2015) PSHA maps. Currently set for maps 10% PoE in 50 years and 2% PoE in 50 years.
psha_map/psha_map_comparison/hodge_2015_psha_comparison.m: Optional. Script to recreate Hodge 2015 PSHA results for Malawi, and then compare ground motions with MSSM results. Requires h2015_map_values and shape file of Hodge et al (2015) sources as input. Currently set for 2% PoE in 50 years only. Saves results so can combine with GEM comparison in gem_psha_comparison. Note minimum return period is 1 in 500 year (I.e. less than 10% PoE in 50 years). To compare with MSSM files, PSHAmap_MSSM_figures.m must be run first and output seismic hazard values stored in txt files
psha_map/psha_map_comparison/gem_psha_comparison.m: Optional. Compares PSHA maps to those produced by GEM (Poggi et al 2017) and Hodge et al (2015). Data from gem stored in folder in psha_map/gem_gm.mat. Note this data is for 2% and 10% PoE only. For option to combine with figure with Hodge 2015 maps comparison, hodge_2015_psha_comparison must be run first. Also provides some quantitative comparisons between GEM and MSSM PSHA maps.
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