Introduction. The Supplement shows results of locking using a range of smoothing parameters α, and checkerboard tests.

Transcription

1 Auxiliary Material Submission for Paper 2014JB Robert McCaffrey Portland State University Inter-seismic locking on the Hikurangi subduction zone: Uncertainties from slow-slip events Introduction The Supplement shows results of locking using a range of smoothing parameters α, and checkerboard tests. Also given are the GPS velocity fields used. Velocity fields: These have been rotated into the Australian reference frame JB ts01.txt Survey mode GPS velocity field 1.1 Column "Site", Site name 1.2 Column "Long.", degrees, longitude of site, east of Greenwich. 1.3 Column "Lat.", degrees, latitude of site, north of equator. 1.4 Column "Ve", mm/yr, East velocity of site 1.4 Column "Se", mm/yr, East velocity uncertainty 1.5 Column "Vn", mm/yr, North velocity of site 1.6 Column "Sn", mm/yr, North velocity uncertainty JB ts02.txt Continuous GPS velocity field 2.1 Column "Site", Site name 2.2 Column "Long.", degrees, longitude of site, east of Greenwich. 2.3 Column "Lat.", degrees, latitude of site, north of equator. 2.4 Column "Ve", mm/yr, East velocity of site 2.5 Column "Vn", mm/yr, North velocity of site 2.6 Column "Vz", mm/yr, Up velocity of site 2.7 Column "Se1", mm/yr, East velocity uncertainty (Williams method) 2.8 Column "Sn1", mm/yr, North velocity uncertainty (Williams method) 2.9 Column "Sz1", mm/yr, Up velocity uncertainty (Williams method) 2.10 Column "Se2", mm/yr, East velocity uncertainty (Hackl method) 2.11 Column "Sn2", mm/yr, North velocity uncertainty (Hackl method) 2.12 Column "Sz2", mm/yr, Up velocity uncertainty (Hackl method) 2.13 Column "Start_Yr", Year, Start time of GPS site 2.14 Column "End_Yr", Year, End time of GPS site 2.15 Column "Duration_Yr",Years, Duration of GPS site JB ts03.txt Continuous GPS velocity field 3.1 Column "Site", Site name 3.2 Column "Duration",Years, Duration of GPS site 3.3 Column "Model_T",Years, Duration of Monte Carlo simulation 3.4 Column "Se", mm/yr, East velocity uncertainty (Monte Carlo method) 3.5 Column "Sn", mm/yr, North velocity uncertainty (Monte Carlo method) 3.6 Column "Sz", mm/yr, Up velocity uncertainty (Monte Carlo method) 3.7 Column "Ve", mm/yr, East velocity of site due to transients 3.8 Column "Vn", mm/yr, North velocity of site due to transients

2 3.9 Column "Vz", mm/yr, Up velocity of site due to transients JB ts04.txt Offsets from transients 4.1 Column "Site", Site name 4.2 Column "Start_Yr", Year, Start time of GPS site 4.3 Column "End_Yr", Year, End time of GPS site 4.4 Column "Duration_Yr",Years, Duration of GPS site For each site: 4.5 Time in Years 4.6 East offset, mm 4.7 North offset, mm 4.8 Up offset, mm JB fs01.eps (Figure S-1). Data misfit for given smoothing exponents. Black dots are for Gaussian model and red for Exponential model. Labels at bottom are model names JB fs02.eps (Figure S-2) Locking results for models with different smoothing exponents. In each pair, at left is Exponential model and at right is Gaussian model. Labels give the model name ni5x, followed by data chi-squared misfit and moment rate in Nm/yr. For models ni5h and ni56, α = 10^4, for models ni5i and ni59, α = 10^ JB fs03.eps (Figure S-3a) For these tests a velocity field was generated from the locking distribution shown in the top panel. Random errors were added to the velocities at the sites according to the uncertainty in the observed velocities. The simulated data were then inverted for the slip distribution. The two test cases use the same distribution of patches but the locking fraction was reversed (0 = free-slip or 1 = fully locked). The middle figure shows the result when the starting model was a fully locked fault and in the bottom figure the starting model was a fully free-slip fault. This was done to see if the data or the moment-damping constraint drove a patch to be free-slip. The results are quite similar for the two starting models. These tests show that locking in the up-dip part of the fault is unresolved and the deeper parts of the fault have lower resolution JB fs04.eps (Figure S-3b) For these tests a velocity field was generated from the locking distribution shown in the top panel. Random errors were added to the velocities at the sites according to the uncertainty in the observed velocities. The simulated data were then inverted for the slip distribution. The two test cases use the same distribution of patches but the locking fraction was reversed (0 = free-slip or 1 = fully locked). The middle figure shows the result when the starting model was a fully locked fault and in the bottom figure the starting model was a fully free-slip fault. This was done to see if the data or the moment-damping constraint drove a patch to be free-slip. The results are quite similar for the two starting models. These tests show that locking in the up-dip part of the fault is unresolved and the deeper parts of the fault have lower resolution.

3 Supplementary Material for: McCaffrey, R., Inter-seismic locking on the Hikurangi subduction zone: Uncertainties from slow-slip events, JGR submitted. See also the README file Smoothing tests: Figure S-1. Data misfit for given smoothing exponents. Black dots are for Gaussian model and red for Exponential model. Labels at bottom are model names. Figure S-2. Locking results for models with varying smoothing exponents. In each pair, at left is Exponential model and at right is Gaussian model. Labels give the model name ni5x, data chi-squared misfit and moment rate in Nm/yr. For models ni5h and ni56, α = 10 4, and for models ni5i and ni59, α = Checkerboard tests: Figure S-3. For these tests a velocity field was generated from the locking distribution shown in the top panel. Random errors were added to the velocities at the sites according to the uncertainty in the observed velocities. The simulated data were then inverted for the slip distribution. The two test cases use the same distribution of patches but the locking fraction was reversed (0 = free-slip or 1 = fully locked). The middle figure shows the result when the starting model was a fully locked fault and in the bottom figure the starting model was a fully free-slip fault. This was done to see if the data or the moment-damping constraint drove a patch to be free-slip. The results are quite similar for the two starting models. These tests show that locking in the up-dip part of the fault is unresolved and the deeper parts of the fault have lower resolution. Test of Error Models: To compare the uncertainties estimated by the Hackl et al. [2011], Williams [2003b] and Monte Carlo methods, I generated a 10-year long time series that had 40 evenly spaced, random offsets. The offsets followed a Gaussian distribution with variance of 1 mm 2 and a mean of zero. The Williams predicted velocity variance is p σ d 2 / T where p = 40/(10*365.25), σ d 2 =1.0 mm 2, and T = 10*365.25, giving σ = 0.63 mm/yr. For 3 test time series generated with those offsets, the Hackl method gave uncertatintes of 0.62, 0.43 and 0.57 mm/yr. The Monte Carlo method for the same 3 time series gave standard deviation of the slopes of 0.62, 0.65 and 0.56 mm/yr. Offsets: All estimated offsets for slow-slip, volcano deformation and earthquakes are given in an accompanying file 2014JB ts04.txt. 1

4 Velocity fields: These have been rotated into the Australian reference frame JB ts01.txt Survey mode GPS velocity field 1.1 Column "Site", Site name 1.2 Column "Long.", degrees, longitude of site, east of Greenwich. 1.3 Column "Lat.", degrees, latitude of site, north of equator. 1.4 Column "Ve", mm/yr, East velocity of site 1.4 Column "Se", mm/yr, East velocity uncertainty 1.5 Column "Vn", mm/yr, North velocity of site 1.6 Column "Sn", mm/yr, North velocity uncertainty JB ts02.txt Continuous GPS velocity field 2.1 Column "Site", Site name 2.2 Column "Long.", degrees, longitude of site, east of Greenwich. 2.3 Column "Lat.", degrees, latitude of site, north of equator. 2.4 Column "Ve", mm/yr, East velocity of site 2.5 Column "Vn", mm/yr, North velocity of site 2.6 Column "Vz", mm/yr, Up velocity of site 2.7 Column "Se1", mm/yr, East velocity uncertainty (Williams method) 2.8 Column "Sn1", mm/yr, North velocity uncertainty (Williams method) 2.9 Column "Sz1", mm/yr, Up velocity uncertainty (Williams method) 2.10 Column "Se2", mm/yr, East velocity uncertainty (Hackl method) 2.11 Column "Sn2", mm/yr, North velocity uncertainty (Hackl method) 2.12 Column "Sz2", mm/yr, Up velocity uncertainty (Hackl method) 2.13 Column "Start_Yr", Year, Start time of GPS site 2.14 Column "End_Yr", Year, End time of GPS site 2.15 Column "Duration_Yr",Years, Duration of GPS site JB ts03.txt Continuous GPS velocity field 3.1 Column "Site", Site name 3.2 Column "Duration",Years, Duration of GPS site 3.3 Column "Model_T",Years, Duration of Monte Carlo simulation 3.4 Column "Se", mm/yr, East velocity uncertainty (Monte Carlo method) 3.5 Column "Sn", mm/yr, North velocity uncertainty (Monte Carlo method) 3.6 Column "Sz", mm/yr, Up velocity uncertainty (Monte Carlo method) 3.7 Column "Ve", mm/yr, East velocity of site due to transients 3.8 Column "Vn", mm/yr, North velocity of site due to transients 3.9 Column "Vz", mm/yr, Up velocity of site due to transients JB ts04.txt Offsets from transients 4.1 Column "Site", Site name 4.2 Column "Start_Yr", Year, Start time of GPS site 4.3 Column "End_Yr", Year, End time of GPS site 4.4 Column "Duration_Yr",Years, Duration of GPS site 2

5 For each site: 4.5 Time in Years 4.6 East offset, mm 4.7 North offset, mm 4.8 Up offset, mm JB fs01.eps (Figure S-1). Data misfit for given smoothing exponents. Black dots are for Gaussian model and red for Exponential model. Labels at bottom are model names JB fs02.eps (Figure S-2) Locking results for models with different smoothing exponents. In each pair, at left is Exponential model and at right is Gaussian model. Labels give the model name ni5x, followed by data chi-squared misfit and moment rate in Nm/yr. For models ni5h and ni56, α = 10^4, for models ni5i and ni59, α = 10^ JB fs03.eps (Figure S-3a) For these tests a velocity field was generated from the locking distribution shown in the top panel. Random errors were added to the velocities at the sites according to the uncertainty in the observed velocities. The simulated data were then inverted for the slip distribution. The two test cases use the same distribution of patches but the locking fraction was reversed (0 = free-slip or 1 = fully locked). The middle figure shows the result when the starting model was a fully locked fault and in the bottom figure the starting model was a fully free-slip fault. This was done to see if the data or the moment-damping constraint drove a patch to be freeslip. The results are quite similar for the two starting models. These tests show that locking in the up-dip part of the fault is unresolved and the deeper parts of the fault have lower resolution JB fs04.eps (Figure S-3b) For these tests a velocity field was generated from the locking distribution shown in the top panel. Random errors were added to the velocities at the sites according to the uncertainty in the observed velocities. The simulated data were then inverted for the slip distribution. The two test cases use the same distribution of patches but the locking fraction was reversed (0 = free-slip or 1 = fully locked). The middle figure shows the result when the starting model was a fully locked fault and in the bottom figure the starting model was a fully free-slip fault. This was done to see if the data or the moment-damping constraint drove a patch to be freeslip. The results are quite similar for the two starting models. These tests show that locking in the up-dip part of the fault is unresolved and the deeper parts of the fault have lower resolution. 3