Electronic Supplement to
Fault-Slip Source Models for the 2011 M 7.1 Van Earthquake in Turkey from SAR Interferometry, Pixel Offset Tracking, GPS, and Seismic Waveform Analysis
by Eric J. Fielding, Paul R. Lundgren, Tuncay Taymaz, Seda Yolsal-Çevikbilen, and Susan E. Owen
Summary
This electronic supplement contains two main types of supplemental information, "Additional point-source waveform analysis" and "Finite-fault source modeling". More details on each of these is provided below.
Additional point-source waveform analysis
Figure S1 shows the observed and synthetic waveforms obtained from an alternative point-source inversion for broadband teleseismic P waveforms for the mainshock. Figure S2 shows comparisons of selected waveforms from our preferred point-source mechanism to CMT solutions from other sources for the mainshock. Figures S3-S7 show point-source mechanism solutions of 2011 Van earthquake aftershocks that are listed in Table 2 of the main text.
Finite-fault source modeling
The fault slip evolution of our bodywave finite-fault model described and in Figure 3 of the main text is shown as a set of snapshots in Figure S8 and as a movie (Movie S1). The velocity model used in the finite-fault inversion is shown in Table S1. A schematic representation of the problem configuration of the Green's function of teleseismic body waves and definition of the fault orientation parameters strike (φ), dip (δ) and rake (λ) are given in Figure S9 (after Aki & Richards, 1980). The source time function parameterization in terms of a series of (a) box-functions and (b) overlapping isosceles triangle functions (after Nabelek, 1984; Taymaz, 1990) is illustrated in Figure S10.
Following Langston and Helmberger (1975), the time function Ω(τ) may be defined by a series of box-functions ΔƬt of equal durations ∆Ƭ but of variable amplitude ωκ (Figure S10a).
One of the problems with this type of parameterization (Figure S10a: box-functions) is that unless sufficiently small time increments are chosen, the synthetic seismograms generally have too high a frequency content. Even though the earthquake spectra are characterized by ω-2 decay at high frequencies (see Aki 1967 and 1972; Papageorgiou, 1988; Smith et al., 1991), the box-function decay is, however, only ω-1 (Nabelek, 1984). A more realistic choice is a triangle function (Figure S10b: triangle functions) which has the proper decay. Thus a time function parameterization using overlapping isosceles triangles has been introduced for the detailed study of individual earthquakes, which has the form:
The triangle function TΔT(t-τk) can be also written as a convolution of two box-car functions, BΔT(t) of equal duration, ∆Ƭ , Nabelek (1984 and 1985):
where: Ƭk= ∆Ƭ (k-1) t =time, k =source time function element, N =number of the source time function elements,
τk=time shift of a time function element,
ωk=weight (amplitude) of the source time function element.
By experimenting with source time function parameterization, amplitudes ωk of the individual overlapping isosceles triangles are determined by the inversion, but the number N∆Ƭ of time function elements and their duration ∆Ƭ have to be chosen a priori. The inversion is started with a source time function duration that exceeds the expected total duration of the source. The number of isosceles triangles is then adjusted until no significant improvement in the seismogram is observed, or until the data are matched to their expected accuracy, or until the amplitudes of the later overlapping isosceles triangles become insignificant. The derived source time function is generally recognized as one of the most important source parameters, and is related to the time history of the rupture process. The number of significant isosceles triangle elements determines the overall length of the time function, (i.e. the duration of faulting). The area under the envelope of the source time function is proportional to the scalar moment.
In addition, parameterization of the faulting area in the waveform slip inversion model is shown in Figure S11.
There is a plot of the vertical and horizontal residuals from the most probable model fits shown in Figure S12.
An animation of the fault slip evolution from the waveform finite fault inversion is shown in Movie S1.
Table
▼ Table S1. Jeffreys-Bullen (1940) velocity model used in finite-source slip inversion.
Layer No.
Vp (km/s)
Vs (km/s)
Density gr/cm3
Thickness (km)
1
5.57
3.36
2.65
15
2
6.50
3.74
2.87
18
3
8.10
4.68
3.30
half-space
Figures
Click figures to view at larger size.
▲ Figure S1.P observed waveforms and synthetics for the single-source model. Synthetics are dashed. Minimum misfit solution of the October 23, 2011 Van earthquake (Mw: 7.2) determined by teleseismic broadband P-waveform inversion. Header information is as in Figure 2 of main text.
▲ Figure S2. Comparison of our minimum misfit solution with the source parameters reported by Harvard-CMT and USGS-NEIC catalogs. The top row shows waveforms from our preferred long-period minimum misfit solution. Synthetics are dashed. The stations are identified at the top of each column, with the type of waveform marked by P- and SH- and followed by the instrument type. At the start of each row are the P- and SH- focal spheres for the focal parameters represented by the five numbers (strike, dip, rake, depth and seismic moment), showing the positions on the focal spheres of the stations chosen. X and ✓ show matches of observed to synthetic waveforms that are worse and better than in the minimum misfit solution, respectively.
▲ Figure S3.P and SH observed waveforms and synthetics for minimum misfit solution of the October 23, 2011 Van earthquake (Mw: 5.8) determined by teleseismic long-period P- and SH-waveform inversion. Other symbols are the same as in Figure S1.
▲ Figure S4.P observed waveforms and synthetics for minimum misfit solution of the October 23, 2011 Van earthquake (Mw: 5.8) determined by teleseismic broadband P-waveform inversion. Other symbols are the same as in Figure S1.
▲ Figure S5.P and SH observed waveforms and synthetics for minimum misfit solution of the October 25, 2011 Van earthquake (Mw: 5.6) determined by teleseismic long-period P- and SH-waveform inversion. Other symbols are the same as in Figure S1.
▲ Figure S6.P observed waveforms and synthetics for minimum misfit solution of the October 25, 2011 Van earthquake (Mw: 5.6) determined by teleseismic broadband P-waveform inversion. Other symbols are the same as in Figure S1.
▲ Figure S7.P and SH observed waveforms and synthetics for minimum misfit solution of the November 09, 2011 Van earthquake (Mw: 5.6) determined by teleseismic long-period P- and SH-waveform inversion. Other symbols are the same as in Figure S1.
▲ Figure S8. The finite-fault slip evolution for the model shown in Figure 3 is represented by snapshots of the cumulative slip distribution for various times (1s – 19s) at 2s intervals after rupture initiation at the hypocenter (white star). The color scale shows the amount of slip in meters.
▲ Figure S9. (Left) A schematic representation of the problem configuration of the Green'sfunction of teleseismic body waves. gS(t) represents the effect of the Earth's crust in the source region. Cr(t) is the effect of the crust under the receiver, and M(t) in the mantle response. G, A(t,t*), and d (t-tm) represent contributions due to geometrical spreading, anelastic attenuation and travel time in the mantle respectively (modified from Nabelek,1984). (Right) Definition of the fault orientation parameters strike (φ), dip (δ) and rake (λ). ū is the displacement vector (after Aki & Richards, 1980; Yolsal, 2008; Yolsal-Çevikbilen and Taymaz, 2012).
▲ Figure S10. Illustration of the source time function parameterization in terms of a series of (a) box-functions and (b) overlapping isosceles triangle functions (after Nabelek, 1984; Taymaz, 1990).
▲ Figure S11. Parameterization of the faulting area in slip inversion models. The star presents the initial break of rupture propagation. The rupture in each cell starts after Tmn time delay. Slip rate function is defined by L iscosceles triangles with a rise time t in seconds. Two components of slip vector with rakes slip 0 ± 45° (Yagi and Kikuchi, 2000; Tan and Taymaz, 2006; Yolsal-Çevikbilen and Taymaz, 2012).
▲ Figure S12. Plot of residuals of horizontal (black arrows) and vertical (red arrows) GPS measurements after subtracting the most probable geodetic slip model. Black lines outline Lake Van and other lakes. This is the same as the plot in the lower right panel of Figure 10, but without the error ellipses and error bars.
▲ Movie S1. MPEG-4 movie of the finite-fault slip evolution for the model shown in Figure 3 of the main text is represented as an animation of the cumulative slip distribution for various times (1s – 20s) after rupture initiation at the hypocenter (white star). The animation is approximately in real time. The color scale shows the amount of slip in meters.
References
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