Apart from the ΔCFSm imparted by megathrust events, the tectonic stress rate also plays an important role in determining the Coulomb Failure Stress acting on a fault at any time. Here we denote the tectonic stress contribution to CFS on the GSF as ΔCFSt. The higher the tectonic stress rate, the faster the fault can be brought back to its critical condition after rupture, and vice versa (Hori and Oike 1999). The tectonic stress acting on the GFS comes from two sources: (1) coupling of the oblique convergence at the megathrust, which transmits the stress acting on the megathrust through the forearc sliver and onto the GSF, and (2) arc-parallel motion of the forearc sliver itself, which exerts an additional traction on the GSF (Fitch 1972; Malod and Kemal 1996). Earlier studies (e.g., McCaffrey 2009) suggested there is a strong northward increase of the slip rate of the GSF, which would result in stretching of the forearc and imply a commensurate northward increase in tectonic stress rate. However, the more recent study of Bradley et al. (2017) uses GPS measurements of crustal velocities to show that the Sumatra forearc sliver undergoes little or no internal permanent deformation, but experiences arc-parallel movement that is consistent with an almost constant slip rate of 15 mm/yr along the GSF indicated by revised geologic estimates of the slip rate (Bradley et al. 2017; Natawidjaja et al. 2017).
We calculate ΔCFSt for two cases: (1) tectonic stress solely due to coupling of the oblique plate convergence at the megathrust, and (2) tectonic stress due to the megathrust coupling as well as sliver movement with respect to the Sunda plate as described by Bradley et al. (2017). The former, no-sliver-movement case, is useful for comparison with other forearcs, like SW Japan, that are buttressed and have less sliver movement. The latter, sliver movement case, is preferred because it better explains the available GPS data (Bradley et al. 2017).
We derive coupling models for both cases, using the 3-block model of Bradley et al. (2017) for the transition between Indian and Australian plate motion with respect to the Sunda Plate, as illustrated in Fig. 5. For case (1) with no sliver motion, all of the oblique plate convergence between these blocks and the Sunda plate is applied as a “back-slip” dislocation on the megathrust (Savage 1983). For case (2), the arc-parallel motion of the forearc sliver is subtracted from the oblique plate convergence in order to determine the back-slip applied on the megathrust, and then the forearc sliver movement is added to all the velocities calculated in the sliver. In both cases we have allowed coupling in the four segments: Aceh-Nias, Batu, Padang and Enggano to vary, as indicated in Fig. 5. We used a grid search over these four coupling values to find the combination resulting in the best fit to the GPS data for each of cases (1) and (2) – shown in Fig. 5a and b, respectively. We note that in both cases, similar fits to the GPS data were obtained for the Padang and Batu segments, but only case (2), with sliver movement, results in a good fit for the data in the Aceh-Nias and Enggano segments.
In order to model the elastic deformation of the forearc sliver due to coupling of the plate convergence at the megathrust, an appropriate distribution of coupling is applied along the megathrust. We use the Triangular Dislocation Element (TDE) approach of Meade (2007) to calculate the elastic deformation due to back-slip applied on triangular elements used to tesselate the irregular shape of the SLAB2.0 model (Hayes 2018) for the Sumatra megathrust (see Fig. 5). We can estimate the stress tensor using Hooke’s law, \(\sigma =\lambda tr\left(\epsilon \right)\mathbf{I}+2\mu \epsilon\), where \(\epsilon\) is the strain tensor caused by the back-slip dislocation, \(tr\left(\epsilon \right)\) is the trace of the strain tensor and \(\mathbf{I}\) is the identity matrix. The shear stress and normal stress can then be resolved on each segment of the GSF to calculate the associated ΔCFSt according to Equation 2. For case 1, with no sliver movement, this corresponds to the total Coulomb stress change ΔCFSt1 (Table 3).
Table 3
Estimation of the rates of increase in tectonic stress on the GSF for the two cases considered: (1) no forearc sliver movement and (2) forearc sliver movement from Bradley et al. (2017). In each case, Δτ and Δσ are perturbations to shear and normal stress, respectively on each GSF segment caused by the coupling of oblique convergence at the Sumatra megathrust. For case (1), these are combined according to eq. (2) to yield ΔCFSt1. For case (2), an additional term Δτs, calculated from the slip deficit Δus on each GSF segment associated with sliver movement according to Kanamori & Anderson (1975), is added to Δτ in order to calculate the change in Coulomb stress ΔCFSt2. θ is the angle between the forearc sliver and Sunda plate motion and at each segment.
Segment | No Sliver Movement | Sliver Movement |
Δτ | Δσ | ΔCFSt1 | Δτ | Δσ | Δus | Δτs | θ | ΔCFSt2 |
kPa | kPa | kPa | kPa | kPa | mm | kPa | o | kPa |
Seulimeum | 1.2 | -3.8 | 0.8 | 0.6 | -3.5 | 16 | 17.7 | 19 | 18.0 |
Aceh | 1.0 | -4.4 | 0.6 | 0.5 | -4.0 | 15 | 16.7 | 25 | 16.8 |
Tripa North | -0.9 | -4.1 | -1.3 | -0.9 | -3.5 | 12 | 13.0 | 44 | 11.7 |
Tripa South | 1.4 | -3.9 | 1.0 | 1.1 | -3.8 | 16 | 17.3 | 12 | 18.0 |
Renun | 0.9 | -4.2 | 0.5 | 0.7 | -4.3 | 15 | 17.1 | 12 | 17.4 |
Toru | 0.7 | -3.2 | 0.3 | 0.5 | -3.5 | 16 | 17.3 | -3 | 17.5 |
Angkola | 0.7 | -1.9 | 0.5 | 0.5 | -1.9 | 16 | 17.3 | 2 | 17.6 |
Barumun | 0.9 | -1.5 | 0.7 | 0.6 | -1.6 | 15 | 16.6 | -16 | 17.1 |
Sumpur | 1.5 | -1.9 | 1.4 | 1.6 | -2.2 | 15 | 16.5 | -18 | 17.9 |
Sianok | 1.8 | -3.5 | 1.4 | 1.9 | -4.3 | 16 | 17.3 | -6 | 18.8 |
Sumani | 1.9 | -4.2 | 1.5 | 2.0 | -5.5 | 15 | 17.2 | -11 | 18.6 |
Suliti | 1.6 | -4.7 | 1.1 | 1.3 | -6.4 | 16 | 17.4 | -7 | 18.1 |
Siulak | 1.8 | -4.9 | 1.3 | 1.4 | -6.7 | 16 | 17.4 | -10 | 18.1 |
Dikit | 1.4 | -5.0 | 0.9 | 0.7 | -6.7 | 16 | 17.6 | -5 | 17.7 |
Ketaun | 1.0 | -5.0 | 0.5 | -0.2 | -6.4 | 16 | 17.7 | -6 | 16.8 |
Musi | 0.9 | -3.4 | 0.6 | -0.8 | -3.9 | 16 | 17.5 | -12 | 16.3 |
Manna | 1.2 | -3.1 | 0.8 | -0.3 | -1.9 | 16 | 17.9 | -4 | 17.4 |
Kumering | 1.7 | -3.7 | 1.3 | 0.5 | -1.9 | 16 | 17.6 | -12 | 17.9 |
Semangko | 2.4 | -3.89 | 2.0 | 0.79 | -2.11 | 15.6 | 17.38 | -16 | 18.0 |
As for the case (2) with sliver movement, the whole calculation is similar to what we have used for no sliver movement, however, we use the forearc rigid block movement of Bradley et al. (2017) to calculate a slip deficit for each GSF segment (Δus in Table 3). Then, we calculate the corresponding shear stress accumulation Δτs based on the relation of Kanamori and Anderson (1975), and add this to the shear stress Δτ obtained from dislocation modelling for Sumatra megathrust coupling, to obtain the total ΔCFSt2 for case (2) as:
$$\varDelta CFS=\varDelta +\varDelta {\tau }_{s}+\mu \text{'}\varDelta \sigma$$
3
An important caveat to this approach is its failure to account for fault-normal sliver movement, as indicated in Table 3 by the angle θ between the forearc sliver and Sunda plate motion and at each segment. Except for the Tripa North segment, this angle is generally less than 20o, with mostly negative angles indicating extension in the south and positive angle indicating compression in the north, consistent the forearc sliver’s pole location and sense of rotation (Bradley et al. 2017). The fault-normal movement must be accommodated either by oblique motion on the GSF itself, or by faulting and/or folding in the forearc sliver. Since there is little or no information on the dip of the GSF segments and internal strain rates of the sliver are not detectable using currently available GPS data (Bradley et al. 2017), we do not account for this motion here.