A New Strategy to Compare Inverted Rupture Models Exploiting the Eigenstructure of the Inverse Problem

The electronic supplement contains an explanation of the conversion of inverted models from the Source Inversion Validation (SIV) database (model SIV2a) to a unified spatial–temporal discretization, a table with description of the inverted models, and figures showing all the inverted models in full spectrum and after singular value decomposition (SVD) truncation.

The fault plane in the SIV2a benchmark is 40 km × 20 km. The integral in the representation theorem is discretized assuming 1.5 km × 1.0 km subfaults and 0.4 s time step. The displacement Green’s functions are Butterworth filtered (one way, four poles, bandpass 0.05–0.5 Hz). These settings follow the recommended relations between space–time sampling and frequency to guarantee sufficient accuracy (e.g., Spudich and Archuleta, 1987; Beresnev, 2003). The spectrum of the matrix G is shown in Figure 1c of the main article.

Models Gallovic0.01 and Gallovic0.1 were obtained assuming the above-mentioned discretization. The other models considered (Target, Hoby, CedricT3, and Asano) were resampled to the common discretization according to the following procedure:

- Rupture times, rise times, and slip values are bilinearly interpolated onto a grid 10 times denser than the common one (150 m × 100 m) and temporally interpolated at 10 times higher sampling rate (0.04 s).
- The slip rates evaluated on the dense grid are smoothed by a running mean over 10 × 10 samples in space and 10 samples in time.
- The slip rates are then downsampled to 1.5 km × 1.0 km and 0.4 s.

This procedure correctly captures the shape of the slip-rate functions considered by the authors; that is, it minimizes aliasing effects that could be significant, especially when dealing with sharp triangular slip rates considered in some of the methods (see Table S1).

Table S1. List of the inverted models of the SIV2a benchmark with brief explanation of the applied inversion techniques.

Figure S1. Inversion results of the SIV2a benchmark obtained by various authors (see Table S1): slip distributions (top-most panels) and slip-rate snapshots (bottom panels).

Figure S2. Target model and individual inversion results (columns) truncated with cut-off at 1/10 of the largest singular value: slip distributions (top-most panels) and slip-rate snapshots (bottom panels). The original target model is shown on the left for reference and is in the same color scale.

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