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To check this assumption, we performed an additional inversion test.

Figure 2 Synthetic data used in the inversion test.

We also conducted the inversion test with a smoothly varying circular slip distribution (Fig. 3).

For the numerical inversion test, we calculated the true values of these hyperparameters from the true slip s t.

The robust solvability of the transition problem is establisheda priorivia a dynamic inversion test, and the actual transition is constructed by solving a dynamic optimization problem.

A numerical inversion test was conducted to assess how efficiently the proposed method can reproduce the original distribution of slip from noise-overlapped synthetic displacement data.

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Synthetic inversion tests.

Our inversion tests support our interpretation of the simulations.

Synthetic inversion tests were able to show the effectiveness and validity of the proposed model by appropriately reducing the statistical noise from the observations.

We confirmed that these differences are significant and not artifacts because of the high conductivity at the uppermost layers, through synthetic inversion tests (see Additional file 2: Figure S2).

Inversion tests are similar to those for the type 1 model and appear to trace the most conductive profile in mid-lithosphere but are consistent with the average profile in the lower lithosphere.

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