| Problem Statement | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
To date, ground motion simulations of the Canterbury earthquakes have been carried out using the Graves and Pitarka (2010) hybrid broadband ground motion simulation methodology which combined deterministic finite difference simulations at low frequencies with stochastic simulations at high frequencies. However, this methodology does not include tomographic waveform inversion capabilities and therefore other methodologies must be employed to integrate seismic waveform data to improve the Canterbury Velocity Model (CantVM). Specfem3D is a spectral element-based method which has tomographic waveform inversion capabilties which can be utilized in improving the CantVM. In order to verify that our installation and usage of the Specfem3D software is correct, results from Specfem3D are compared against results from the deterministic low frequency simulations from Graves and Pitarka (2010) (Emod3D) for several scenarios. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Project Members | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Robin Lee, Brendon Bradley, and Seokho Jeong (QuakeCoRE) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Description (Objectives / Outcomes) | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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Tasks | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Produce the following inputs for Specfem3D and Emod3D:
Run the Specfem3D and Emod3D simulations while varying the following parameters:
Compare the output from Specfem3D and Emod3D by examining:
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Schedule | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
This project is currently ongoing, the provided schedule is a rough outline of what has been completed to date and what is expected in the foreseeable future: June - Installation of Specfem3D on local machine and HPC (Fitzroy). July - Learning to use Specfem3D and running the test case examples. August - Producing inputs for Specfem3D, running real cases for Specfem3D. September - Learning to run Emod3D, producing inputs consistent with Specfem3D, improving post-processing. October - Comparison of Specfem3D and Emod3D outputs through waveform comparisons, Fourier spectra, Intensity measures and goodness of fit. November - Finalize comparisons and properly document results. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Verification | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
As the Specfem3D and Emod3D methodologies have different formulations of the wave propagation problem, and hence take different inputs, the methods have some inherent differences which can lead to differences in their output. The following two sections documents the specific details of the Specfem3D and Emod3D simulations carried out and the controls taken to ensure as much consistency between how the two methods are utilized. The prescribed velocities for both methods are determined from the NZVM code developed by Thomson et al. (2017) using the same parameters (although the specfem input required some additional postprocessing). Specfem3D Simulation Details
Emod3D Simulation Details
Simulation Domain The domain of interest for the verification is a rectangular subregion of the Canterbury region spanning longitudes [172.25° 172.75°] and latitudes [-43.8° -43.4°] as shown in Figure 1. 7 sites of varying azimuth from the source are chosen as locations where the comparisons are carried out and are also shown in Figure 1. This provides various ray paths through the various velocity models considered which can be used to differentiate different physical phenomena observed from the simulations.
Figure 1. Verification domain for the 19th October 2010 earthquake including the source and station locations. Both Specfem3D and Emod3D will be run as equivalently as possible for several scenarios (as shown in Table 1 of the Results section) provided the inherent differences in the numerical methods (and current limitations and issues). The output from Specfem3D and Emod3D are filtered at various frequencies to determine their similarities and differences within different frequency bands, highlighting in particular the difference between frequencies which the simulation configurations can and cannot resolve. The frequency bands considered are 0.05-0.2Hz, 0.05-0.5Hz and 0.05-1Hz. Considering the configuration of the simulations, the highest frequencies which can be resolved should be roughly 0.5Hz (considering 5 nodes per wavelength). Hence the frequency band of 0.05-0.2Hz highlights the well resolved components of the output, the frequency band of 0.05-0.5Hz highlights what is expected to be resolved of the output, and the frequency band of 0.05-1Hz highlights the output with the inclusion of unresolved frequencies. In this regard, the frequency band of 0.05-0.2Hz has the greatest weight in determining the verdict of the verification, followed by the frequency band of 0.05-0.5Hz, and lastly the frequency band of 0.05-1Hz is provided to solely show the effect of including unresolved frequencies. Result The scenarios with their respective parameters are listed in Table 1 along with the results of and comments on the verification. While it is not plausible to include all results here, the CBGS site is used as an example here to highlight the main features of the comparison. Other important features are mentioned in either the notes/figures in Table 1 or in the Discussion and Conclusions. Table 1. Results of the Specfem3D and Emod3D comparisons for the various scenarios tested.
Discussion and Conclusions The verification process has concluded that the outputs from Specfem3D and Emod3D are practically exact in some scenarios, and similar in others for the relevant frequencies. In particular, smooth velocity models (such as the homogeneous halfspace and tomography only models) produce practically exact results between Specfem3D and Emod3D. Sharp models (1D velocity, tomography + 1D basin, and tomography + 3D basin models) which have sharp interfaces produce increasing differences in the phase of later arrivals but match first arrivals and amplitudes in general well. The findings here are supported by work carried out by Chaljub (2015) who also found Specfem3D to lag behind other numerical wave propagation methods, including finite difference schemes. The differences here are likely attributed to the formulation of the wave propagation problem between each method as well as the discrete representation of the velocity model input. Chaljub (2015) has presented some options to mitigate these problems. The primary solution to this problem is to create a mesh which has edges which follow the velocity interfaces (sharp changes in velocity, such as geologic unit boundaries). This removes any element which crosses velocity interfaces and therefore removes the need for sharp changes in velocities to occur within elements. However, the computational requirement to produce this kind of mesh, and also to run the simulations in 3D are beyond what is currently plausible. The second solution to this problem is to smooth the velocity model such that the sharp velocity interfaces are not as significant. However, the purpose of using the Specfem3D code is for tomographic waveform inversion to improve the velocity model which intrinsically smooths the velocity model. With this overarching objective in mind, it seems unreasonable to manually smooth the velocity model. Numerical dispersion and instability is also a likely factor for the differences observed, as seen in the Fourier spectra where the low frequencies are reasonably consistent between the two methods, but significantly different at higher frequencies. As the methods are only expected to resolve up to roughly 0.5Hz, the significant differences in Fourier amplitude above the cutoff frequency likely cause some differences in the time series. Therefore results which are filtered at a lower cutoff frequency, such as 0.2Hz, are given more weight in determining the results of the verification. Considering the overarching objective of ground motion simulations in Specfem3D, inherent differences in the two simulation methodologies, and current limitations, the verification of Specfem3D and Emod3D is considered a success. |
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