Fast Computation of Global Sensitivity Kernel Database based on Spectral-element Simulations

This site is a companion to the paper Fast Computation of Global Sensitivity Kernel Database based on Spectral-element Simulations, by E. Sales de Andrade and Q. Liu, submitted to Pure and Applied Geophysics.

In it, we take advantage of the symmetry of 1D reference models to efficiently compute sensitivity kernels for seismic phases at any epicentral distance using a pre-computed strain field database, which significantly reduces both the number of simulations and the amount of storage required. We compute traveltime, amplitude and/or boundary kernels of isotropic and radially anisotropic elastic parameters for various (P, S, Pdiff, Sdiff, depth, surface-reflected, surface-wave, S660S boundary, etc.) phases for 1D ak135 model, in preparation for future global tomographic inversions.

Examples

Some example images from the paper follow, as described with the figure:

Fig. 3 (a) K α cross-correlation traveltime kernel for vertical P waves recorded at a station (red inverse triangle) of 60° epicentral distance on the surface. An explosive source (denoted by the red star) is placed on the surface. The corresponding ray path between the source and receiver in the 1D ak135 model is indicated by the black line. (b) The vertical velocity seismogram recorded at the receiver used to produce the adjoint source. The time window of the P phase is indicated by the black box and the theoretical arrival time predicted by the ray theory is indicated by the red line. Additional arrivals are also identified in red above the phases. The velocity axis is given here in ×10-9 m / s and in all subsequent figures for traveltime kernels. (c) K α cross-correlation kernel computed using the adjoint method of Liu and Tromp, 2006 for the same setup as (a).
Fig. 4 (a) K α cross-correlation amplitude kernel for the P phase at an epicentral distance of 60°. Amplitude kernels do not have the doughnut shape and have significant sensitivity right on the ray path. (b) The vertical displacement seismogram recorded at the receiver which is windowed at the P phase to produce the corresponding adjoint source. For displacement seismograms, the vertical axis is given in ×10-6 m. The theoretical arrival predicted by ray theory is indicated by the red vertical line. Additional arrivals are also identified in red above the phases.
Fig. 5 (a) The K β traveltime kernel for the SH phase shown for a station at epicentral distance of 60°. This kernel is thinner with larger amplitudes than the P phase kernel in Fig. 3. (b) The transverse-component velocity seismogram recorded at the receiver used to produce the adjoint field. The theoretical arrival predicted by ray theory is indicated by the red vertical line. Additional arrivals are also identified in red above the phases.
Fig. 6 (a) The K β amplitude kernel for the SH phase at an epicentral distance of 60°. (b) The transverse-component velocity seismogram at the receiver with the SH phase windowed to produce the adjoint field.
Fig. 7 (a) K α kernel at an epicentral distance of 110° for the Pdiff phase that diffracts along the CMB before returning to the surface. Unlike the predicted ray path (black line), this kernel covers regions up to several hundred kilometres above the theoretical diffracted path along CMB. (b) Map view of the same kernel on the CMB. The kernel sensitivity shows an elliptical pattern, sampling a much larger area than the diffracted ray path (shown as thick black line). (c) The windowed Pdiff phase on the vertical velocity seismogram recorded at the receiver used to produce the adjoint source.
Fig. 8 Similar to Fig. 7 but for Sdiff phase.
Fig. 9 (a) K β kernel for the ScS phase at 60° epicentral distance. (b) Map view of the same kernel on the CMB. The reflection point is indicated by a black cross. (c) The transverse-component velocity seismogram recorded at the receiver used to generate the adjoint source. Note, the seismogram has been cropped outside the ± 400 ×10-9 km / s range to ensure the ScS phase is more prominently displayed.
Fig. 10 (a) K α kernel for the surface-reflected PP phase at an epicentral distance of 114°. The kernel exhibits more complex sensitivity in the vicinity of the reflection point compared to the predicted theoretical ray path. (b) Map view of the same kernel at a depth of 50 km, showing the characteristic ‘X’ pattern below the reflection point indicated by a black cross. (c) The PP phase window on the vertical velocity seismogram used to produce the adjoint field.
Fig. 11 (a) K β kernel for the SS phase shown here at an epicentral distance of 114°. (b) Map view of the same kernel at a depth of 50 km. (c) The SS phase window on the transverse velocity seismogram used to produce the adjoint field.
Fig. 12 (a) The K β traveltime kernel for the S660S phase at an epicentral distance of 140°. (b) Map view of the K d boundary kernel for the same phase as (a) for the 660 km discontinuity, showing the characteristic ‘X’ pattern below the reflection point indicated by a black cross. (c) The S660S phase window on the transverse velocity seismogram used to produce the adjoint field. Note that since this phase is fairly weak, the nearby SS phase has been cropped.
Fig. 13 (a) K β kernel for the sS phase at an epicentral distance of 90° for a source at 650 km depth. (b) Map view of the same kernel at a depth of 100 km. (c) The sS phase window on the transverse velocity seismogram used to produce the adjoint field.
Fig. 14 (a) Surface view of the K β kernel for Rayleigh waves filtered between 60 s -- 80 s for a station at an epicentral distance of 60° and a source at 15 km depth. (b) The same K β kernel in cross-section view. (c) Cross-section view of the corresponding K α kernel for the Rayleigh waves.
Fig. 15 Anisotropic sensitivity kernels for the P phase at an epicentral distance of 76° with a source at 600 km depth for the Love parameters (a) A (b) C (c) F (d) L and (e) N , and for the alternative transverse isotropic parameters (f) η (g) α h (h) α v (j) β h and (k) β v , and for the isotropic parameters (i) α and (l) β calculated from the averaging of anisotropic parameters.
Fig. 16 Anisotropic sensitivity kernels for the SH phase at an epicentral distance of 76° with the source at 600 km depth for the Love parameters (a) A (b) C (c) F (d) L and (e) N , and for the alternative transverse anisotropic parameters (f) η (g) α h (h) α v (j) β h and (k) β v , and for the isotropic parameters (i) α and (l) β calculated from the anisotropic parameters.

Downloads

The source code for SPECFEM3D_GLOBE patched to output strain fields as required by the paper may be downloaded here. Code to pick seismograms and combine strain fields into sensitivity kernels may be obtained here. Please see the README file within this package for information on its usage.

References

LT06
Qinya Liu and Jeroen Tromp. Finite-frequency kernels based on adjoint methods. Bulletin of the Seismological Society of America, 96:2383–2397, December 2006. doi:10.1785/0120060041.