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Continents: Qucik review. Surface wave Tomography Love waves-SH Raleigh waves-P-SV Sinusoidal-acoustic
๏จEvanescence wave ๐ด ๐ง โ eโฮทฯ^ z
low frequency wave is more sensitive to deep structure. Therefore, low frequency wave should
arrive earlier than high frequency wave.
๏จDifferent modes: Fundamental and Higher modes/overtones.
Surface wave Tomography
Recall from the travel time tomography:
๐
= ๐จ๐ (1)
where ๐
, is the data; ๐จ , is the projector; and ๐ is the model.
๐๐๐๐๐๐
Where ๐
๐ is the observation; ๐ฎ๐ ๐ is greenโs function/kernel (Sensitivity kernel) e.g. travel time
tomography; and ๐ ๐ is the model perturbation.
๐น๐ = ๐ป๐๐๐ โ ๐ป๐๐๐ = (^) ๐๐๐๐ โ๐๐
๐Integration over the ray path (3)
Slower, increasing ฮป
decreasing ฯ
Sensitivity kernel
wavespeed
decreasing ฯ
ฯ
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When we do surface wave tomography, we measure the phase (or group) velocity:๏ค ci
for an earthquake i. As with the body wave tomography, we will look at perturbations between the model and the data:
๐ค๐๐ฃ๐๐ ๐๐๐ก โ
๐ด๐^ ๐ = ๐ด๐^ ๐ด๐
(๐ด๐^ ๐ด)โ^1 ๐ดโ^1 ๐ = ๐
Those phase velocity maps are first constructed for a particular frequency. But, because of the evanescence of the surface waves, we can see what frequency is sensitive to a particular depth.
Convert ๏ท to z. To do so, we look at the sensitivity kernel for different frequencies. We use
๏ถ c ๏ถ๏ข
and we get
๐ค๐๐ฃ๐๐ ๐๐๐ก โ
is a phase velocity map of particular frequency ๐.
receiver Source
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Figure: Sensitivity of 1-D waveform inversions to focal depths. The effects of varying focal depth for two events: (a) focal depth 2 km (b) focal depth 9 km. Fits of final synthetic (dashed) to observed (solid) seismograms for shifts in focal depths of 10-50 km are shown on the left and the corresponding inversion velocity models (thin lines) are shown on the right along with the velocity model for the correct depth (thick line). The misfit and maximum frequency achieved by the waveform inversion are denoted to the right of each waveform fit. Maggi, Alessia & Priestley, Keith Surface waveform tomography of the Turkish-Iranian plateau. Geophysical Journal International 160 (3), 1068-1080. doi: 10.1111/j.1365-246X.2005.02505.x
Updated by: Sami Alsaadan Sources: April 20,2005 by Sophie Michelet โAn Introdution to Seismology, Earthquakes, And Earth Structureโ by Stein &Wysession (2007).
Figure removed due to copyright restrictions.
