Radon transform p ( s , ) f ( x , y ) ( x c y s o s ) d is n x
where p is the radon transform of f(x, y), and is a Dirac Delta Function (an infinite spike
3. AK135 速度模型 Kennett et al. (1995)；
Montagner and Kennett (1996).
另外 还有： MC35， STW105， TNA/SNA.模型等
• • 莫霍诺维齐（前南斯拉夫）——莫霍面（壳幔边界） • －－地壳与地幔分界面的发现者
• 古登堡（美国）——核幔边界 • －－地幔与地核分界面的发现者
at 0 with an integral area of 1) p is also called sinogram, and it is a sine wave when f(x, y) is a point value.
.
Shepp-Logan Phantom (human cerebral)
Present Generation of models: Dense receiver sets, all rotating, great coverage and crossing rays.
Brain Scanning Cool Fact:
According to an earlier report, the best valentine’s gift to your love ones is a freshly taken brainogram. The spots of red shows your love, not your words!
• 莱曼（丹麦，女）—— （内外核边界）
•
－－外核与内核分界面的发现者
.
地球一维结构是远远不够的！ Plate tectonics
Topography
.
mantle convection
Travel time table from ak135 model
Travel time picks
.
Shearer, 2009
第六章 地震层析成像
.
From IRIS
Seismic waves
• Seismic wave is currently the only effective tool that can penetrate the entire earth
.
1939:
Jeffreys & Bullen
First travel-time tables：JeffreysBullen Seismological Tables 区域地震层. 析成像
大洋中脊 区域地震层. 析成像
俯冲带 区域地震层. 析成像
局部地震层析成像
.
地震层析成像的基础——Radon 变换 Tomo— Greek for “tomos” (body), graphy --- study or subject Where it all began: Radon transform: (Johan Radon, 1917): integral of function over a straight line segment.
3-D variations of Earth’s Structure from Seismic Tomography
Seismic waves in the Earth
Traveltime/waveform
3-D wave speeds
Inverse problem
Researchers at MIT and Harvard, led by Keiti Aki and Adam Dziewonski in late 1970’s and 1980’s, pioneered the technique of se.ismic tomography.
Input
Radon Projected
Recovered (output)
Back projection of the function is a way to solve f() from p()
(“Inversion”):
f ( x , y ) p ( x c y s o ) ) d i , s n
Cunningham & Jurdy, 2000
Broader fan beam, Moving source, fixed receivers, fast moving (1976)
Different “generations” of X-Ray Computed Tomography (angled beams are used to increase resolution). Moral: .good coverage & cross-crossing
PREM模型给出了地球的一维结构，而地球内部三维结构需要更精细的刻画。 地震层析成像方法是给出地球内部三维结构的最重要的方法。 某种意义上说，地震是照亮地球内部的明灯。 地震层析成像方法可以给出：
全球地球结构的横向不均匀性； 典型地球动力学过程的三维结构：俯冲带、地幔柱、大洋中脊等； 小尺度的构造（断层等）； 地震分布特征。
0
.
A few of the early medical tomo setups
Parallel beam
Fan beam, Multi-receiver, Moves in big steps
Broader fan beam, Coupled, moving source receivers, fast moving
→ 1D Earth model
Jeffreys-Bullen 1-D Earth Model
.
地球内部结构
PREM一维全球速度模型
1. PREM参考地球模型： Preliminary Reference Earth Model (Dziewonski & Anderson, 1981)
2. IASP91速度模型 (Kennett and Engdahl, 1991)