PTAM

September 30, 2021 · View on GitHub

Peak Trough Averaging Method (峰谷平均法).

License

The MIT License

Author

Tche LIU, seistche@gmail.com, USTC

Description

mod_ptam is a fortran module used to implement the peak trough averaging method (PTAM) to an external function.

To illustrate how to use the fortran module, I take the equation (6b) in (张海明等, 2001) as an example:

∫0+∞e−αkJ1(βk)dk=1β[1−αα2+β2]\int_0^{+ \infty} e^{ - \alpha k} J_1 (\beta k) dk = \frac{1}{\beta} \left[ 1 - \frac{\alpha}{\sqrt{\alpha^2 + \beta^2}} \right]

In the source file main.F90, I defined a function exfunc followed the example formula. After compiling the source files by gfortran mod_ptam.F90 main.F90 -o a.out, we can run the example by ./a.out, and the output will be similar with the following:

The PTAM result is: 0.333209425
The analytical result is: 0.333222240
The relative error is: -0.384578125E-4

Besides, example is a simple and useful instance that do NOT use the completely accurate algorithm of PTAM as mod_ptam.

Reference

  • 张海明, 陈晓非, 张似洪, (2001). 峰谷平均法及其在计算浅源合成地震图中的应用. 地球物理学报: 44(6), 805-813
  • Zhang, H. M. , Chen, X. F. , & Chang, S., (2003). An efficient numerical method for computing synthetic seismograms for a layered half-space with sources and receivers at close or same depths. Birkhäuser Basel.