Time-scale phase-weighted stack

Software to compute the time-scale phase-weighted stack (ts-PWS), including the two-stage stack and the unbiased phase coherence strategies (Ventosa et al., GJI 2017).

The software packages of fast phase cross-correlation and ts-PWS stacking are basic building blocks in the design of efficient signal extraction methods from interstation correlations.

Main features

• Fast: The time-frequency expansion used in the ts-PWS is implemented using frames of wavelets (Morlet and Mexican hat wavelets are available). The most demanding operation is conventionally reading the data.
• Better filtering: The two-stage stacking and the unbiased phase coherence help to reduce signal attenuation and increase noise attenation.
• Simple setup: All parameters are automatically set, e.g., when w0, Q or number of cycles is changed the parameters describing the frame are adapted accordingly.
• Resampling techniques: The bootstrap and jackknife techniques can be applied to build a pull of stacked sequences for a subsequent error analysis.

Compilation

To compile execute "make" in the src directory. Use "make clean" to remove any previouly compiled code.

• The Seismic Analysis Code (SAC) is used to read and write sac files.
• The SACHOME enviorment variable should provide the path to directory where sac is installed. For example, in bash this can be defined as:
  export SACHOME=/opt/sac
  Change "/opt/sac" to your current sac directory if necessary.
• OpenMP is used to speed up computations. When OpenMP is not available, use make -f makefile_NoOpenMP".

Compile SAC

The precompiled sac libraries may not work in some systems/compilers. If you use the gcc compiler on, e.g., Ubuntu you may have errors similar to:

/usr/bin/ld: /opt/sac/lib/sacio.a(getfhv.o): relocation R_X86_64_32 against undefined symbol 'kmlhf' can not be used when making a PIE object; recompile with -fPIC

This can be solved by compiling the source version of SAC. From the source directory of sac do:

./configure --enable-optim=2 --prefix=/opt/sac CFLAGS='-march=native -fPIC' \ make \ make install

The key detail here is the -fPIC flag, you can adapt the other options to your needs. The flag --prefix=/opt/sac sets the directory where sac will be installed when doing "make install". You can change this directory, e.g., to keep using your current version of SAC for other purposes.

Warming up

1. Read ./examples/example.sh
2. Execute it, e.g., bash example.sh
3. Do ts-pws for the parameters usage.

Origin of PWS

Schimmel M. & J. Gallart, 2007. Frequency-dependent phase coherence for noise suppression in seismic array data, Journal of Geophysical Research, 112, B04303, doi: 10.1029/2006JB004680

Schimmel M. & H. Paulssen, 1997. Noise reduction and detection of weak, coherent signals through phase weighted stacks, Geophysical Journal International, 130, 497-505, doi: 10.1111/j.1365-246X.1997.tb05664.x

Paper to be cited

Ventosa S., Schimmel M. & E. Stutzmann, 2017. Extracting surface waves, hum and normal modes: Time-scale phase-weighted stack and beyond, Geophysical Journal International, 211(1), 30-44, doi: 10.1093/gji/ggx284

2024/06/26 Sergi Ventosa Rahuet (sergiventosa(at)hotmail.com)