Adaptive Stacking


Adaptive stacking provides a powerful and rapid procedure for estimating traveltime residual patterns across a network of seismic stations. The approach exploits predictions from some propagation model to achieve an approximate alignment of traces which are then stacked to form a reference trace. Iterative improvement of the alignment by comparison of the reference trace with each station trace leads to a direct estimate of the residuals from the propagation model. Our implementation is fast and robust in the presence of significant noise and waveforms of different character. The major difference from earlier forms is the use of a direct minimization scheme for determining the best match between the reference stacked trace and each recorded trace based on an L3 measure of misfit. This approach has the benefit of generating automatic error estimates. For teleseismic applications, the ak135 model has proved to be very effective for selection of the window around the desired phase and in achieving initial alignment. The approach can be applied to both first motion (P) and later phases (e.g. PcP), with extraction of absolute time via the improved signal to noise properties of the stacked trace, after full alignment.

The paper below gives a detailed description of adaptive stacking, its history, and potential applications. References are also made to papers which describe other residual estimation techniques, such as Multi-Channel Cross Correlation (MCCC) and optimum trace construction with simulated annealing. Several examples which demonstrate adaptive stacking with real array data are also provided.

Adaptive Stacking Code

The adaptive stacking code is written in FORTRAN 77, and should run on most computers that have access to a fortran compiler such as g77. The complete source code, a detailed manual and example input files, can be downloaded here. Enquires should be directed to the author. You will need to register with iEarth prior to download.

To unpack the contents of this file, type something like:

gunzip -c tcasv1.0.tar.gz | tar xvof -

The contents of the tar archive will be placed in a subdirectory called astack.

ak135 Moveout Corrections

In order to use the adaptive stacking code, the input data (in the form of trace time series) will need to be approximately aligned using model predictions. In the case of teleseismic data, ak135 moveout corrections should be sufficient. These can be obtained using the ttimes traveltime software that is available for free at:

Alternatively, a simpler version of ttimes that only permits list input and output for a specified phase called aktime can be downloaded here, and should be easy enough to incorporate in your data extraction program.

To unpack the contents of this file, type something like:

gunzip -c aktimev1.0.tar.gz | tar xvof -

The contents of the tar archive will be placed in a subdirectory called aktime . A README.txt file explains how to compile and run the program.


    Rapid estimation of relative and absolute delay times across a network by adaptive stacking. , Rawlinson, N. and Kennett, B. L. N.Geophys. J. Int., 157 , 332-340, 2004. doi:10.1111/j.1365-246X.2004.02188.x