The Institute of Statistical Mathematics

Jun 9, 2023 (Ver. 1.0.9-1)

[Japanese/English]

1. Introduction

SASeis (Statistical Analysis of Seismicity) is a program package for statistical analysis and modeling of point process time series such as seismic activity and has been developed at the Institute of Statistical Mathematics. This program package collects TIMSAC84-SASE Version 2, SASeis-W (SASeis for Windows), IASPEI-SASeis-VB (SASeis Visual Basic) and SASeis2006. The source files of TIMSAC84-SASE Version 2 and SASeis2006 are written in FORTRAN77 and output numerical files for graphics.

Each of the software packages TIMSAC84-SASE Version 2 and SASeis2006 are published in Computer Science Monographs No.32 and 33. TIMSAC84-SASE Version 2 is an updated version of TIMSAC84-SASE by Ogata and Katsura, which is published in Computer Science Monographs No.23. The programs in the original TIMSAC package for point-process analysis were developed for the PCDOS (Utsu and Ogata, 1977) 4. The main features of the updation is that the calculation outputs are simplified by removing the GPSL language for plotting the figures. In SASeis2006 parameter values in the Omori-Utsu formula and the ETAS (Epidemic Type Aftershock Sequence) model are estimated. The Omori-Utsu formula is an empirical relation for the temporal decay of aftershock rates. The ETAS model is an extension of the Omori-Utsu formula, and it can be used to appropriately evaluate background seismic activity and represent characteristics of seismic activity of the region. The residual between the aftershock activity and the theoretical curve can be used for the diagnostic analysis or the detection of anomalies in the aftershock sequence.


2．Package functions

We provide following functions corresponding to each Fortran source file of TIMSAC84-SASE Version 2 and SASeis2006. Although source files eptren.f and pgraph.f are included in both packages, eptren() and pgraph() are based on the update version in SASeis2006．

ptspec() :

　　 Provide the periodogram of point process data with the significant band (0.90, 0.95 and 0.99) of the maximum power in searching a cyclic component for stationary Poisson Process.

linlin() :

　　 Perform the maximum likelihood estimates of linear intensity models of self-exciting point process with another point process input, cyclic and trend components.

simbvh() :

　　Perform the simulation of bi-variate Hawkes’ mutually exciting point processes.

linsim() :

　　 Perform simulation of a self-exciting point process whose intensity also includes a component triggered by another given point process data and a non-stationary Poisson trend.

momori() :

　　Compute the maximum likelihood estimates (MLEs) of parameters in the Omori-Utsu (modified Omori) formula representing for the decay of occurrence rate of aftershocks with time.

eptren() :

　　Compute the maximum likelihood estimates of intensity rates of either exponential polynomial or exponential Fourier series of non-stationary Poisson process models.

etasap() :

　　Compute the maximum likelihood estimates of five parameters of ETAS model.

etasim() :

　　Produce simulated dataset for given sets of parameters in the point process model used in ETAS.

pgraph() :

　　Provide the several graphical outputs for the point process data set.

respoi() :

　　Compute the residual of modified Omori Poisson process and display the cumulative curve and magnitude vs. transformed time.

etarpp()

　　Compute the residual data using the ETAS model with MLEs.


Execution example

The Following figures show trend and cycle of intensity rates after running eptren()．

Execution example 1 of eptren() eptren()の実行結果2

The following figure shows that predicted seismic activity (red line) by the ETAS model using etarpp() fits well. Actual earthquake frequency is considered active if it is higher than the prediction, on the other hand inactive if it is lower.

Execution example of etarpp()


3. Package installation

We provide source files and binaries built with R-4.2.3 on Windows 11.
SAPP packages are registered as Contributed Packages, and binaries for macOS can be downloaded here.

3.1 Installation on Windows
  1. Download the binary SAPP_1.0.9-1.zip to a suitable folder, then start R (RGui).

  2. From the Packages menu
    　　 —> Install package(s) from local zip files…
    　　 —> Select files
    　　 —> SAPP_1.0.9-1.zip
    3. 　
  3. From the Packages menu
    　　 —> Load Package..
    　　 —> Select one
    　　 —> SAPP
  4. For details on models, see “A Guide to SAPP”.
    　　> vignette(“SAPP”)
3.2 Installation on Linux
  1. Download the source file SAPP_1.0.9-1.tar.gz to a suitable directory.

  2. Start R in a terminal, and then type
    　　> install.packages(“download path/SAPP_1.0.9-1.tar.gz”, repos=NULL)
    　　> library(SAPP)

  3. For details on models, see “A Guide to SAPP”.
    　　> vignette(“SAPP”)

You can download the reference manual here.



4. References

[1] H. Akaike, T. Ozaki, M. Ishiguro, Y. Ogata, G. Kitagawa, Y. Tamura, E. Arahata, K. Katsura and R. Tamura (1985).
TIMSAC-84 Part 2, Computer Science Monographs, No.23, The Institute of Statistical Mathematics, Tokyo.

[2] Y. Ogata, K. Katsura and J. Zhuang (2006).
Statistical Analysis of Series of Events (TIMSAC84-SASE) Version 2, Computer Science Monographs, No.32, The Institute of Statistical Mathematics, Tokyo.

[3] Y. Ogata (2006). Statistical Analysis of Seismicity - updated version (SASeis2006), Computer Science Monographs, No.33,
The Institute of Statistical Mathematics, Tokyo.

Please send bug reports to ismrp(at)grp.ism.ac.jp.