membraneSphere - membrane waves on a spherical Earth

membraneSphere is a software package to simulate waves on a spherical membrane. It implements the membrane wave method introduced by Tanimoto (1990). Membrane waves are an analogue for seismic surface waves. The zero-thickness sphere is discretized by a geodesic grid (Tape, 2003). Wave propagation on this sphere is solved by a finite-difference scheme for such hexagonal grids (Tape, 2003; Heikes & Randall, 1995a).

The theory behind this software implementation of the membrane waves is explained in these publications:

• Peter, D., C. Tape, L. Boschi and J. H. Woodhouse, 2007.
  Surface wave tomography: global membrane waves and adjoint methods,
  Geophys. J. Int., 171: p. 1098-1117.
  doi:10.1111/j.1365-246X.2007.03554.x

• Tape, C. H., 2003.
  Waves on a Spherical Membrane,
  M.Sc. thesis, University of Oxford, U.K.
  thesis membrane

Quick start

Installation and compilation

Download sources: $ git clone https://github.com/danielpeter/membraneSphere.git

Compile binaries: $ cd membraneSphere/ $ ./configure $ make all

The compilation requires to have a Fortran compiler and corresponding MPI library installed on your system. To use a specific compiler, one can for example run the configuration for an Intel compiler installation with $ ./configure FC=ifort MPIFC=mpiifort You can also modify the Makefile according to your specific needs.

Run a membrane wave simulation

Go to the examples/Love_waves_150s/ folder: $ cd examples/Love_waves_150s/ and run the simulation script: $ ./run_this_example.sh

This will run two membrane wave simulations, one for a homogeneous phase-velocity map and another one with a heterogeneous phase-velocity map. It then computes the cross-correlation time lag between the two resulting traces.

Details

Infos about the repository folders

• data/griddata/

  holds the data for the grid construction

• data/phasedata/

  has two examples of phase speed models which can be used for a heterogeneous background earth in the membrane wave simulation

• src/propagation/

  the main executables propagation, timelag & adjointMethod are located therein

• src/include/

  contains source files for routines

Main executables are in the folder src/propagation/

• propagation.f90 - forward modeling of membrane waves

  The main program 'propagation' calculates a simulation of membrane waves propagating over a sphere.

  It reads the main input file Parameter_Input. Other parameters can be set in the commonModules.f90 file.

  File output is the seismogram (format: time/displacement, time in seconds), written in the data directory given in Parameter_Input.

  For checking, it also outputs the used phase map (format: longitude/latitude/phasespeed) and the phase speed squared at the vertices (format: verticeID/phasespeedsquared).

  Visualization of the seismograms can be done with the GNUPLOT application. The scripts/ folder holds a bash-script for visualization of the phase map with GMT.

• adjointMethod.f90 - kernel construction by membrane waves

  The executable performs a simulation, where no scatterer is present, and calculates the adjoint source. Then it makes a time-reversed simulation and computes the kernel values.

  It reads the main input file Parameter_Input. Other parameters can be set in the commonModules.f90 file.

  The kernel values are written to a file in the data directory given in Parameter_Input (format: longitude/latitude/kernelvalue/vertexID). Kernel values are evaluated at the vertices of the spherical membrane grid only. The kernel-file name can be set in Parameter_Input as well.

  To visualize the kernel, there are two bash-scripts in the scripts/ folder using GMT. These scripts gmtplot_2Dkernel.sh (plot as 2D map) and gmtplot_3Dkernel.sh (plot in 3D perspective) interpolate the kernel file and output cross-sections at different longitudes as well.

• timelag.f90 - phase shift/time shift of two seismograms

  This utility program calculates the time lag between two seismograms.

  It reads only the input file Timelag_Input. Other parameters (especially the filter parameters) are taken from commonModules.f90.

  The time shift result is written to the console.

• heterogeneousPhaseshift.f90 - synthetic phase-shift calculations

  This program outputs a synthetic database of phase-shift measurements for any heterogeneous input model.

  Given a source/station file specified in the Parameter_Input file, it numerically calculates the phase shift for each particular setup, based on cross-correlations between a reference trace (PREM) and the synthetic trace for any heterogeneous background phase-velocity model.

Parameters to change on different machines

• codes are written in Fortran90, use the appropriate compiler flags in the Makefile by setting F90, FFLAGS, LDFLAGS

• in src/include/constants.h you have to choose precision (use single, it'll do).

• in src/include/commonModules.f90 you have to choose source parameters (see Carl Tape's thesis) and filter parameters. There are also a few others, but defaults should do it.

• For simulation runs, you probably want to create a new work directory. Examples are given in examples/ subdirectory. The main program propagation reads in simulation parameters from file Parameter_Input, where you can choose the physical model (grid refinement level, simulation times and wave type) and set the source/receiver geometry. You can also select to place a scatterer and/or use a heterogeneous background phase speed model.

The program timelag reads in parameters from file Timelag_Input. You would want to specify two traces and a window size to compute the time lag between those trace sections.