**IFOS2D** (**I**nversion of **F**ull **O**bserved **S**eismograms) is a 2D elastic full waveform inversion code.
**IFOS2D** (**I**nversion of **F**ull **O**bserved **S**eismograms) is a 2-D elastic full waveform inversion code.
The inversion problem is solved by a conjugate gradient method and the gradients are computed in the time domain with the adjoint method.
The inversion problem is solved by a conjugate gradient method and the gradients are computed in the time domain by the adjoint state method.
The forward modeling is done by a time domain finite difference scheme.
The forward modeling is done by a time domain Finite-Difference scheme.
IFOS2D is the reverse (inverse) of our 2D finite difference forward solver [**SOFI2D**](https://git.scc.kit.edu/GPIAG-Software/SOFI2D).
IFOS2D is the reverse (inverse) of our 2-D Finite-Difference forward solver [**SOFI2D**](https://git.scc.kit.edu/GPIAG-Software/SOFI2D).
The [**manual**](https://git.scc.kit.edu/GPIAG-Software/IFOS2D/wikis/home) is included in the download archive or can be downloaded [here](https://git.scc.kit.edu/GPIAG-Software/IFOS2D/wikis/home).
The [**manual**](https://git.scc.kit.edu/GPIAG-Software/IFOS2D/wikis/home) is included in the download archive or can be downloaded [here](https://git.scc.kit.edu/GPIAG-Software/IFOS2D/wikis/home).
# Download and Newsletter
# Download and Newsletter
You can Download the [**latest Release**](https://git.scc.kit.edu/GPIAG-Software/IFOS2D/tags/Release_2.0) or the current [**Beta-Version**](https://git.scc.kit.edu/GPIAG-Software/IFOS2D/tree/master)
You can download the [**latest Release**](https://git.scc.kit.edu/GPIAG-Software/IFOS2D/tags/Release_2.0.1) or the current [**Beta-Version**](https://git.scc.kit.edu/GPIAG-Software/IFOS2D/tree/develop).
To receive news and updates please [register](http://www.gpi.kit.edu/Software-FWI.php) on the email list [IFOS@lists.kit.edu](http://www.gpi.kit.edu/Software-FWI.php).
To receive news and updates please [register](http://www.gpi.kit.edu/Software-FWI.php) on the email list [IFOS@lists.kit.edu](http://www.gpi.kit.edu/Software-FWI.php).
Please use this list also to ask questions on using the software or to report problems or bugs.
Please use this list also to ask questions or to report problems or bugs.
Five built-in wavelets of the seismic source are available. The corresponding source time functions are defined in \texttt{src/wavelet.c}. You may modify the time functions in this file and recompile to include your
Five built-in wavelets of the seismic source are available. The corresponding source time functions are defined in \texttt{src/wavelet.c}. You may modify the time functions in this file and recompile to include your
own analytical wavelet or to modify the shape of the built-in wavelets.
own analytical wavelet or to modify the shape of the built-in wavelets.
s3(t)=0.75 \pi f_c \sin(\pi(t+t_d)f_c)^3\quad\mbox{if}\quad t \in[t_d,t_d+1/fc]\quad\mbox{else}\quad s3(t)=0
s3(t)=0.75 \pi f_c \sin(\pi(t+t_d)f_c)^3\quad\mbox{if}\quad t \in[t_d,t_d+1/fc]\quad\mbox{else}\quad s3(t)=0
\label{eq_s3}
\label{eq_s3}
\end{equation}
\end{equation}
First derivative of a Gaussian function (SOURCE\_SHAPE=5):
SOURCE\_SHAPE=5, First derivative of a Gaussian function:
\begin{equation}
\begin{equation}
f(t)= -2.0 a (t-t_s) \exp(-a (t-t_s)^2)\quad\mbox{with}\quad a=\pi^2 f_c^2 \quad\mbox{and}\quad t_s=1.2/f_c
f(t)= -2.0 a (t-t_s) \exp(-a (t-t_s)^2)\quad\mbox{with}\quad a=\pi^2 f_c^2 \quad\mbox{and}\quad t_s=1.2/f_c
\label{eq_deriv_of_gaussian}
\label{eq_deriv_of_gaussian}
\end{equation}
\end{equation}
Delta pulse (SOURCE\_SHAPE=6):
SOURCE\_SHAPE=6, delta pulse: Lowpass filtered delta pulse. Note, that it is not clear if the lowpass filter used in the current version works correctly for a delta pulse.\\
Lowpass filtered delta pulse. Note, that it is not clear if the lowpass filter used in the current version works correctly for a delta pulse.\\
Source time function from SIGNAL\_FILE in su format (SOURCE\_SHAPE=7).\\
% Source time function from SIGNAL\_FILE in su format (SOURCE\_SHAPE=7).\\
In these equations, t denotes time and $f_c=1/TS$ is the center frequency. $t_d$ is a time delay which can be defined for each source position in SOURCE\_FILE. Note that the symmetric (zero phase) Ricker signal is always delayed by $1.0/f_c$, which means that after one period the maximum amplitude is excited at the source location. Three of these 5 source wavelets and the corresponding amplitude spectra for a center frequency of $f_c=50$ Hz and a delay of $t_d=0$ are plotted in Figure \ref{fig_source_wavelets_json}. Note the delay of the Ricker signal described above. The Fuchs-M\"uller wavelet has a slightly higher center frequency and covers a broader frequency range.
In these equations, t denotes time and $f_c$ is the center frequency. $t_d$ is a time delay which can be defined for each source position. Note that the symmetric (zero phase) Ricker signal is always delayed by $1.0/f_c$, which means that after one period the maximum amplitude is excited at the source location. Three of these 5 source wavelets and the corresponding amplitude spectra for a center frequency of $f_c=50$ Hz and $t_d=0$ are plotted in Figure \ref{fig_source_wavelets_json}. Note the delay of the Ricker signal described above. The Fuchs-M\"uller wavelet has a slightly higher center frequency and covers a broader frequency range.
\newline
\begin{figure}
\begin{figure}
\begin{center}
\begin{center}
...
@@ -162,8 +163,9 @@ spectrum, c) phase spectrum. }
...
@@ -162,8 +163,9 @@ spectrum, c) phase spectrum. }
\label{fig_source_wavelets_json}
\label{fig_source_wavelets_json}
\end{figure}
\end{figure}
You may also use your own time function as the source wavelet (for instance the signal of the first arrival recorded by a geophone at near offsets). Specify SOURCE\_SHAPE=3 and save the samples of
\newpage
your source wavelet in ASCII-format in SIGNAL\_FILE. SIGNAL\_FILE should contain one sample per line. It should thus look like:
SOURCE\_SHAPE=3 allows you to use your own time function as the source wavelet stored in ASCII-format in SIGNAL\_FILE. SIGNAL\_FILE should then contain one sample per line. It should thus look like:
{\color{blue}{\begin{verbatim}
{\color{blue}{\begin{verbatim}
0.0
0.0
...
@@ -175,12 +177,17 @@ your source wavelet in ASCII-format in SIGNAL\_FILE. SIGNAL\_FILE should contain
...
@@ -175,12 +177,17 @@ your source wavelet in ASCII-format in SIGNAL\_FILE. SIGNAL\_FILE should contain
The time interval between the samples must equal the time step interval (DT) of the FD simulation (see above)! Therefore it might be necessary to resample/interpolate a given source time function with a smaller sample rate. You may use the matlab script mfiles/resamp.m to resample your external source signal to the required sampling interval.
The time interval between the samples must equal the time step interval (DT) of the FD simulation (see above)! Therefore it might be necessary to resample/interpolate a given source time function with a smaller sample rate. You may use the matlab script mfiles/resamp.m to resample your external source signal to the required sampling interval.
\newline
\newline
It is also possible to read different external source wavelets for each shot. Specify SOURCE\_SHAPE=7 and save the wavelets in su format in SIGNAL\_FILE.shot<no\_of\_shot>. The wavelets in each su file must equal the time step intervel (DT) and the number of time steps of the FD simulation!
SOURCE\_SHAPE=7 is used for reading different external source wavelets for each shot. The wavelets in SU-format need to be saved in SIGNAL\_FILE.shot<shotnumber>.su.
If you want to use the source time function inversion (INV\_STF==1, section \ref{sec:STF}) with an external wavelet, this wavelet needs to be provided at SIGNAL\_FILE.shot<shotnumber>\_start.su and the inverted wavelets will be stored in SIGNAL\_FILE.shot<shotnumber>.su (or SIGNAL\_FILE.<workflowstage>.<shotnumber>.su if you use the WORKFLOW option).
The wavelets in each su file must have the same number of samples as specified by TIME/DT!
\newline
\newline
The following source types are availabe: explosive sources that excite compressional waves only (SOURCE\_TYPE=1), and point forces in the x- and y-direction (SOURCE\_TYPE=2,3).
The following source types are availabe: explosive sources that excite compressional waves only (SOURCE\_TYPE=1), and point forces in the x- and y-direction (SOURCE\_TYPE=2,3).
The force sources excite both P- and S-waves. The explosive source is located at the same position as the diagonal elements of the stress tensor, i.e. at (i,j) (Figure \ref{fig_cell}).
The force sources excite both P- and S-waves. The explosive source is located at the same position as the diagonal elements of the stress tensor, i.e. at (i,j) (Figure \ref{fig_cell}).
The forces are located at the same position as the corresponding components of particle velocity (Figure \ref{fig_cell}). If (x,y) denotes the position at which the source location is defined in source.dat, then the actual force in x-direction is located at (x+DX/2,y) and the actual force in y-direction is located at (x,y+DY/2). With SOURCE\_TYPE=4 a custom directive force can be defined by a force angle between y and x. The angle of the force must be specified in the SOURCE\_FILE after AMP. This force is not aligned along the main directions.
The forces are located at the same position as the corresponding components of particle velocity (Figure \ref{fig_cell}). If (x,y) denotes the position at which the source location is defined in source.dat, then the actual force in x-direction is located at (x+DX/2,y) and the actual force in y-direction is located at (x,y+DY/2). With SOURCE\_TYPE=4 a custom directive force can be defined by a force angle between y and x. The angle of the force must be specified in the SOURCE\_FILE after AMP. This force is not aligned along the main directions.
\newline
The locations of multiple sources must be defined in an external ASCII file (SOURCE\_FILE) that has the following format:
The locations of multiple sources must be defined in an external ASCII file (SOURCE\_FILE) that has the following format:
{\color{blue}{\begin{verbatim}
{\color{blue}{\begin{verbatim}
...
@@ -620,6 +627,7 @@ smaller than PRO the inversion aborts or in case of using frequency filtering (T
...
@@ -620,6 +627,7 @@ smaller than PRO the inversion aborts or in case of using frequency filtering (T
\newpage
\newpage
\section{Source wavelet inversion}
\section{Source wavelet inversion}
\label{sec:STF}
To remove the contribution of the unknown source time function (STF) from the waveform residuals, it is necessary to design a filter which minimizes the misfit to the field recordings and raw synthetics. Therefore, a second forward simulation is applied. The first one is done with the wavelet specified in SOURCE\_SHAPE and the second one with the optimized source wavelet saved in SIGNAL\_FILE (see Section~\ref{sec:sources}). This optimized source wavelet is kept constant within N\_STF or within a frequency range (see below).\\
To remove the contribution of the unknown source time function (STF) from the waveform residuals, it is necessary to design a filter which minimizes the misfit to the field recordings and raw synthetics. Therefore, a second forward simulation is applied. The first one is done with the wavelet specified in SOURCE\_SHAPE and the second one with the optimized source wavelet saved in SIGNAL\_FILE (see Section~\ref{sec:sources}). This optimized source wavelet is kept constant within N\_STF or within a frequency range (see below).\\
