fracspy.detection.stacking.estimate_origin_times#
- fracspy.detection.stacking.estimate_origin_times(idp, ds_full, tt, dt, x, y, z)[source]#
Estimate origin times of the events detected with diffraction stacking.
Estimate origin times of the events using traveltimes and the time indices determined from the maximum stack function (MSF) using STA/LTA analysis.
- Parameters:
- idp
numpy.ndarray Integer array of time indices of determined peaks
- ds_full
numpy.ndarray Diffraction stack full 4D array of shape (nt, nx, ny, nz)
- tt
numpy.ndarray Traveltime table of size \(n_r \times n_x \times n_y \times n_z\)
- dt
float Time step
- x
numpy.ndarray Imaging area grid vector in X-axis
- y
numpy.ndarray Imaging area grid vector in Y-axis
- z
numpy.ndarray Imaging area grid vector in Z-axis
- idp
- Returns:
- eot
numpy.ndarray Array of estimated origin times for each of the determined peaks
- eot
Notes
For each determined MSF peak, the origin time \(t_{est}\) of the corresponding event can be determined from peak time \(t_{peak}\) as
\[\mathbf{t}_{est} = t_{peak} - \min_{R} T_R(\mathbf{r}_{peak}).\]where \(T_R(\mathbf{r}_{peak})\) is the traveltime to receiver \(R\) from \(\mathbf{r}_{peak}\) - the location determined from the maximum of the 4D imaging function \(F(\mathbf{r},t)\) at the time moment \(t_{peak}\):
\[\mathbf{r}_{peak} = \arg\!\max_{\mathbf{r}} F(\mathbf{r},t_{peak}).\]