fracspy.detection.stacking.maxdiffstack

fracspy.detection.stacking.maxdiffstack(data, x, y, z, tt, dt, stack_type=None, swsize=0, polcor_type=None, recs=None)

Maximum diffraction stack function for microseismic event detection.

This routine uses diffraction stacking to obtain the time-dependent maximum stack function used for microseismic event detection.

Parameters:

datanumpy.ndarray

Data of shape \(n_r \times n_t\)

xnumpy.ndarray

Imaging area grid vector in X-axis

ynumpy.ndarray

Imaging area grid vector in Y-axis

znumpy.ndarray

Imaging area grid vector in Z-axis

ttnumpy.ndarray

Traveltime table of size \(n_r \times n_x \times n_y \times n_z\)

stack_typestr, optional, default: None

Diffraction stacking type (imaging condition), default None is the same as squared. Types: absolute (absolute value), squared (squared value), semblance (semblance-based).

swsizeint, optional, default: 0

Sliding time window size for semblance-based type, amount of time steps

polcor_typestr, optional, default: None

Polarity correction type to be used for amplitudes. None is default for no polarity correction, mti is for polarity correction based on moment tensor inversion.

recsnumpy.ndarray, optional, default: None

Array of shape (3, nrec) containing receiver coordinates. Must be provided if polcor_type is not None

Returns:

msfnumpy.ndarray

Time-dependent maximum stack function

ds_fullnumpy.ndarray

Diffraction stack array reshaped to 4D (nt,nx,ny,nz)

Notes

For every time step \(t\) the maximum of the diffraction stacking imaging function \(F(\mathbf{r},t)\) over all potential locations \(\mathbf{r}\) is evaluated [1]:

\[F_t(t) = \max_{\mathbf{r}} F(\mathbf{r},t),\]

where \(F_t(t)\) is referred to as the maximum stack function or MSF [2].

References

[1]

Anikiev, D. (2015). Joint detection, location and source mechanism determination of microseismic events (Doctoral dissertation). St. Petersburg State University. St. Petersburg. https://disser.spbu.ru/files/phdspsu2015/Anikiev_PhD_web_final.pdf

[2]

Anikiev, D., Valenta, J., Staněk, F. & Eisner, L. (2014). Joint location and source mechanism inversion of microseismic events: Benchmarking on seismicity induced by hydraulic fracturing. Geophysical Journal International, 198(1), 249–258. https://doi.org/10.1093/gji/ggu126