# pylops.utils.seismicevents.hyperbolic3d¶

pylops.utils.seismicevents.hyperbolic3d(x, y, t, t0, vrms_x, vrms_y, amp, wav)[source]

Hyperbolic 3D events

Create 3d hyperbolic events given intercept time, root-mean-square velocities, and amplitude of each event

Parameters: x : numpy.ndarray space axis in x direction y : numpy.ndarray space axis in y direction t : numpy.ndarray time axis t0 : intercept time at $$x=0$$ of each of hyperbolic event vrms_x : root-mean-square velocity in x direction for each hyperbolic event vrms_y : root-mean-square velocity in y direction for each hyperbolic event amp : amplitude of each hyperbolic event wav : numpy.ndarray wavelet to be applied to data d : numpy.ndarray data without wavelet of size $$[n_y \times n_x \times n_t]$$ dwav : numpy.ndarray data with wavelet of size $$[n_y \times n_x \times n_t]$$

Notes

Each event is created using the following relation:

$t_i(x, y) = \sqrt{t_{0,i}^2 + \frac{x^2}{v_{\text{rms}_x, i}^2} + \frac{y^2}{v_{\text{rms}_y, i}^2}}$

Note that velocities do not have a physical meaning here (compared to the corresponding pylops.utils.seismicevents.hyperbolic2d), they rather simply control the curvature of the hyperboloid along the spatial axes.