Imaging condition: envelope stacking

In microseismic imaging, the objects of imaging are source locations. Recently, Sun et al. (2015) and Nakata and Beroza (2016) proposed a cross-correlation imaging condition for time reverse microseismic imaging; Trojanowski and Eisner (2016) reviewed imaging conditions based on diffraction stacking method, including envelope stacking imaging condition suggested by Gharti et al. (2010).

In the proposed workflow, we first extend passive seismic data $D(t,x)$ into a shifted domain $D(t,x,\tau)$, in which $\tau$ represents the source onset time:

$$D(t,x,\tau) = D(t+\tau,x).$$ (5)

For each $\tau$ slice of $D(t,x,\tau)$, we apply diffraction imaging to image passive seismic events, resulting in image $I(t_0,x_0,\tau )$.

In the image volume $I(t_0,x_0,\tau )$ created by path-integral time-domain migration, we apply envelope stacking along $\tau$ axis so that sources can be highlighted at their true location in time coordinates. Phase information is not discarded in this case because migration is applied before envelope stacking. Additionally, we apply a Laplacian sharpening operator in the image domain after envelope stacking to emphasize the maxima for easier visual picking.

After spatial localization of passive seismic sources, each time-delay trace is extracted from image volume $I(t_0,x_0,\tau )$ at position ($t_0,x_0$), showing the activation time of each source.