The general form of pressure dynamics (see Universal view of 1D-Radial low-compressibility diffusion):

p(t, {\bf r}) = p_i + \frac{qB}{4 \pi \sigma} F \left(\frac{r^2}{4 \chi t} \right)

suggest that isobars

p(t, {\bf r}) = p_i + \frac{qB}{4 \pi \sigma} F \left(\frac{r^2}{4 \chi t} \right) = \rm const

will be honouring the following equation:

\frac{r^2}{4 \chi t}  = \rm const

or

r(t) = r_w + 2 \sqrt{\chi t}

which means it will be moving with the phase velocity (see also Formation Pressure Dynamics):

u_{p= {\rm const}} = \sqrt{\frac{\chi}{t}}

and slowing down in time.

The practical range for this velocity is around 0.01 m/s which is much higher than actual fluid propagation in typical subsurface reservoirs 3 · 10^-6 m/s (circa 100 metres per year) .

This makes pressure pulsation an effective reservoir scanning technique.

See Also