IEEE Signal Processing - March 2018 - 102

z Axis

0.2
0
-0.2

Radiation
0.5

Pattern

y Axis
-

-0.5

N
W

0.5

0
-0.5

x Axis

S
(a)

(b)

Figure 3. An illustration of the P-wave radiation pattern from a shear source. The (a) gray image shows a vertical fault with a horizontal motion of two
blocks (San Andreas type, strike-slip). The white and red beach ball on top shows a corresponding representation of this source mechanism. The red
color in the beach ball represents P-wave motion away from the source while white represents parts of the unit sphere where the P-wave motion is toward the source. This is also shown in the (b) 3-D plot where red denotes positive outward amplitudes of P-waves and blue negative inward amplitudes.

volumetric or shear-only changes. Volumetric changes, a
mode I failure, can be expected as the injected fluids are incompressible and the hydraulic fracture is a volume-changing
process, unlike most of the natural earthquake activity observed worldwide. Additionally, hydraulic fracturing in the

Northing
Easting
Traces on Sensors
in Red Oval

Traces on Sensors
in Blue Oval

Figure 4. Sample traces of microseismic data received on two spokes of
the star-pattern sensor array. The sign change can be observed in the onfigure magnifiers, where the wave fronts were denoted by a black curve.
The SNR of the P-wave arrival is lower, near the apex of the moveout due
to the radiation pattern of the source.

102

oil and gas industry often uses solid particles suspended in the
fracturing fluid especially designed to be incompressible and
keep the fracture open. As a result, a new volume is created
by hydraulic fracturing, and the associated seismicity possibly
may be the result of this volume change.
The other type of source mechanisms, shear-only events,
are similar to natural earthquakes and represent a mode II
failure. They result from increased pore pressure along natural fractures as the ratio of shear-to-normal stress on these
fracture changes due to fluid injection. For example, in a
homogeneous isotropic medium, a shear failure creates both
a P- and S-wave at the origin time of the seismic event. The
radiated P-waves are polarized parallel to the source-receiver direction, while the shear waves are polarized perpendicular to the P-waves. Note that the P- and S-wave polarization
differs in four quadrants (sign changes) as illustrated by the
beach ball patterns in Figure 3(a). Then, in Figure 4, we
show sample microseismic data received on two spokes of
the star pattern sensor array, where, in the on-figure magnifiers, we can see the different signs of the wiggles due to the
source mechanism.
For a shear source, the ratio of the S-wave peak (maximum)
amplitude to the P-wave peak amplitude is (v p /v s) 3 . In sedimentary rock formations the P-wave to S-wave velocity ratio
(v p /v s) is usually close to two, resulting in significantly stronger S-waves. Thus, downhole monitoring arrays usually record
much stronger S-waves. Analogous characterization of P-wave

IEEE Signal Processing Magazine

March 2018

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