American Oil and Gas Reporter - July 2020 - 56

SpecialReport: Geophysics & Computing

CRAM Gathers Enhance 3-D Inversion
By Elive Menyoli
AUSTIN TX.-Elastic inversion from
common reflection angle migration
(CRAM) gathers can accurately capture
lithology-driven lateral variations in reservoir properties, particularly in a strongly
deformed and faulted geologic environment. Compared with angle gathers transformed from post-migration offset gathers,
the intrinsic angle gathers from CRAM
have three critical advantages:
· Reliable angle gathers greater than
40 degrees;
· A robust and reliable amplitude
and phase preservation; and
· Regularly sampled gathers.
Many practitioners have shown that
in order to obtain reliable density, compressional- and shear-wave velocities
(Vp/Vs), Poisson ratio and total organic
carbon (TOC) content from prestack simultaneous seismic inversion, seismic
gathers with sufficient angle range greater
than 40 degrees are required.
It has been shown in shale resource
plays that the TOC content has a stronger
influence on the density of the rock-and
quite often density correlates to gamma
ray curves (lithology predictor) or petrophysical properties such as porosity-than
on velocities. However, the contribution
of density to the overall seismic amplitude

generally is present only on large angles
greater than 40 degrees. Therefore, having
a migration algorithm that naturally produces reliable large-angle gathers is critical.
The conventional Kirchhoff migration
produces offset gathers that must later be
converted into angle gathers prior to seismic inversion. Computing an accurate
offset-to-angle conversion can be crucial
to predicting subsurface lithology, particularly in shale plays with consolidated
rocks that may have rapid lateral and
vertical lithology changes.
Whereas a conventional normal moveout-based transform is increasingly inaccurate with increasing angles, especially
in the presence of anisotropy, the CRAMbased method generates angle gathers directly using an intrinsic ray tracing procedure.
Generating CRAM Gathers
Unlike a conventional common shot
or common offset Kirchhoff migration,
which begins at the acquisition surface,
common reflection angle domain migrations start at the depth image point. From
each subsurface point, a fan of upgoing
rays is shot at uniform emergence angle
increments. This approach allows the
direct application of correct summation
weighting factors, resulting in continuous

FIGURE 1
VTI Migrated Offset Gathers (Left) versus
Common Angle Gathers (Right)

56 THE AMERICAN OIL & GAS REPORTER

amplitude and phase-preserved image
gathers for a wide range of reflection angles.
By shooting dense upgoing rays at
uniform emergence angle increments, a
uniform illumination is obtained directly
at the image points from all directions
(dips and azimuths), which is essential
for the accurate reconstruction of angle
image gathers that is required for seismic
inversion.
Each event in the common image
gather is constructed by summing all
seismic data reflected from the image
points with the same opening reflection
angle. The relevant contributing data
points are defined by the various ray
paths from the image point. The illumination of the image points from all directions ensures uniform data sampling
for building the image.
CRAM gathers are organized naturally
according to opening angles at each subsurface point, rather than according to
source-receiver offset at the surface. Figure 1 compares an example of CRAM
with a common offset Kirchhoff migration gather. Within the yellow-boxed
zone, CRAM gathers are much cleaner,
more continuous, and have better amplitude distribution.
CRAM gathers also are affected less
by migration stretch at the far angles
(area circled in red). This phenomenon
is intrinsic to angle gathers and is another
important advantage of CRAM migration.
Avoiding migration stretch makes such
angle gathers ideally suited for impedance
inversion of elastic properties, even in
complex geologic areas.
CRAM compensates equally for amplitude preservation and multiray path
arrivals, and accounts for wavelet phase
shift caused by caustics along the ray
paths. Accounting for the total ray phase
shift is important for keeping the wavelet
phase stationary during propagation. Maintaining a stationary phase wavelet is one
of the assumptions for seismic inversion.
It is worth noting that even in layercake geologic formations such as in South
Texas, strong lateral and vertical velocity
variations across fault boundaries may
cause multiarrivals and ray caustics.
While CRAM gathers are organized
in angles and depth, Kirchhoff gathers
are organized naturally in offsets and
depth. For inversion purposes, the Kirch-

American Oil and Gas Reporter - July 2020

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