t Special section: Karst

Attribute expression of fault-controlled karst — Fort Worth Basin,

Texas: A tutorial
Jie Qi1, Bo Zhang1, Huailai Zhou1, and Kurt Marfurt1
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Abstract
Much of seismic interpretation is based on pattern recognition, such that experienced interpreters are able to
extract subtle geologic features that a new interpreter may easily overlook. Seismic pattern recognition is based
on the identification of changes in (1) amplitude, (2) phase, (3) frequency, (4) dip, (5) continuity, and (6) re-
flector configuration. Seismic attributes, which providing quantitative measures that can be subsequently used
in risk analysis and data mining, partially automate the pattern recognition problem by extracting key statistical,
geometric, or kinematic components of the 3D seismic volume. Early attribute analysis began with recognition
of bright spots and quickly moved into the mapping of folds, faults, and channels. Although a novice interpreter
may quickly recognize faults and channels on attribute time slices, karst terrains provide more complex
patterns. We sought to instruct the attribute expression of a karst terrain in the western part of the Fort Worth
Basin, Texas, United States of America. Karst provides a specific expression on almost every attribute. Spe-
cifically, karst in the Fort Worth Basin Ellenburger Group exhibits strong dip, negative curvature, low coher-
ence, and a shift to lower frequencies. Geomorphologically, the inferred karst geometries seen in our study
areas indicate strong structural control, whereby large-scale karst collapse is associated with faults and where
karst lineaments are aligned perpendicularly to faults associated with reflector rotation anomalies.

Introduction sissippi lime play of northern Oklahoma and southern

The word karst is a German word that denotes the Kansas where the average water cut is 95%, the deeper
area of modern Slovenia known as Kras and known Ordovician-age karst Arbuckle (Ellenburger equivalent)
to the ancient Romans as Carso. The well-drained lime- Formation provides the capacity to dispose of the water
stone terrain and extensive system of natural caverns (Elebiju et al., 2010).
make Kras an important wine-producing area. The word The Fort Worth Basin Texas Barnett Shale was the
karst is now used to describe a carbonate terrain that first successfully exploited shale resource play in North
has undergone significant diagenetic alteration, which America. Like most resource plays, the low-permeabil-
gives rise to enhanced joints, caves, and collapse fea- ity Barnett Shale serves as the source rock, reservoir
tures. Paleokarst plays many roles in oil and gas reser- rock, trap, and seal. Production is most often achieved
voirs. The Ordovician paleokarst is a main oil and gas through the use of horizontal wells and hydraulic frac-
reservoir in the Tarim Basin, China, in which the reser- turing. In the core producing area of the Fort Worth
voir depth can reach 6–7 km (Chen et al., 2010). Across Basin, the Barnett Shale lies below the Marble Falls
the Central Basin Platform of West Texas, karst proc- Limestone and above the Viola Limestone (Figure 1).
esses are responsible for the vuggy reservoir rock, and In general, quartz- and dolomite-rich rocks are brittle,
also the anhydrite-plugged updip seal (Duo et al., 2011). whereas calcite-rich rocks are ductile (Wang and Gale,
In shale resource plays, such as the Barnett Shale un- 2009). In our study area, the Barnett Shale lies uncon-
conformably lying upon the Ellenburger in many areas formably on top of the relatively brittle, dolomitic
of the Fort Worth Basin, karst can form geohazards. Ellenburger Group (Holtz and Kerans, 1992). Here,
Wells that intersected collapse features and diageneti- the extensively karst-modified Ellenburger presents nu-
cally altered faults and joints will produce much water merous drilling-related risks.
from the underlying aquifer, which should be aban- Faults and fractures, associated with Ellenburger col-
doned. In the Barnett and Eagle Ford shale, such haz- lapse, often propagate through the overlying Barnett
ards are often fault controlled, and many interpreters Shale. Sullivan et al. (2006) and Roth and Thompson
call this a string of pearls (Schuelke, 2011). In the Mis- (2009) describe fault-controlled collapse features in a

1
University of Oklahoma, ConocoPhillips School of Geology and Geophysics, Norman, Oklahoma, USA. E-mail: kmarfurt@ou.edu; jie.qi@ou.edu;
bo.zhang-1@ou.edu; zhouhuailai06@cdut.cn.
Manuscript received by the Editor 1 December 2013; revised manuscript received 8 May 2014; published online 4 August 2014. This paper appears
in Interpretation, Vol. 2, No. 3 (August 2014); p. SF91–SF110, 22 FIGS.
http://dx.doi.org/10.1190/INT-2013-0188.1. © 2014 Society of Exploration Geophysicists and American Association of Petroleum Geologists. All rights reserved.

Interpretation / August 2014 SF91

 survey without a Viola hydraulic fracture
barrier in western Wise County, Texas
(Figure 1). Khatiwada et al. (2013) de-
scribe basement control of karst using
the same survey described in this paper.
Hardage et al. (1996) and McDonnell et al.
(2007) describe how these deeper
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collapse features locally enhanced ac-

commodation and provided depocenters
for Pennsylvanian-age Bend Conglom-
erates.
Seismic attributes are routinely used
to map geologic features of interest.
Coherence (e.g., Bahorich and Farmer,
1995) is routinely used to identify faults
and channel edges. Curvature (e.g., al-
Dossary and Marfurt, 2006) is used to
map folds and flexures. Spectral compo-
nents (e.g., Partyka et al., 1999) are used
to constrain lateral variations in channel
thickness. Qi and Castagna (2013) illu-
minate faults and karst detection using
amplitude and phase spectrum and PCA
fault-detection attribute, which calcu-
lates the first principal component of
the most-positive curvature, coherence,
variance, and phase spectrum. Often, in-
terpreters want to know which attribute
is best for illuminating a particular geo-
logic feature. In this tutorial, we illustrate
the value of using multiple seismic attri
butes to illuminate paleokarst terrain fea-
tures common within the Fort Worth
Basin. We will argue that the integrative
use of mathematically independent attri-
butes can reduce the risk of inter-
preter error.
We begin our tutorial with a brief sum-
mary of the geology of the study area.
Next, we describe poststack data condi-
tioning that suppresses migration arti-
facts and improves spectral bandwidth.
Then, we introduce a suite of seismic
attributes, first, displaying them as time
slices through attribute volumes, then
as horizon slices along the upper Ellen-
burger. As we discuss each attribute, we
attempt to link the attribute expression
to a specific component of the geology
(e.g., the structural dip of collapse fea-
tures). We will also address potential
Figure 1. (a) Stratigraphic cross section and (b) stratigraphic column of the Fort interpretation pitfalls when mathemati-
Worth Basin. In the core study area of Wise and Denton Counties to the east, the cally coupling attributes. We conclude
Barnett Shale is subdivided into upper and lower units by the intervening Forest- by providing insights into the geology
burg Lime. The calcite-rich geomechanical ductile Marble Falls and Viola Lime- of the Fort Worth Basin and showing
stones from hydraulic fracture barriers. The Viola fracture barrier pinches out
to the west, such that the Barnett Shale lies unconformably on top of the more
the value of multiattribute visualization.
brittle, dolomitic Ellenburger Group. The survey in the following figures is on The details of algorithm descriptions
strike with the area of Young County in this image (after Pollastro et al., 2007). can be found in Appendix A.

SF92 Interpretation / August 2014

 Geologic background Mississippi Valley type lead-zinc deposits occur further
The Fort Worth Basin is one of several basins that east in the tristate area of Oklahoma, Kansas, and Mis-
formed during the late Paleozoic Ouachita Orogeny, souri (Leach et al., 1993). Elebiju et al. (2010), Sullivan
generated by convergence of Laurasia and Gondwana et al. (2006), and Khatiwada et al. (2013) provide evi-
(Bruner and Smosna, 2011). The Mississippian-age dence of basement-controlled faulting, hydrothermal
organic-rich Barnett Shale gas reservoir is a major re- mineralization, and collapse chimneys in the Fort Worth
source play in the Fort Worth Basin. It extends more Basin. We expect similar mineralization and bottoms-up
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than 28;000 mi2 with most production coming from a karst within our study area.
limited area, in which the shale is relatively thick and
isolated between effective hydraulic fracture barriers. Data conditioning
Conformably overlying the Barnett Shale is the Marble A 3D seismic acquisition program was undertaken
Falls Formation. The lower Marble Falls consists of in 2006 by Marathon Oil Company using 16 live receiver
a lower member of interbedded dark limestone and lines forming a wide-azimuth survey with a nominal
gray-black shale. Underlying the Barnett Shale are the 16 × 16 m (55 × 55 ft) CDP bin size to image the
Ordovician Viola-Simpson Formations, which domi- Barnett Shale at approximately 914 m (3000 ft) true
nantly consist of dense limestone, and dolomitic Lower vertical depth subsea (TVDSS) or 0.7 s two-way time
Ordovician Ellenburger Group. (TWT) (Roende et al., 2008). Although data quality is
The upper surface of the Ellenburger records the excellent, minor improvements through poststack data
second-order Sauk-Tippecanoe erosional unconform- conditioning can significantly facilitate and improve
ity, which is characterized by extensive karst and subsequent interpretation. Our poststack data-condi-
solution collapse (Loucks, 2003). Lucia (1971) first rec- tioning workflow is shown in Figure 3a. This workflow
ognized the genetic relationship between karst dissolu- contains two major steps: The first step is application of
tion and breccias seen in the Ellenburger Group. Kerans principal-component structure-oriented filtering (SOF)
(1989, 1990) establishes the karst and cave models and the second step is spectral balancing. Figure 3b
(Figure 2) and their development in the Ellenburger indicates general steps of principal-component SOF.
Group. This paleocave model forms the basis of the We can create a single waveform, which best fits with
paleokarst model, which includes a paleocave floor, each original seismic trace (steps 1 and 2, Figure 3b).
fill, and roof. Faulting and local subsidence may also The waveform is the best coherent wavelet that fixes
be associated with karst and solution-collapse features each trace by the approximate scale, which calculates
on the top of the Ellenburger Group (Gale et al., 2007). from the best-fit waveform and each trace. The lateral
Pore networks in the Ellenburger Group are complex variation of the amplitude along the structural dip is
because of the amount of brecciation and fracturing called the eigenmap vð1Þ . One can take derivatives of this
associated with karst. In the Fort Worth Basin, the El- eigenmap. Such derivatives will be the input for sub-
lenburger Group is almost always a water-bearing sequent calculations of amplitude curvature. Figure 4
formation. Faults and karst in the Ellenburger Group shows the spectrum for the entire survey before (a)
provide vertical conduits into the overlying Barnett and after (b) and a representative seismic line before
Shale. Hydraulic fracturing may open these zones of (c) and after (d) the data-conditioning workflow. A
weakness resulting in a well that produces large quan- common spectral balancing approach is to estimate
tities of water. For this reason, mapping karst, joints, the coherent (signal) part of the seismic trace as that
and fault geohazards in the Ellenburger Group is an which crosscorrelates with neighboring traces. We esti-
important precursor to successful Barnett Shale com- mate the coherent part of the seismic trace using two
pletion.
Karst-related fractures are common
in the upper Ellenburger (Kerans, 1989).
Tectonic faults can serve as conduits
for meteoric fluids that water circulation,
which favor subsequent dissolution
(Loucks, 2008). Preferential dissolution
along intersecting joints and faults give
rise to elliptical collapse features (Sulli-
van et al., 2006). Although karst is usually
associated with meteoric waters, bot-
toms-up karst (i.e., hydrothermal altera-
tion) can also occur (Sullivan et al.,
2003). Operators have found copper min-
eralization in at least one Wise County
well. Mineralization of Mississippi lime Figure 2. Genetic paleocave model for the Lower Ordovician of West Texas
fractures are common in Osage County, showing cave floor, cave roof, and collapsed breccia (modified after Kerans,
Oklahoma, and commercially exploitable 1988, 1989).

Interpretation / August 2014 SF93

 passes of a nine-trace structure-oriented filter. To Karst on attribute time slices
minimize the risk of impact of removing geology, we then Seismic amplitude
apply a single time-variant spectral balancing operator to Seismic amplitude is the most common attribute
the entire volume. Note that low-amplitude (but annoy- used in seismic interpretation. If a geologic feature
ing) crosscutting migration noise is suppressed, and fault is not measurable by seismic amplitude and phase,
and karst edges are preserved. This data-conditioning no derivative attributes will enable identification.
routing focuses on improving the resolution in the thin In Figure 4c and 4d, we see two strong reflections
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Barnett Shale and the Ellenburger Group. representing the top of Marble Falls and the top of El-
lenburger. The organic-rich Barnett
Shale
is located between these two units (Fig-
ure 1). Three karst collapse features are
recognizable on this section. The largest
karst doline is visible along the margins
of a fault, and two smaller compaction-
induced sags are situated some distance
away from any faults. Below the top of
the collapses, within the Ellenburger,
and below collapse features, rapid
changes in reflector dip, a decrease in
continuity, and a decrease in frequency
are seen. Figure 5 shows a time slice at
t ¼ 0.750 s through the seismic ampli-
tude volume. Red arrows indicate faults
that are better delineated by attribute
processing. However, note that the
larger karst doline features indicated
by the yellow arrows are clearly seen
within the traditional amplitude volume.
This appearance is our first example of
mixed attribute response. That is, the el-
liptical features are not a function of lat-
eral changes, but rather lateral change
in reflection time, or dip, resulting in the
onion ring. The green arrow marks a
smaller karst features that is to be seen
in seismic amplitude slices.

Structural dip
A major characteristic of karst col-
lapse is their bowl-shape appearance
with strongly dipping sides. Figure 6
shows time slices at t ¼ 0.750 s for
apparent dip components at 0°, 45°,
90°, and 135° from north. Figure 7
shows the mathematical model in defin-
ing reflector dip. Figure 8a shows their
corresponding dip magnitude, and Fig-
ure 8b illustrates the dip azimuth modu-
lated by dip magnitude using a 2D color
bar. The larger karst collapses (yellow
arrows), and the major faults (red ar-
rows) exhibit high-dip anomalies. Very
subtle flexures and joints are best illumi-
Figure 3. Workflow (a) to precondition the seismic data prior to attribute com- nated by the apparent dip component
putation and (b) illustrating the steps for SOF based on principal component
analysis (modified after Marfurt, 2006). The filtered seismic amplitude is then
perpendicular to them. As observed in
spectrally balanced using the average time-frequency distribution computed us- Figure 6, large bowl-shaped karst col-
ing a matching-pursuit spectral decomposition algorithm described by Liu and lapse features are coincident with large
Marfurt (2007). faults with laterally extensive damage

SF94 Interpretation / August 2014

 zones. The red dashed lines in Figure 8a and 8b suggest
that these large karst collapse features are structurally
linked by faults or joints, giving rise to what many in-
terpreters refer to as a string of pearls (Schuelke,
2011). We interpret the features indicated by the blue
arrows to be eroded valleys or cave collapses described
in Kerans (1988, 1989, 1990) paleocave models. Other
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low-magnitude anomalies (green arrows) are likely

smaller scale karst features that are relatively distal
to the major fault zones. Orange arrows indicate a rel-
atively rugose surface that is free of large collapse.
These rugose areas fall below the interface between
the top Ellenburger and the lower Barnett Shale.
Correlating the dip-magnitude, dip-azimuth attribute
time slices (Figure 8) to the apparent dip components
(Figure 6), reveals collapse features that are expressed
as steeply dipping edges which in this image appear as
black ellipses. Although the components of vector dip Figure 5. Time slice at t ¼ 0.750 s through the seismic ampli-
are useful for interpretation, they also serve as input tude volume at the approximate top Ellenburger horizon.
for other attributes. Reflector curvature, rotation, and Faults are indicated by red arrows. Large karst appear as cir-
convergence are directly computed from vector dip, cular features (yellow arrows). Smaller karst (green arrow) are
whereas coherence, amplitude gradients, textures, less obvious but can also be seen. The location of line AA′
shown in the previous image is indicated by the red dashed line.

Figure 4. Average time-frequency spectrum for the entire survey (a) before and (b) after spectral balancing using a bluing factor
of f β , where β ¼ 0.3. Note the increase in frequency content between t ¼ 0.6 and t ¼ 0.8 s. Line AA′ (c) before and (d) after time-
variant spectral balancing. Note the increase in frequency content within the target Barnett Shale interval between t ¼ 0.6 and
t ¼ 0.8 s as well as the interval above the top basement (green arrows). The red arrow indicates one normal fault, and yellow
arrows indicate large-scale karst dolines and collapse features.

Interpretation / August 2014 SF95

 and structure-oriented filtering (SOF) are computed
along vector dip.
When reflectors are horizontal, displays of azimuth
calculations are meaningless. To overcome this limita-
tion, we modulate dip azimuth by dip magnitude using a
2D color bar as shown in Figure 8b. Here, the broad ma-
genta (northeast) and green (southwest) bands indicate
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rotation about the major normal faults cutting the sur-

vey. The dissolutional caves are “brighter” with a radial
pattern mimicking the 2D color bar indicating the re-
flections are dipping into the collapse features.
Additionally, although these faults (numbers 1–4)
exhibit a similar orientation, they are of different scales
in dip magnitude (Figure 8a), and they are of different
anomalies in apparent dip (Figure 6) and dip azimuth
(Figure 8b). Fault (no. 4) has opposite hanging wall
and footwall position (this difference can be seen on Figure 7. Mathematical model in defining reflector dip (modi-
the time-structure map). We interpret these faults to fied after Marfurt, 2006). By convention, n ¼ unit vector normal
have been caused by the same normal geologic stress, to the reflector; a ¼ unit vector dip along the reflector; θ ¼
dip magnitude; ϕ ¼ dip azimuth; ψ ¼ strike; θx ¼ the apparent
dip in the xz- plane; and θy ¼ the apparent dip in the yz- plane.

Figure 6. Time slices at t ¼ 0.75 s through apparent dip volumes at (a) 0°, (b) 45°, (c) 90°, and (d) 135° from the north. Yellow
arrows indicate channels or cave collapse. Red arrows indicate major faults, pink arrows indicate minor flexures, and blue arrows
indicate joints.

SF96 Interpretation / August 2014

 but perhaps cutting different lithologies, giving rise to dif- do not appear to be fault controlled. Green arrows in-
ferent patterns on the left and right areas of the dicate small karst features.
time slice.
We zoom in on two zones of interest seen on the dip Spectral decomposition
magnitude time slice in Figure 9a and display them in Lateral changes in layer thickness and impedance
Figure 9b and 9e. We then draw two profiles that cut produce lateral variation in spectral components. Karst-
the collapse and fault features of interest and display related diagenetic products generate lateral changes in
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line BB′ in Figure 9c and line CC′ in Figure 9d. Line porosity, and from limestone to dolomite (Lucia, 1995).
BB′ (Figure 9c) crosses a major fault (red arrow), two In our study area, dissolution collapse features within
large-scale karst collapse features (yellow arrow) and a the underlying Ellenburger Group generate small faults
channel-like collapse feature (blue arrow). Line CC′ (<1∕4λ) and fractures in the overlying Barnett Shale,
(Figure 9d) crosses three large-scale karst collapse reducing velocity and acoustic impedance and in turn
features and a major fault. The karst and channel-like resulting in lateral changes in tuning thickness. Chaotic
collapse features exhibit synclinal cross sections at the collapse features and rugose surfaces give rise to non-
Top Marble Falls and the Top Ellenburger. Light green specular scattering, with constructive interference at
arrows indicate a bright spot anomaly under the largest low frequencies and destructive interference and at
karst collapse feature, which we interpret to be due to high frequencies, thereby shifting the spectra lower.
infill with lower impedance, perhaps fractured or brec-
ciated material. Green arrows in Figure 9e indicate
small-scale karst collapse features, which exhibit less
bright basal reflections in Figure 9g. Not all karst col-
lapse features exhibit bright bottom reflections, sug-
gesting heterogeneity in their fill.

Coherence
Karst not only gives rise to changes in reflector dip
and azimuth, but also to changes in the seismic wave-
form continuity. We use vector dip as input for princi-
pal-component SOF in the most coherent window,
which represent lateral amplitude variation, to con-
strain random and coherent noise and improve vertical
resolution (Marfurt, 2006). Figure 10 shows a time slice
through a coherence volume computed by taking the
ratio of the energy of a principal-component (struc-
tural-oriented) filtered data based on the workflow
shown on Figure 3b to the energy of the original data.
Comparing this image with the previous image of reflec-
tor dip we note that the faults (red arrows) and large
collapse features (yellow arrows) do appear somewhat
weaker. Because coherence is computed along struc-
tural dip, this implies that there is a small offset
(<1∕4λ) and only small changes in waveform across the
edges of the collapse. Low coherence and high dip mag-
nitude at yellow arrows indicates that this incised valley
has little offset along its flanks. When examining verti-
cal slices time through the amplitude data (Figure 4c
and 4d), note that the dissolution within the Ellenburger
is significantly less at t ¼ 0.7 s at the Barnett Shale
level, with the shale layers draped over the collapse fea- Figure 8. Time slice at t ¼ 0.750 s through (a) volumetric dip
and (b) the dip azimuth modulated by dip magnitude using a
ture. Similarly, the blue arrows indicates karst valleys, 2D color bar. Red arrows indicate faults that control many of
which are not as well defined as those observed in the the larger collapse features. Dashed red lines show a string-of-
dip magnitude volume. We conclude that these large pearls feature, which, when correlated with the most-negative
collapse features are coherent in lateral amplitude or curvature, indicates control by diagenetically altered joints
waveform; however, their laterally variable dip is not or faults with little vertical offset. We interpret the feature
imaged using coherence. Orange arrows indicate inco- indicated by the blue arrows to be a valley or cave collapse,
or channel-like collapse features. The green arrow indicates
herent, rugose eroded surfaces that are free of large small-scale karst that are far from major fault zones. Orange
collapse features, which suggests lithology changes arrows indicate a relatively rugose surfaces that are free of
from southwest to northeast. These incoherent surfaces large collapse features.

Interpretation / August 2014 SF97

 Figure 11a shows a time slice at t ¼ 0.750 s through the Peak frequency and peak phase are meaningful if the
peak spectral magnitude volumes computed using a corresponding magnitude is above the noise level. If so,
matching pursuit algorithm described by Liu and Mar- we suggest using magnitude to modulate these images
furt (2007). Note the improved resolution of the peak (Figure 11b). Note the shift to low values of peak fre-
spectral magnitude in illuminating the dissolutional quency (magenta to red) above collapse features, which
cave edges and internal discontinuities. Blue arrows in- represents the destructive interference at the higher
dicate suspected paleovalleys or collapsed paleoca- frequencies. The high frequencies (cyan to blue) record
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verns that reveal low spectral magnitude. Orange thinner layers in the Barnett Shale (low magnitude). In
arrows indicate large karst features, which were iden- Figure 11b, the orange arrows point to low-frequency
tifiable using previously described coherence image features that correspond to rugose surfaces as shown
(Figure 10). in the coherence attributes (Figure 10) and peak mag-

Figure 9. Time slice at t ¼ 0.750 s through (a) volumetric dip, and (b and e) zoomed in zones. (c, d, f, and g) are seismic section
view of lines BB′, CC′, DD′, and EE′ show large-scale karst collapse features (yellow arrows), major faults (red arrows), channel-
like collapse features (blue arrows), and small-scale karst collapse features. Notice that not all karst collapse features exhibit
bright bottom reflections, suggesting heterogeneity in their fill.

SF98 Interpretation / August 2014

 nitude attributes (Figure 11a). Given the rugose nature
of this surface, time slices through the peak phase spec-
trum provide only limited interpretational value.

Structural curvature, reflector rotation,

and reflector convergence
Structural curvature is computed by taking the deriv-
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atives of the dip components as shown in Figure 6. As

such, we expect curvature to highlight joints and frac-
tures characterized by more subtle, longer wavelength
joints and flexures. Reflections that exhibit similar
waveforms, that is, those having small offset (<1∕4λ)
and subtle changes in dip across faults, will generate
curvature, but not coherence anomalies (Al-Dossary
and Marfurt, 2006). The amplitude of the curvature
anomaly is inversely proportional to the radius of cur-
vature at each voxel, with negative values indicating
synclinal, and positive values anticlinal deformation
Figure 10. Time slice at t ¼ 0.750 s through eigenstructure-
(Figure 12). based coherence. Note that the faults (red arrows), channel-
Figure 13a and 13b contrasts the most-positive and like collapse features (blue arrows), and large collapse fea-
most-negative structural curvature along the same time tures (yellow arrows) do not appear as strong as in the dip
slice. In this survey, the major faults are expressed by a magnitude image. Orange arrows indicate incoherent, rugose
positive curvature anomaly across the footwall, which surfaces that are free of large collapse features.

Figure 11. Time slice at t ¼ 0.750 s through

(a) the peak spectral magnitude volumes
computed using a matching pursuit algorithm
described by Liu and Marfurt (2007) and
(b) peak magnitude and frequency modulated
images corendered with dip magnitude image.
Yellow arrows indicate large-scale karst fea-
tures. Red arrows indicate faults, blue arrows
channel-like collapse, and green arrows indi-
cate small karst shown in the previous image.
Orange arrows indicate a relatively rugose
surfaces that are free of large collapse fea-
tures.

Interpretation / August 2014 SF99

 is laterally offset from a corresponding negative curva- (2008). The dip magnitude and coherence anomalies fall
ture anomaly across the hanging wall. This curved ap- between the two curvature anomalies. In this image
pearance is commonly observed in 3D seismic volumes (Figure 13), the bowl-shaped collapse features express
of carbonate terrains associated with conjugate faults, a negative value and appear as blue ellipses (yellow and
which are below seismic resolution and are morpho- green arrows). The rugose surface (orange arrows) is a
logically similar to those described by Ferrill and Morris product of a shorter wavelength and indicates less de-
formation. Yellow polygons enclose an area, in which
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large collapse features are coincident with high-angle

normal faults. The dissolution caves zone is coincident
with through-going faults terminate in the Marble Falls
formation. The fault damage zone consist of fractures
and small-scale faults shown as small red lines on
the most-positive curvature and blue channels crossed
between faults and karst. To visualize the relation be-
tween karst and faults, we corender most-positive
and most-negative curvature with dip magnitude (Fig-
ure 13c and 13d). The dip-magnitude attribute accu-
rately maps the location of faults and karst
boundary, while the shape of karst features and
more-subtle faults is confidently mapped using curva-
Figure 12. Curvature model shows curvature value change ture attributes. When examining Figure 13c and 13d,
based on the plane angle (modified after Marfurt and Rich, note that the large karst features appear fault controlled
2010).
and are cut by smaller faults or joints. These smaller
scale features may record compaction-
induced fracturing across paleocavern
roofs similar to that described by Kerans
(1989, 1990). Additionally, reflector ro-
tation and convergence computed from
the curvature dip components (Marfurt
and Rich, 2010). Reflector rotation (Fig-
ure 14a) shows a strong northwest–
southeast succession of lineaments,
which are strongly aligned and almost
perpendicular to northeast–southwest
trending faults. Corendering the reflec-
tor rotation with dip azimuth as shown
in Figure 14a reveals a strong correla-
tion between rotation and inferred karst
anomalies. We cannot say without fur-
ther analysis and outcrop analogues
whether this “rotation” is a cause or
an effect of the karst features. Interpre-
tations based solely on reflector-vector
convergence attributes provides
ambiguous results. However, when cor-
endered with dip magnitude (Fig-
ure 14b), we recognize that strongly
convergent areas correspond to areas
characterized by a greater density of
Figure 13. Time slice at t ¼ 0.750 s through the (a) most-positive and (b) most-
negative structural curvature and the (c) most-positive and (d) most-negative
faults and karst features. The varying
structural curvature corendered with dip magnitude. In this survey, the major strike of the faults and the elliptical
faults are expressed by a positive curvature anomaly on the footwall which lat- nature of the karst give rise to a complex
erally offset from a corresponding a negative curvature anomaly on the hanging but easy-to-interpret image.
wall. The dip magnitude and coherence anomalies fall between the two curva-
ture anomalies. In this image, the bowl-shaped collapse features express a neg- Amplitude gradients
ative value and appear as blue ellipses (yellow and green arrows). The rugose
surface (orange arrows) is represented by a shorter wavelength, lower deforma-
If we use a lateral 3 × 3 trace by
tion pattern. Yellow polygons indicate the areas where large collapse features n sample analysis window, a principal-
are controlled by faults. Blue arrows indicate channel-like collapse features component (structure-oriented) filter
as red anomalies. produces a lateral pattern (or 3 × 3

SF100 Interpretation / August 2014

 eigenmap) that best represents the lateral variation lithologic changes are generally more easily identified
seen in each of the n vertical amplitude slices. Such fil- on energy than on dip. Large faults and karst are seen
ters were used in the SOF described in Figures 3 and 4. in amplitude gradient and structural dip images. Ampli-
Figure 15 is the coherent energy attribute, which is the tude gradients are computed along the dip, which elim-
energy of the filtered data. Computing the energy with inates dip variability. Such correlation provides
an analysis window (
10 ms), we show in Figure 16 the independently derived and mutually supportive evi-
gradient of coherent energy at 0°, 45°, 90°, and 135°. dence that the imaged features are likely karst and
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These amplitude gradients are the derivatives of the ei- faults. For Figure 16, green arrows mark small-scale
genmap, weighted by its energy. Coherent energy gra- karst and blue arrows indicate channel-like dissolution
dient maps can be quite effective for identifying faults features; these dissolutions appear as caves and eroded
and fractures, and can provide constrains for mapping zones on gradient of coherent energy (Figure 16), but
channels, which can be emphasized using lateral they appear as points and discontinuities on coherence
changes in tuning (Marfurt, 2006). Like apparent dip, (Figure 10).
amplitude gradients can be calculated at any azimuth
(Figure 6). Overlaying amplitude gradient maps with Amplitude curvature
the coherent energy results in a suite of images that sim- Whereas structural curvature is a derivative of struc-
ulates shaded illumination, but of energy, not of time tural dip, amplitude curvature is computed by calculat-
structure. For example, note the shorter wavelength ing the derivative of amplitude gradients. Figure 17a
variation of the amplitude gradient images in Figure 16 and 17b shows the most-positive and most-negative am-
compared with the structural dip images in Figure 8a. plitude curvature derived from high-resolution ampli-
The yellow arrows in Figure 8a indicate high dip anoma- tude gradients. With the exception of the dip
lies, which are well defined on gradient maps of coher- compensation in the structural curvature computation,
ent energy (Figure 16). Lateral variations related to the size and the values of both curvature operators are
exactly the same. In Figure 17a and 17b, the yellow
dashed lines zones indicate complex fault-controlled
karst features. Fewer fractures and karst are developed
in the areas far away from fault zones. Figure 17c and
17d is the same image way corendered with dip magni-
tude to highlight karst and better show the relationship
among the faults, joints, and karst.
Compared with structural curvature, amplitude cur-
vature delineates several previously overlooked, small
circular features in the southern part of the survey
where the time slice cuts below the top Ellenburger
Dolomite (Figure 18a). Zooming in (Figure 18b), we

Figure 14. Time slice at t ¼ 0.750 s through (a) rotation cor-

endered with dip azimuth and (b) vector convergence coren- Figure 15. Time slice at t ¼ 0.750 s through coherent energy
dered with dip magnitude. Red arrows indicate major Yellow attributes. Note that the red arrows indicate major faults, and
polygons indicate fault-controlled karst features. the yellow polygon indicates fault-controlled karst features.

Interpretation / August 2014 SF101

 draw several vertical lines through the seismic ampli- lapse features widely seen in the Tarim Basin, China
tude map and display them in the Figure 18c–18f map. (Chen et al., 2010; Liu et al., 2011; Feng et al., 2012).
The small radius amplitude curvature anomalies appear In the Tarim Basin, the collapse features are filled with
as bright spot anomalies on the seismic section. Several Aeolian sands and form excellent oil and gas reservoirs.
of them exhibit the string-of-pearls pattern (green arrows These subtle karst collapse features within the Ellen-
in Figure 18c–18e) suggesting they are fault controlled. burger have a very different morphology from those
Those vertical karst anomalies within the Ellenburger that cut the Ellenburger and continue into the overlying
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have an almost identical appearance to infilled karst col- Barnett Shale and Marble Falls Formations seen in

Figure 16. Time slices at t ¼ 0.750 s through

at (a) 0°, (b) 45°, (c) 90°, and (d) 135° from the
north amplitude gradients computed along the
structural dip. Large karst do not appear to
give a strong amplitude anomaly, although
small karst (green arrow) do. There does not
appear to be a significant acquisition footprint
in either of the gradient images. Faults (red ar-
rows) and channel-like collapse features (blue
arrows) appear differently on each degree am-
plitude gradients.

Figure 17. Time slices at t ¼ 0.750 s through

the (a) most-positive and (b) most-negative
amplitude curvature and the (c) most-positive
and (d) most-negative amplitude curvature
volumes corendered with dip magnitude vol-
umes. Dashed yellow polygons indicate areas
of fault-controlled karst. Although the struc-
tural curvature is computed by taking the
derivative of the inline and crossline dip com-
ponents, the amplitude curvature is computed
by taking the derivative of the inline and
crossline amplitude gradients shown in the
previous image. Yellow dashed line indicates
zone dominated by fault-controlled karst. Al-
though northwest–southeast and northeast–
southwest lineaments could be the acquisition
footprint, we interpret lineaments at other azi-
muths to indicate diagenetically altered joints
giving rise to laterally variable reflectivity.
Green arrows indicate the small karst. Some
of those can only be highlighted by the ampli-
tude gradient and amplitude curvature.

SF102 Interpretation / August 2014

 Figures 9 and 18d. These subtle karst caves appear to be any unconformity, autotrackers fail when the overlying
restricted within the Ellenburger and do not significantly strata juxtapose lateral changes in impedance. Inter-
alter the base of the Barnett Shale. preting karst topography is exceedingly difficult as
Figure 18f shows a subtle collapse-caused fault in the unconformity frequently crosscuts strata with dif-
seismic section view. The left blue arrow indicates a ferent lithologies characterized by highly variable
curved, but continuous feature, whereas the right blue impedance. Where conventional 3D interpretation fails,
arrow indicates finite displacement along a small fault. incorporation of horizon slices from attribute
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Figure 19 shows the subtle faults on different attributes. volumes provide an increasingly valuable alternative
Notice that dip magnitude, most-positive and most- method for interpreting complex stratigraphic features,
negative amplitude curvature can detect two kinds of such as karst.
anomalies (blue arrows) at the edges of this subtle Figure 20 shows the time-structure map at the top
collapse-caused faults; however, coherence can only Ellenburger Group corendered with a representative
detect the discontinuity associated with the faulted vertical slice through the seismic amplitude volume.
edge. The structure map shows increased rugosity of the sur-
face toward the south. Figure 21a and 21b shows a hori-
Karst on attribute horizon slices zon slice through the most-positive and most-negative
Conventional interpretation is based on mapping curvature volumes. Dashed yellow lines indicate fault-
faults and horizons. Although faulted horizons are dif- controlled karst within the Ellenburger Group. Fig-
ficult and time consuming to interpret, karst surfaces ure 21c and 21d shows the same horizon slices through
are particularly tedious for the interpreter because of the curvature corendered with coherence volumes.
their discontinuous character and high rugosity. As with Black anomalies indicate discontinuities (faults, joints,

Figure 18. Time slice at t ¼ 0.750 s through (a) most-negative amplitude curvature and (b) zoomed in zone, (c-f) are seismic
section view of lines FF′, GG′, HH′, and II′. Circular collapse features are contained entirely within the Ellenburger Dolomite
Formation and do not propagate shallower. Several of them exhibit the string-of-pearls pattern, suggesting that they are controlled
by faults or joints.

Interpretation / August 2014 SF103

 and karst), the latter of which correlate to red, most- ding. Such information should be presented during
positive curvature and blue, most-negative structural interdisciplinary, prespud meeting to alert the drilling
curvature anomalies. and completion engineer of potential difficulties before
Figure 22 shows similar horizon slices but now finalization of the drilling and completion program.
through the amplitude curvature volume. As seen Karst collapse generate a distinct morphologic pat-
previously on the time slices, the amplitude curvature tern on 3D seismic data. When plotted using a gray
varies more rapidly laterally, likely indicating changes scale, karst dolines appear on coherence and dip
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in impedance interpreted as variations in diagenetic magnitude time slices as characteristically circular to

alteration. Figure 22a and 22b shows the most-positive elliptical features, which provide a karst “fingerprint.”
and most-negative amplitude curvature. Although these In this and many other surveys in the Fort Worth Basin,
images are similar to Figure 21a and 21b, they indicate
different concepts. The blue in the structural curvature
indicates anomalously low structure, whereas the
blue in the amplitude curvature indicates anomalously
low amplitude. Thus, we observe lower reflectivity in-
side the structurally low-collapse features, which likely
results from anomalous attenuation and/or scattering.

Conclusions
Karst, faults, and joints are known to form geologic
hazards for most Barnett Shale wells in the Fort Worth
Basin. In the best cases, these drilling-related geoha-
zards form conductive features that draw off expensive
hydraulic fracturing fluid from the targeted shale forma-
tion. In the worst cases, the completed wells are hy-
Figure 20. Time structure map of the top Ellenburger Group
draulically connected to the underlying Ellenburger horizon. Karst collapse and three major faults are clearly seen.
aquifer and produce large amounts of water with little Note the increased rugosity of the surface toward the south
hydrocarbon. Three-dimensional seismic data are rou- and increased karst collapse toward the north. Orange arrows
tinely acquired to map such geohazards prior to spud- indicate a rugose surface. Red arrows indicate major faults.

Figure 19. Time slice of zoomed in area at t ¼ 0.750 s through the (a) dip magnitude, (b) coherence, (c) most-positive amplitude
curvature, and (d) most-negative amplitude curvature. Note that the blue arrows indicate the subtle collapse-caused fault.

SF104 Interpretation / August 2014

 the karst are strongly correlated with fractures and lies, but no coherence anomalies, suggesting either de-
joints, which in turn are clearly rendered on coherence layed collapse or continued diagenetic alteration of the
and most-negative curvature images. The chaotic Ellenburger from below. Solution-enlarged joints and
nature of reflectors internal to the karst features, such faults may remain partially open, or be fill with imper-
as paleocavern fill, often result in low-frequency anoma- meable clays or preferentially cemented. In either
lies. The loss of higher frequencies has two possible case, they will give rise to lateral changes in amplitude
causes: the existence of fluid-filled fractures and cracks measured by amplitude gradients and amplitude
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within the karst collapse features giving rise to intrinsic curvature. Karst-related architectural elements include
attenuation, and scattering from the chaotic infill giving dolines, paleocaverns, karst towers, solution-enlarged
rise to geometric attenuation. In this survey area, and joints, and rugose topography that can inferred from
throughout much of the Fort Worth Basin, wells that attributes by integrating modern and ancient analogues,
penetrate karst features or coincident fault and fracture thereby providing mutually supportive lines of evidence
system will produce water from the Ellenburger Group for a compelling interpretation.
and thus, are not intentionally drilled. Time slices through seismic attributes provide a rapid
Reflectors dip into the collapse features giving an in- yet quantitative delineation of karst terrains, delaying
ward radial display when dip azimuth is plotted against and perhaps circumventing the need to carefully pick
a cyclical-color bar. Vector convergence shows the the top of the difficult-to-pick Ellenburger unconformity.
complementary image, with reflectors converging out- Indeed, many areas covered by 3D seismic data in the
ward toward the collapse edges. Reflectors at shallower Fort Worth Basin have few wells, in which the engineers
levels in the Barnett Shale and Marble Falls intervals turn to less intensely karsted areas to complete.
also show down warping into the karst but with parallel Interpreters often wish to know which attribute is
(nonconvergent) bedding and near constant thickness, “best” to delineate a given geologic feature of interest.
implying that the actual collapse took place long after We propose using mathematically independent attrib-
these formations were deposited. At the shallow utes, coupled through the underlying geology, to pro-
Pennsylvanian-age Caddo horizon, the reflectors show vide a means of confirming or rejecting a given
strong negative curvature and dip magnitude anoma- interpretation hypothesis.

Figure 21. Vertical slice through seismic amplitude and horizon slices along the top Ellenburger Group horizon though the
(a) most-positive and (b) most-negative structural curvature and (c) most-positive and (d) most-negative structural curvature
corendered with coherence. Red arrows indicate major faults, and yellow dashed lines indicate where karst is developed and
is larger than the other area where there are no major faults. Yellow arrows indicate surface folds and joints.

Interpretation / August 2014 SF105

 Apparent inline dip
For time-migrated data, the apparent dip is the
change in reflector time from with respect to distance
in a given direction and is measured in units of s∕m.
Using the SEGY convention, in which the y-axis is north
and the x-axis is east, the apparent north component of
dip py and the east component of dip px are given by
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∂t
px ¼ ; (A-1)
∂x
and
∂t
py ¼ : (A-2)
∂y

In our examples, we computed the inline and cross-

line components of dip using a multiwindow Kuwahara
semblance search technique described by Marfurt
(2006). The apparent dip in the ξ-direction (in this
paper, 0°, 45°, 90°, and 135° from north) is
∂t
pξ ¼ ¼ ðcos ξÞpy þ ðsin ξÞpx : (A-3)
∂ξ

Figure 22. Vertical slice through seismic amplitude and hori-

zon slices along the top Ellenburger Group horizon though the Dip magnitude and dip azimuth
(a) most-positive and (b) most-negative amplitude curvature. The dip magnitude is measured in s∕m and jpj is the
Red arrows indicate major faults. Blue arrows indicate fault-
magnitude of the vector dip p given by
controlled karst. Yellow arrows indicate surface folds and
joints. The fractures are developed in zones where faults and
karst are also developed. Green arrows indicate that the zones jpj ¼ ðp2x þ p2y Þ1∕2 : (A-4)
have no fault effects, so that fractures are not developed.
Conversion to angular dip θ requires the use of a
velocity V P , which we set to 15;000 ft∕s, representative
Acknowledgments of the Barnett Shale and Ellenburger Dolomite, and it is
The authors would like to thank Marathon Oil for given by
providing the data and key insight in the data analysis

V
of this region. We also thank J. Rush, Y. Sun, S. Chavez- θ ¼ tan−1 P ðp2x þ p2y Þ1∕2 : (A-5)
Perez, and D. Herron for reviewing this manuscript and 2
providing supportive comments. Financial support and
The dip azimuth from north is
most attribute computation was supported by the Uni-
versity of Oklahoma (OU) Attribute-Assisted Seismic ψ ¼ ATAN2ðpy ; px Þ; (A-6)
Processing and Interpretation (Consortium). Data dis-
play was done using Petrel software provided to OU where ATAN2 produces a result that ranges between
for use in research and education. −1800 and þ1800 .

Coherence
Appendix A Coherence is a measure of waveform similarity. In
Simple definitions of attributes our examples, we estimate the coherence of J traces
and operations used within a
K sample analysis window as the ratio be-
In this appendix, we summarize several of the seis- tween the coherent energy within an analysis window
mic attributes used in the paper. Several of these to the total energy within the analysis window:
definitions are extracted from the glossary in Chopra

PþK PJ 2
j¼1 ðdj Þ
coh
and Marfurt (2007), which in turn were adapted k¼−K
from definitions in Sheriff (2002). Much greater c¼
: (A-7)
detail can be found at http://geology.ou.edu/aaspi/ PþK PJ orig 2
k¼−K j¼1 ðd j Þ
documentation/.

SF106 Interpretation / August 2014

 Semblance-based coherence estimates the coherent (2007). After balancing and bluing the magnitude spec-
part of the data by the average trace within the analysis tra, the balanced and blued output trace is recon-
window. In the examples we show here, we estimate structed by adding its complex (modified magnitude
the coherent part of data using a Karhunen-Loeve filter. and unchanged phase) components.
We always compute coherence along the structural dip.
Structural curvature
Structure-oriented filter There is considerable confusion in terms of curva-
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As the name implies, SOF is computed along struc- ture definitions. Mathematically, the curvature is based
tural dip as estimated by equations A-1 and A-2. Our im- on eigenvector analysis. In this definition, the maximum
plementation builds on other previously computed curvature is that curvature that best represents the de-
components. First, we examine the centered window formation at a given voxel. If that best representation is
and examine its coherence. If the coherence is below a syncline, the maximum curvature happens to be neg-
a given threshold (e.g., c < 0.6), then we do not filter ative and the corresponding minimum curvature that
the data in an attempt to preserve a potential “edge.” represents the least deformation at a voxel will have
If the coherence is above the threshold, we compare this a larger signed value. Because most geophysicists do
value with the coherence of all noncentered analysis not live in eigenvector space, this nomenclature is
windows that includes the voxel of interest and choose not used by approximately 50% of the commercial cur-
the one with the highest coherence value. Within this vature software implementations, who propose that the
window, we apply a Karhunen-Loeve filter and output maximum curvature should have a greater than or equal
the filtered sample value. signed value as the minimum curvature. We avoid this
confusion by explicitly defining the most-positive and
Spectral components most-negative principal (i.e., eigenvector) curvatures,
In this paper, we computed spectral components us- where k1 ≥ k2 . We compute volumetric curvature as
ing a matching pursuit algorithm described by Liu and the first derivatives of the volumetric north and east
Marfurt (2007). We begin by computing a library of com- apparent components of dip. The long-wavelength ver-
plex Ricker wavelets. Then, we compute the instantane- sions we compute are band-pass-filtered versions of the
ous envelope and frequency of a given trace. Then, using curvature results, though using the associative law of
a user-defined threshold (in our examples r ¼ 0.8), we linear operators, it is computationally more convenient
extract the time and instantaneous frequency of all enve- to band pass filter the derivative operators rather than
lopes that exceed r times the largest envelope. Wavelets the output curvature result. Details of this implementa-
of unknown complex amplitude α (or alternatively, un- tion can be found in Chopra and Marfurt (2007).
known magnitude and phase) for the given instantane-
ous (average) frequency are then extracted from the Amplitude gradients
dictionary. The values of α are computed using least- Mathematically, amplitude gradients are like time-
squares, scaled complex spectra from the dictionary are structure gradients. Within an analysis window, we
accumulated and the residual trace is generated. This compute the Karhunen-Loeve filtered version of the
process iterates until the residual energy is a small per- data, which has an associated eigenvalue λ, and eigen-
centage of the energy of the original trace. The result is a vector (actually, in 2D, an eigenmap) vðx; yÞ, which has
time-frequency spectral decomposition with a spectrum a magnitude of 1.0. The east and north components of
at each time sample. the energy-weighted (i.e., the eigenvalue weighted) am-
The peak magnitude is the maximum magnitude at a plitude gradient g are then
given voxel and the peak frequency the corresponding
frequency of the spectrum. ∂v
gx ¼ λ ; (A-9)
∂x
Spectral balancing and spectral bluing
Given the spectra at every voxel, we compute the and
average time-frequency spectra for the entire survey. ∂v
After some vertical smoothing (
0.2 s in our example), gy ¼ λ : (A-10)
∂y
we balance the spectra using

1∕2
P peak ðtÞ Amplitude gradients always need to be computed
aj ðt; f Þ ¼
blue
f β aj ðt; f Þ; (A-8)
P avg ðt; f Þ þ εP peak ðtÞ along structural dip. One can also compute impedance
gradients.
where aj ðt; f Þ is the magnitude spectrum of the jth trace
computed using spectral decomposition, P avg ðt; f Þ is the Amplitude curvature
smoothed, average power spectrum for the entire sur- Although structural curvature is computed by taking
vey, P peak ðtÞ is the peak power of the smoothed average the first derivatives of structural dip, amplitude curva-
power spectrum at time t, ε ¼ 0.01 is a prewhitening ture is computed by taking the first derivatives of the
factor, and β ¼ 0.3 is a bluing factor described by Neep amplitude gradient. In our implementation, we apply

Interpretation / August 2014 SF107

 the same long-wavelength filter operators as we do in Devonian Marcellus Shale, Appalachian basin: Techni-
structural curvature. The major difference is that the cal Report DOE/NETL/2011/1478, National Energy
vertical dimension is different in amplitude curvature, Technology Laboratory for the United States Depart-
such that we compute the mathematically simpler most- ment of Energy.
positive and most-negative amplitude curvatures (with- Chen, M., S. Zhan, Z. Wan, H. Zhang, and L. Li, 2010,
out the word principal). This simple calculation delin- Detecting carbonate-karst reservoir using the direc-
eates zones that have extreme values of energy and tional amplitude gradient difference technique: 81st An-
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in our examples shows joints and collapse features. Am- nual International Meeting, SEG, Expanded Abstracts,
plitude curvature can also be computed from imped- 1845–1849.
ances or any other gradient attribute. Chopra, S., and K. J. Marfurt, 2007, Volumetric curvature
Structure rotation and convergence attributes add value to 3D seismic data interpreta-
Geophysicists familiar with fluid mechanics and tion: The Leading Edge, 26, 856–867, doi: 10.1190/1
electromagnetics are comfortable with taking the diver- .2756864.
gence and curl of vectors. The divergence of the struc- Duo, Q., Y. Sun, C. Sullivan, and H. Guo, 2011, Paleokarst
tural dip vector is twice the mean curvature. The curl of system development in the San Andres Formation, Per-
vector dip is in turn a vector. Computationally, it is con- mian Basin, revealed by seismic characterization: Jour-
venient to convert from the dip vector p, to the normal nal of Applied Geophysics, 75, 379–389, doi: 10.1016/j
vector n. Marfurt and Rich (2010) then define the struc- .jappgeo.2011.08.003.
tural rotation (the z-component of the curl vector) as Elebiju, O. O., G. R. Keller, and K. J. Marfurt, 2010, Case
      history investigation of links between Precambrian
∂ny ∂nz ∂nz ∂nx ∂nx ∂ny basement structure and Paleozoic strata in the Fort
r ¼ nx − − ny − − nz − ;
∂z ∂y ∂x ∂z ∂y ∂x Worth basin, Texas, USA, using high-resolution aero-
(A-11) magnetic, HRAM data and seismic attributes: Geophys-
ics, 75, no. 4, B157–B168, doi: 10.1190/1.3435939.
and the structural convergence (the x- and y-compo- Feng, X., Y. Wang, X. Wang, N. Wang, G. Gao, and X. Zhu,
nents of the curl vector) 2012, The application of high-resolution 3D seismic ac-

    quisition techniques for carbonate reservoir characteri-
∂nx ∂ny ∂ny ∂nz
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∂y ∂x ∂z ∂y .1190/1.3686914.

   
∂ny ∂nz ∂nx ∂ny Ferrill, D. A., and A. P. Morris, 2008, Fault zone deforma-
þ^ y nz − − nx −
∂z ∂y ∂y ∂x tion controlled by carbonate mechanical stratigraphy,

    Balcones fault system, Texas: AAPG Bulletin, 92,
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∂x ∂z ∂z ∂y
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.1190/1.2213049. Jie Qi is a Ph.D. student in geophysics
Marfurt, K. J., and J. R. Rich, 2010, Beyond curvature: Volu- and a research assistant at the Univer-
metric estimates of reflector rotation and convergence: sity of Oklahoma, Norman, USA. He
80th Annual International Meeting, SEG, Expanded received an M.D. from the University
Abstracts, 1467–1472. of Houston, Texas, USA, and a B.D.
from the China University of Petro-
McDonnell, A., R. G. Loucks, and T. Dooley, 2007, Quanti-
leum, Beijing, China. In 2011, he stud-
fying the origin and geometry of circular sag structures ied at the University of Houston, and
in northern Fort Worth Basin, Texas: Paleocave col- he also worked as a research assistant
lapse, pull-apart fault systems, or hydrothermal altera- in spectral decomposition and seismic interpretation. His
tion?: AAPG Bulletin, 91, 1295–1318, doi: 10.1306/ research interests include seismic attribute analysis, seis-
05170706086. mic inversion, signal processing, modeling, and migration.

Interpretation / August 2014 SF109

 He is a member of SEG, AAPG, and the Geophysical Soci- work as postdoctoral research faculty in the University
eties of Houston. His current research includes seismic of Oklahoma, USA, from October 2013 to October 2014.
attribute analysis, geologic features interpretation on 3D His research work is mainly focused on research of seismic
seismic data, and prestack imaging. data processing methods, seismic modeling and imaging
by wave equation numerical method, inversion and reser-
voir prediction.
Bo Zhang received a B.S. (2006) in Geophysics from China
Downloaded 07/04/17 to 99.130.119.212. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/

University of Petroleum, and an M.S. (2009) in Geophysics

from the Institute of Geology and Geophysics, Chinese Kurt J. Marfurt joined The university of Oklahoma in
Academy of Sciences. He is currently a doctoral student 2007, where he serves as the Frank and Henrietta Schultz
at the University of Oklahoma and the thesis title is long Professor of Geophysics within the ConocoPhillips School
offset seismic analysis for resources plays. of Geology and Geophysics. His primary research interests
include development and calibration of new seismic attrib-
utes to aid in seismic processing, seismic interpretation,
Huailai Zhouis an associate professor of College of and reservoir characterization. Recent work has focused
Geophysics, in Chengdu University of Technology, and on correlating seismic attributes such as volumetric curva-
postdoctor. He received his PHD degree in Earth Explora- ture, impedance inversion, and azimuthal anisotropy with
tion and Information Techniques, from Chengdu Univer- image logs and microseismic measurements with a particu-
sity of Technology in 2009. He completed the lar focus on resource plays. In addition to teaching and re-
postdoctoral research with Institute of Sedimentary Geol- search duties at OU, he leads short courses on attributes
ogy in Chengdu University of Technology from 2010 to for SEG and AAPG.
2012. He is sponsored by China Scholarship Council to

SF110 Interpretation / August 2014