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Research ArticleSeismic Signature of Transition Zone (Wolf Ramp)
in ShaleDeposits with Application of Frequency Analysis
Anna Kwietniak ,1 Tomasz Maćkowski ,2 and Kamil Cichostępski
1
1Department of Geophysics, University of Science and Technology
AGH, Kraków, Poland2Department of Fossil Fuels, University of
Science and Technology AGH, Kraków, Poland
Correspondence should be addressed to Anna Kwietniak;
[email protected]
Received 5 October 2020; Revised 8 December 2020; Accepted 16
January 2021; Published 29 January 2021
Academic Editor: Kyungbook Lee
Copyright © 2021 Anna Kwietniak et al. This is an open access
article distributed under the Creative Commons Attribution
License,which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is properly
cited.
The concept of a transition zone, known as Wolf ramp, was
incorporated into the seismic interpretation of a 3D seismic
surveysituated within the Baltic Basin (Northern Poland). Within
the survey area, there exists one formation, the Pasłęk
Formation,(Lower Silurian—Llandovery), that exhibits a linear
change of velocity. This characteristic—linear change of
velocity—causes areflection coefficient (i.e., seismic amplitude)
produced at such a boundary to be frequency dependent. The Pasłęk
Formationwas considered to be a potential shale gas reservoir and
it was necessary to determine its structural position and
thickness. Theformation is challenging for robust seismic
interpretation on the migrated seismic section—it does not manifest
a stablereflection coefficient, and the amplitude contrast
associated with the borders of the formation is low. There is no
impedancecontrast that would produce a reflection of high amplitude
at the top or base of the formation which excludes determination
ofthe formation thickness, hence the estimation of reservoir
volume. Within a 3D dataset, there exists only one well with
completelogs that were used for the analysis. The Pasłęk Formation
is a flat-lying layer that continues itself far beyond the 3D
survey. Itis present in wells in the vicinity of the study area.
These wells lay within other 3D or 2D datasets, but the quality of
the seismicis poor, and similar seismic analysis is not possible.
Nevertheless, these wells were incorporated in the research to
reason aboutthe possible link between the existence of transition
zone and mineral content. The method used for recognition of
transitionzone is spectral decomposition and spectral analyses. The
integrated studies enabled us to find a link between the Wolf
rampand mudstone-claystone interval of the Silurian age and give a
new example of a transition zone which is present in shale
plays.The transition zone concept might be applied for shale plays
identification and analysis.
1. Introduction
The concept of a transition zone, a Wolf ramp, is
relativelyold—the original work of Alfred Wolf describing a
rampcomes from the second volume of Geophysics [1]. Thetransition
zone is defined as a layer of a given thickness thatseparates two
half-spaces of different and constant velocityvalues: V1 (upper
layer) and V2 (lower layer). The relationbetween velocities is not
essential. The transition zone ischaracterized by a linear change
of velocity with depth,hence the name. In this model, the density
is neglected[1]. The most important characteristic of this layer is
thatsuch a sequence produces a reflection coefficient that is
afunction of the frequency of the elastic wave for a zero-offset
seismic trace.
The paradigms were extended to a zone of linearly chang-ing
velocity and density within 60-80′. Works of Gupta [2]give solid
analytical solutions for variations of density andvelocity for
elastic waves in liquid media. The idea of thetransition zone is
applicable in many geological settings: Jus-tice and Zuba [3] used
it for permafrost analysis. In the paper,they presented 1D modeling
with the use of convolution tofind a seismic signature link to
permafrost analysis. Thesemodels show that the transition zone is
frequency dependentand that permafrost resembles such a
characteristic.
Recently, the concept was rediscovered and describedwith a
modest approach by Liner and Bodmann [4] whereauthors use the
transition zone model for interpretation ofsea bed. This paper
contains a repeated analytical solutionofWolf. In the paper, the
authors present concept of applying
HindawiGeofluidsVolume 2021, Article ID 6614081, 16
pageshttps://doi.org/10.1155/2021/6614081
https://orcid.org/0000-0002-1683-2608https://orcid.org/0000-0002-8366-0332https://orcid.org/0000-0001-7982-4763https://creativecommons.org/licenses/by/4.0/https://doi.org/10.1155/2021/6614081
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spectral decomposition for indicating reflectivity
dispersionpresent for normal-incidence reflection of a linear
velocitytransition zone. Many different factors may be the
reasonfor linearly changing velocity with depth; one of them is
gassaturation. Gómez and Ravazzoli [5] studied this relation
tocarbon dioxide transition layers. The work gives the applica-tion
of the theory for CO2 storage. They started with Wolfsolution and
added factors related to fluid properties—bulkdensity, bulk
modulus. The numerical solution lays in accor-dance with the
analytical solution, and the effect of carbondioxide saturation
influences the model. This techniqueenables more precise monitoring
of carbon dioxide seques-tration sites.
The model of a transition zone and its attenuating prop-erties
was the subject of a research project [6] for
indicatingshale-bearing deposits within the Polish shale gas
conces-sions. The Pasłęk Formation was one of several
prospectinghorizons for potential shale gas exploration. However,
theformation was challenging to map with the use of themigrated
seismic section. The problem was due to its elasticproperties and
the reflectivity series—the top and bed of theformation cannot be
easily identified on the seismic section.Hence, there was a need to
incorporate other methods forseismic interpretation of this
interval. It was proposed thatthe interval under analysis can be
considered to be a transi-tion zone, and that frequency analysis
might enable its inter-pretation. The main focus of the research
was to applydifferent spectral decomposition algorithms so that the
inter-pretation of the transition zone would be possible. In
thisarticle, we focus mainly on the applicability of the
transitionzone for seismic interpretation of shale reservoir. We
willshow a new example of the transition zone and evaluatespectral
decomposition algorithms and their performance.
2. Materials
2.1. Theory of a Transition Zone. The transition zone is alayer
that separates two intervals of a given velocity, and itsvelocity
characteristic is described by the velocity of theupper layer,
lower layer, and distance between them. Thesimplified model of a
transition zone is presented in Figure 1.
In Figure 1, the layers are indicated by the velocity of
thefirst layer, V1, the velocity of the second layer, V2, and
thetransition zone of the defined thickness h. The densitychanges
are neglected for the initial definition. The relationbetween V1
and V2 is negligible, i.e., V1 can be lower orhigher than V2. By
the definition of only three parameters,the three-layer geological
model is created. The critical prop-erty of the transition layer is
the fact that the reflection coef-ficient produced in the seismic
reflection process is frequencydependent. The reflection
coefficient of the transition zonelayer is defined as [1]
Rw fð Þ =1
2σ + 2γ coth γ log kð Þ½ � , ð1Þ
In Equation (1), a reflection coefficient for absoluteamplitude
R is opposite to the displacement reflection coeffi-cient [5]. The
precise derivation of the reflection coefficient is
presented in many papers, starting with the original paper
byWolf [1], but also more current [4, 7]. In Equation (1), k is
avelocity ratio of the upper and lower part of the transitionzone,
frequency f is in hertz, transition zone thickness, h inmeters, and
σ and γ depend on frequency by
σ fð Þ = i2πf hk − 1ð ÞV1
,
γ fð Þ =ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
14 + σ
2:
r
ð2Þ
Parameter σ is defined according to the upper-layervelocity
V1.
Such defined reflection coefficient (Equation (1)) is afunction
of frequency, which implies that in respect of theconvolutional
model of seismic trace, the same is true forseismic amplitude
value. For example, for a transition zoneof thickness 50 meters,
the maximal spectral energy will con-centrate for frequencies below
20Hz (Figure 2).
The function presented in Figure 2 depicts the behaviourof the
absolute seismic amplitude for a case when V1 is twicebigger than
V2. For other cases, the exact solution will be dif-ferent, but two
of properties of the function will be kept: (1)the existence of
periodicity, i.e., notch width and peak posi-tion, here of 30Hz,
and (2) the decaying value of spectralamplitude. The exact notch
position is specific for the choseninitial parameters. With the
different thickness and velocity
Velocity (m/s)
h (m)
V1
V2
Figure 1: Simplified model of a transition zone (Wolf ramp).
Valu
e
Amplitude
0 20 40 60 80 100
0.2
0.15
0.10
0.5
0
Frequency (Hz)
Figure 2: The amplitude of the 50-meter thick transition zone as
afunction of frequency, the plot obtained by the Equation (1).
2 Geofluids
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ratio, the function will keep the periodicity, but the
notchwidth will vary [5].
For such a defined transition zone, it is, therefore, crucialto
analyze low frequency range of the seismic data. For thisreason,
spectral analysis is an accurate tool for transitionzone
interpretation: given the relative thickness of a layer(geological
information from the well), one can model theexact behaviour of the
amplitude versus frequency responseby incorporating Equation (1)
and analysis of the frequencymaxima (Figure 2). Spectral
decomposition volume relatedto such frequency maxima should reveal
the layer underanalysis and enable its thickness estimation.
2.2. Motivation for Application of Wolf Ramp Concept.
Theconvolutional model of a seismic trace says that the
observedseismic amplitude is relative to reflection coefficient.
Assum-ing a stationary, zero-phase wavelet, the change in
seismicamplitude is proportional to the reflection coefficient.
Thereflection coefficient that is a step function will produce
dis-tinguishable and distinct peak (Figures 3(a) and 3(b)), evenin
the presence of a tuning effect (Figures 3(c) and 3(d)).
Every deviation from a step function that is associatedwith
velocity and/or density gradients will result in a modi-fied
seismic reflection. Such examples are shown inFigures 3(e)–3(n),
and the resulting reflection coefficient
might be extended in time (Figures 3(e)–3(g)) or, if the
thick-ness of a transition zone is lower, the resulting reflection
willbe rotated in phase and scaled in terms of amplitude values.The
exact shape of reflection will be governed by the modeland
interference of the wavelet. The classical Wolf ramp isdepicted in
Figures 3(f) and 3(g). It can be noticed that reflec-tions produced
by Wolf ramp manifest lower amplitudes,even though the impedance
change is the same as for othermodels. Additionally, the reflection
produced by a Wolframp is extended in time. The character of the
reflectionchanges when the transition zone has larger thickness
(com-pare Figures 3(f) and 3(g)), so in terms of layer of
nonuni-form thickness across the study area, seismic signature
willvary in relation to the thickness interval. Nonetheless,
theapplication of frequency analysis, to which the transitionzone
is very sensitive, might give additional information thatwould
result in more accurate seismic interpretation.
2.3. Modeling for Transition Zone Recognition. Before
weproceeded with real data example, we performed a modelingstep. To
do so, we used full-waveform modeling and a syn-thetic geological
model of a Wolf ramp. For a model, we used0-phase Ricker wavelet of
specific dominant frequencies. Themodel is created to simulate the
seismic response from a layerof linear velocity change. The model
consists of the transition
Model
Seismicresponse
(a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) (n)
Figure 3: Reflectivity models (upper row) and their seismic
response obtained by the convolution with zero-phase Ricker wavelet
(lower row)[8], p. 237.
20 Hz 25 Hz 30 Hz 50 Hz 60 Hz
Dep
th (m
)
100
200
300
400
500
35 Hz15 Hz10 Hz 40 Hz
Figure 4: Reflection from a transition zone obtained by
full-waveform modeling with the 0-phase Ricker wavelet of different
dominantfrequencies (see top of the figure). Transition zone
thickness: 50 meters (green area), k = 0:8.
3Geofluids
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zone of a thickness of 50 meters; the V1/V2 ratio is the sameas
in analytical solution (Figure 2) in order to compare theresults
and verify if the transition zone would be visible onthe migrated
seismic section. In Figure 4, the resulting tracesare presented
that were created with different dominant fre-quencies. The trend
is visible—with the increasing frequency,the reflection from a
transition zone decreases. The amplitudescale for all panels is
consistent; for each frequency, ten zero-offset traces are
presented. For frequencies around 30Hz, itis almost impossible to
depict any seismic reflection, even ina complete synthetic
scenario, with no noise added. Thismight suggest that even the
transition zone of significantthickness would not be visible on the
migrated seismic section.
In comparison, in the numerical solution (Figure 2 vs.Figure 4),
it is difficult to indicate the exact amplitude period-icity.
Nonetheless, according to the modeling performed byGomez and
Ravazzoli [5], the response from the transitionzone might as well
reveal only a decaying character of ampli-tude for higher
frequencies. In this respect, the resultsobtained by full-waveform
modeling lay in accordance withthe theoretical solution.
2.4. Geological Setting. A potential transition zone was
indi-cated within the Silurian sediments—the Pasłęk Formation
that lays within the Polish part of Baltic Basin, Poland(Figure
5). The survey area is situated in the Pomeranian Voi-vodeship at
the border of the Wejherowo and Puck counties.The seismic survey
was designed within the concession ofPolish Oil and Gas Company,
and the area that is covered bythe 3D seismic survey is 12.65km2.
The survey area is situatedin the western part of the Peri-Baltic
Syneclise, within therange of the southeastern slope of the Łeba
elevation.
The lithostratigraphic profile of the area is represented bythe
Precambrian crystalline basement, deposits of theEocambrian,
Cambrian, Ordovician, Silurian, Zechstein, Tri-assic, Jurassic,
Cretaceous, and Cenozoic deposits. The clasticseries creates two
main complexes: one is of the Caledonianorogeny and encompasses
deposits of the Cambrian to Silu-rian, and the other is associated
with the Laramian phaseand includes deposits from Permian to
Cretaceous. Thesetwo complexes are divided by the Variscidian gap
that rangesfrom the Devonian to Carboniferous. The
lithostratigraphicprofile of the Paleozoic sequence is presented in
Figure 6,and a more detailed description of the region can be
foundin recently published papers [10, 11]. Within this
sequence,there were two possible shale gas reservoirs—the
Sasinoclaystone formation of Upper Ordovician and the
PasłękFormation of Lower Silurian (Aeronian-Telychian).
0 100 200 km
1
Alpine Orogen
VariscanOrogen
East European Platform
BalticShieldScan
dinavian
Caledo
nides
North GermanPolish Caledonides
TIZ
TIZ
Baltic Basin
L-1
3D seismic survey
Gdansk
O-2
K-1
Figure 5: Location of the survey area within the main tectonic
units of north-central Europe showing the Baltic Basin (dashed
line). TTZ:Tornquist-Teisseyre Zone; O-2, L-1, and K-1—wells
location, after Poprawa et al. [9].
4 Geofluids
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The Pasłęk Formation consists of dark-grey and greyclaystones
that are laminated with the greenish and blackclaystones [12]. The
confirmed thickness of the formationmight reach up to 60 meters in
the Baltic Basin. Mostrecently, the deposits are described as
rhythmic alternationsof black, laminated mudstones and greenish,
bioturbatedmudstones [11]. The formation is considered to be
noncal-cerous and showing variable to the high degree of
bioturba-tion [11]. The top of the formation is gradational, and
thislithological characteristic causes the acoustic impedance ofthe
layer to be gradational hence producing very weak seis-mic
reflection. The specific geological position altogetherwith the
sedimentary history probably explains the sourceof linear changes
in velocity. For the methods and the seismicinterpretation, the
formation can be just treated as a superfi-cial layer that exhibits
linear changes of velocity with depthwhich can be stated after
analysis of well logs (Figure 7).The goal is to verify whether the
Pasłęk Formation can betreated as a transition zone and if yes to
interpret it, applyinga frequency analysis within the 3D seismic
survey in order todetermine its thickness away from the wells.
2.5. Potential Shale Gas Prospects. The Pasłęk Formation canbe
found in in the marine and terrestrial region of the Peri-Baltic
Syneclise. The complete cores of the formation areavailable in
three wells. The formation is very rich in organicdebris, and a
wide variety of graptolites was found in thedeposits. The Lower
Silurian complex can be classified as apotential shale gas
reservoir. While drilling of wellDarżlubie-IG1 (1973), the Lower
Silurian deposits, repre-sented by the Pasłęk Formation, the
hydrocarbon contentin the drilling fluid increased from 2.28% to
9.43% [13]. Morerecent well data from other wells estimated the
reservoirparameters with the total organic content (TOC) of the
Llan-dovery profile to be at the averaged level between 1 and 6%TOC
[14]. Within the study area, the volumetric kerogencontent (VKER)
of the Pasłęk Formation manifests stablelevel of about 4-5% [10].
The hydrogen index (HI) variesgreatly across the East European
Craton, and it is very diffi-cult to indicate the exact type of
kerogen by analyticalmethods due to the high maturity of the
sediments [14].Nonetheless, the Pasłęk Formation manifests slightly
lowermaturity than the neighboring Jantar and Sasino Formationsthat
both manifest higher TOC. The kerogen type, mostconfidently, can be
determined as type II kerogen of algae-marine origin with high
generation potential [14]. In termsof burial and thermal history,
Lower Silurian strata reachtemperatures of 120° and the maturity
modelling has shownthat an increase of temperature and burial was
continuousfrom Late Silurian to the Middle Carboniferous [15].
Thedetailed rock physics modelling of elastic properties
[16]classified the formation under analysis to shales/shales
withorganic matter and hydrocarbons.
3. Methods
Reflection coefficients produced by the transition zoneexhibit
frequency-dependent attenuation (Figure 2). Tointerpret the
interval, we chose methods of spectral
Epoch/Age
420
430
440
450
460
470
480
Prid
oli
Ludl
ow
Ludford-ian
Gorstian
Wen
lock
Hom
eria
n
Shein-woodian
Llan
dove
ry
Ash
gill
Cara
doc
Llan
virn
Are
nig
Trem
adoc
Tely
chia
n
Aeron-ian
Late
Hirnant-ian
Katia
n
Rhuddan-ian
Sand
bian
Mid
dle
Dar
riwlia
n
Daping-ian
Cambrian
Floi
anTr
emad
ocia
n
485.4
Early 477.7
467.3
458.4
453.0
438.5
433.5
443.8
423.0
Silu
rian
Ord
ovic
ian
Age (Ma) Litostratigraphic Units
Piaśnica formation(black kerogenous mudstones)
Kopalino formation(marly and bioclastic limestones)
Jantar mudstone(black kerogenous mudstones)
Paslęk formation(black kerogenous mudstones,green
bioturbated,mudstones,
bentonites and calcareous concretions
Puck fm(calcareous mudstones, marls and
clayey mudstones)Reda Mb (calcisilities and calcareous
mudstones)
Prabuty formation(calcareous mudstones,
marls and clayey mudstones)
Sluchów mudstone(black kerogenous mudstones,green
bioturbated,mudstones,
bentonites and calcareous concretions)
Sasino Formation(black kerogenous mudstones,green
bioturbated,mudstones,
bentonites and calcareous concretions
Pelplin fm(dark mudstones,
bentonites, bioclasticlimestones
and calcareousconcretions)
Kociewie fm(mudstones,
siltstonesand sandstones)
Figure 6: Lithostratigraphic profile of Lower Paleozoic
deposits;Pasłęk Formation: Pasłęk fm; Prabuty mudstone: O3;
Kopalinoformation: OrV; after Porębski and Podhalańska [11].
5Geofluids
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L-1VDOLfraction0 1VLIMfraction0 1
VSANDfraction0 1
VIL
Time (ms)fraction0 1
RHOB
m/s2000 6000DTP
g/cc1.5 3P impedance Synthetic Seismic
traceSeismic data MD (m)
2725
2750
2775
2800
2825
2850
2875
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3000
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fromKB262 265 268 271 274 277 280
seismogram(m/s)⁎(g3000 19000
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Paslek fm
O3
Orv
(a)
(b)
Velocity (m/s)
h (m)
V1
V2
(c)
Figure 7: (a) From left: lithology, Vp (red curve), density
(blue curve), P wave impedance, synthetic seismogram (blue),
seismic traces (red),and seismic with location of well (red line);
(b) enlarged part with a linear approximation of velocity (red
dashed line) and density (bluedashed line); (c) seismogeological
model of a transition zone.
6 Geofluids
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decomposition as the primary tool for analyzing the
spatialcontinuity of the formation. Spectral decomposition
enablesthe definition of the amplitude component associated withthe
given frequency range. For the transition zone, the mostsignificant
result should be associated with the lowerfrequency range (low
frequency anomaly). Firstly, the instan-taneous frequency was
computed, and then spectral decom-position followed.
For spectral decomposition a seismic volume with rela-tive
amplitude preservation (RAP volume) should be prefer-ably used.
Such processing would not modulate bothamplitude relation and
frequency relation [17, 18]. Moreinvasive processing sequences may
introduce some fre-quency range [10] that will affect the response
for a transitionzone. For these reasons for spectral decomposition,
we used aseismic volume without amplitude modulations and gain.
For analysis, three algorithms of spectral decompositionare
used: fast Fourier transform (FFT), continuous wavelettransform
(CWT), and complete ensemble empirical modedecomposition (CEEMD).
The results of spectral decomposi-
tion are consistent but differ in details. These differences
arehighlighted in the next section.
FFT algorithm is based on a linear transform and per-forms
Fourier analysis in a given time window. This algo-rithm performs
well in situations, where the approximatetime span of the event can
be defined beforehand. For thisreason, it is crucial to use
information from a borehole andverify the potential thickness of
the interval in question. Forour research, we have information from
3 wells. Additionally,the layer under analysis is not much involved
tectonical-ly—we can assume that it is a flat-lying formation that
doesnot manifest any structural deformations.
CWT algorithm works with the library of wavelets thatare
modified Gaussian wavelets—called Morlet wavelets.The decomposition
process is based on the scaled and shiftedMorlet wavelets (unlike
the FFT that uses sine functions).CWT algorithm can reach a higher
temporal resolution anddoes not require any information on the
scale of the geolog-ical feature. By applying CWT, the results are
reliable forsmall features (insignificant thicknesses) and more
massive
Table 1: Decomposition parameters used in the analysis.
Decomposition method Parameters
FFT Window length: 30ms; taper length: 32ms; taper type: Haan
wavelet
CWT Used wavelet: Morlet
CEEMDGaussian noise: 25%
Realization number: 20A
mpl
itude
1
0.9
00 20 40 60 80 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Frequency (Hz)
RW, CWT, trace 247/271
FFT 30 ms
(a)
RW, FFT, trace 247/271
0 20 40 60 80 100
FFT 30 ms
Frequency (Hz)
Am
plitu
de
1
0.9
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
(b)
Figure 8: Amplitude spectra for the transition zone: (a)
spectrum obtained by the CWT decomposition and (b) the spectrum
obtained by theFFT decomposition. Both spectra are shown for the
same time position.
7Geofluids
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objects (significant thicknesses) which are especially helpfulin
the case of no geological information from a borehole.
CEEMD algorithm is based on Huang decomposition[19] and uses the
sifting process: the local minima and
maxima of a seismic trace are found and then based on thedefined
points, and the upper and lower envelope is com-puted. Next, the
mean of the envelope is computed, and thisis called the first
intrinsic mode functions (IMFs). The first
O3
OrV
L-1
Paslęk fm
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246 248 250 252 254 256 258 260 262 264 266 268 270 272 274
L-1276 278 280 282 284 286 288 290 292 294 296 298 300 302 304
306 308 310 312Xline
Well
(a)
O3
OrV
L-1
Paslęk fm
Well L-1216 218 220 222 224 226 228 230 232 234 236 238 240 242
244 246 248 250 252 254 256 258 260 262 264 266 268 270 272 274 276
278 280 282 284 286 288 290 292 294 296 298 300 302 304 306
Frequency
150147144141138134131128125122119116113109106103100979491888481787572696663595653504744413834312825221916139630
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Xline
(b)
Figure 9: Zoomed seismic profile that goes through the well: (a)
migrated seismic section, (b) instantaneous frequency attribute.
The curve isP wave velocity. In (b), red colours indicate lower
frequencies, and purple indicates higher frequencies.
Horizons’marks are O3: the top of thePrabuty formation and Orv: top
of the Kopalino formation. Black arrows indicate the
characteristics of the low frequency anomaly (describedin text),
and blue arrow indicates tuning effect.
8 Geofluids
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IMF is subtracted from the signal, and the whole processrepeats.
In order to secure mode mixing phenomena, adefined portion of
Gaussian noise is added to the signalbefore the process starts. The
decomposition continuous
until the remaining signal is monotonic. The advantage ofthe
decomposition is that it does not need a predefined setof the
decomposition kernels, and the IMFs are purelydesigned to fit the
specific seismic trace.
O3
OrV
L-1
Paslęk fm
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308 310 312XlineWell
(a)
O3
OrV
L-1
Paslęk fm
Well L-1216 218 220 222 224 226 228 230 232 234 236 238 240 242
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278 280 282 284 286 288 290 292 294 296 298 300 302 304 306
Frequency
150147144141138134131128125122119116113109106103100979491888481787572696663595653504744413834312825221916139630
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1890Time (ms)
Xline
(b)
Figure 10: Zoomed seismic profile that goes through the well:
(a) migrated seismic section, (b) spectral decomposition based on
the FFTalgorithm. The curve is P wave velocity. In (b), red colours
indicate lower frequencies, and purple indicates higher
frequencies. Horizons’marks are O3: the top of the Prabuty
formation and Orv: top of the Kopalino formation. Arrows indicate
the characteristics of the lowfrequency anomaly (described in
text).
9Geofluids
-
The parameters used for the specific decomposition arepresented
in Table 1. The parameters were tested, and thepresented set is
optimal. Tests were run on the seismic traces
from the vicinity of wells and adjusted so that to reach in
thiscontrol, positions required resolution verified by the
syn-thetic seismograms and real traces. For the FFT algorithm,
O3
OrV
L-1
Paslęk fm
Time (ms)1890
1880
1870
1860
1850
1890
1830
1820
1810
1800
1790
1780
1770
1760
1750
1740
1730
1720
1710
1700
1690
1680
1670
1660
216 218 220 222 224 226 228 230 232 234 236 238 240 242 244 246
248 250 252 254 256 258 260 262 264 266 268 270 272 274L-1
276 278 280 282 284 286 288 290 292 294 296 298 300 302 304 306
308 310 312XlineWell
(a)
O3
OrV
L-1
Paslęk fm
Well L-1216 218 220 222 224 226 228 230 232 234 236 238 240 242
244 246 248 250 252 254 256 258 260 262 264 266 268 270 272 274 276
278 280 282 284 286 288 290 292 294 296 298 300 302 304 306
Frequency
150147144141138134131128125122119116113109106103100979491888481787572696663595653504744413834312825221916139630
1660
1670
1680
1690
1700
1710
1720
1730
1740
1750
1760
1770
1780
1790
1800
1810
1820
1830
1840
1850
1860
1870
1880
1890Time (ms)
Xline
(b)
Figure 11: Zoomed seismic profile that goes through the well:
(a) migrated seismic section, (b) spectral decomposition based on
the CEEMDalgorithm. The curve is P wave velocity. In (b), red
colours indicate lower frequencies, and purple indicates higher
frequencies. Horizons’marks are O3: the top of the Prabuty
formation and Orv: top of the Kopalino formation. Arrows indicate
the characteristics of the lowfrequency anomaly (described in
text).
10 Geofluids
-
we tested window lengths between 15 and 50ms. For theCWT
algorithm, other types of wavelet were applied: Rickerand Gaussian;
for the CEEMD realization number, it wasincreased up to 50 that
substantially elongated computation
time. The results were comparable, and we decreased thenumber of
realizations to the point when the results exhibitedthe same rate
of details, and the computation time wasacceptable, resulting in 20
being optimal.
O3
OrV
L-1
Paslęk fm
Time (ms)1890
1880
1870
1860
1850
1890
1830
1820
1810
1800
1790
1780
1770
1760
1750
1740
1730
1720
1710
1700
1690
1680
1670
1660
216 218 220 222 224 226 228 230 232 234 236 238 240 242 244 246
248 250 252 254 256 258 260 262 264 266 268 270 272 274L-1
276 278 280 282 284 286 288 290 292 294 296 298 300 302 304 306
308 310 312XlineWell
(a)
O3
OrV
L-1
Paslęk fm
Well L-1216 218 220 222 224 226 228 230 232 234 236 238 240 242
244 246 248 250 252 254 256 258 260 262 264 266 268 270 272 274 276
278 280 282 284 286 288 290 292 294 296 298 300 302 304 306
Frequency
150147144141138134131128125122119116113109106103100979491888481787572696663595653504744413834312825221916139630
1660
1670
1680
1690
1700
1710
1720
1730
1740
1750
1760
1770
1780
1790
1800
1810
1820
1830
1840
1850
1860
1870
1880
1890Time (ms)
Xline
(b)
Figure 12: Zoomed seismic profile that goes through the well:
(a) migrated seismic section, (b) spectral decomposition based on
the CWTalgorithm. The curve is P wave velocity. In (b), red colours
indicate lower frequencies, and purple indicates higher
frequencies. Horizons’marks are O3: the top of the Prabuty
formation and Orv: top of the Kopalino formation. Arrows indicate
the characteristics of the lowfrequency anomaly (described in
text).
11Geofluids
-
4. Results and Discussion
4.1. Results of Spectral Analysis. In Figure 8, the
normalizedamplitude spectra computed by FFT and CWT decomposi-tion
are presented. These spectra were computed for a singletrace that
lays in a location of well L-1 for the time positioncorresponding
to the middle point in a transition zone.
Spectra shown in Figure 8 are similar: they both
indicateapproximately the same dominant frequency, that is,
20Hz,and for the FFT method, it is higher, around 30Hz. Thehigher
amplitudes for lower frequency content agree withthe synthetic
example (Figure 2). For the CWT results, higherspectral dynamics
are visible, and two frequency peaks arevisible (20 and 60Hz). The
second peak has twice loweramplitude. Similar characteristics are
visible for the FFTmethod; nevertheless, the rate of changes is not
as prominent;the amplitude drop for the second notch is at the
level of 20%.However, the periodicity of the spectral peaks is the
same(notch width is app. 40Hz).
Such a behaviour of the frequency spectra is typical forWolf
ramp that was shown for the modelled data [1, 4, 5]In real data
example, the shape of the frequency spectra isaffected by many
factors, e.g., attenuation, interference, andthe existence of the
multiples; hence, the function presentedin Figure 8 is not smooth.
Nevertheless, the lower than aver-aged dominant frequency (dominant
frequency of the surveyis 35Hz) might suggest that the interval
under analysis can beunderstood as a transition zone.
Instantaneous frequency (IF) manifests the rate ofchanges in the
phase of the signal, and it is linked to the max-imal spectral
amplitude [20]. The results of IF are shown inFigure 9(b), in
comparison with the migrated seismic section(Figure 9(a)).
In Figure 9(a), the top of the Pasłęk Formation is markedby a
light blue line. The reflection that corresponds to the topof the
formation diminishes from left to right, losing its
strength, which complicates the interpretation and excludesthe
application of the automatic horizon picking. InFigure 9(b), the
interval under analysis is similarly indicated,by the frequency
drop that corresponds to the transition zoneis more continuous. The
formation manifests itself by lowervalues of instantaneous
frequency, at the level between 15and 25Hz. It also can be seen
that the top of the transitionzone resembles very low frequencies.
The presented low fre-quency anomaly has a continuous character and
can bevisible within all span of a 3D seismic survey. The
anomalyhas symmetric character around the time of 1755ms, andits
position correlates with the interval, where the velocity
isapproximated by a linear function. The bottom of the anom-aly is
clearly defined by a significant increase in the frequencyvalue
(indicated by black arrows), and this change indicatesthe top of
the Ordovician (O3). Another interesting effectthat can be seen is
associated with decreasing thickness ofthe top of the
Ordovician—Prabuty formation, and it ismarked by a blue arrow in
Figure 9(b). The Prabuty forma-tion undergoes tuning effect that
can manifest itself by asudden change in frequency value. Such
effect was modelledand explained by Zeng [21], and we present a
real data exam-ple of how changes in thickness can be interpreted
on themigrated seismic profile (see Figure 9(b), blue arrow in
theleft-hand side).
A similar comparison is presented in Figure 10. Aftercomputing
decomposition with the use of the FFT method,it is possible to
extract dominant frequency—the frequencyvalue for which the
amplitude value reaches its maximum(Figure 10(b)).
In the case of spectral decomposition performed with theuse of
the FFT algorithm, results for a transition zone areconsistent with
the previously presented IF. However, thelow frequency anomaly has
higher values of frequency. Also,there exists an increase in
frequency (app. 45Hz) around theOrV seismic horizon; this also
occurs in IF display.
0
5
10
15
20
25
3050
252525
2525
Well location
35
40
Tim
e (m
s)
45
50
55
60
2000 m
Figure 13: Averaged temporal thickness distribution of the low
frequency anomaly (the Pasłęk Formation) interpreted with the use
of theCEEMD, IF, and FFT algorithms.
12 Geofluids
-
L-1
Paslęk fm.
O3
VDOLfraction0 1
VLIMfraction0 1
VSANDfraction0 1
VILMD (m)
2775
2800
2825
2850
2875
2900
2925
1800
1790
1780
1770
1760
1750
1740
1730
1720
1810
Time (ms) TopsfromKB
fraction0 1DTPm/s3000 6000
RHOB
L-1
g/cc1.5 3
(a)
Paslęk fm.
O3
L-1
VDOLfraction0 1
VLIMfraction0 1
VSANDfraction0 1
VILMD (m)
Time (ms) TopsfromKB
fraction0 1DTPm/s3000 6000
RHOB
O-2
g/cc1.5 3
2725
2750
2775
2800
2825
2850
2875
2900 1790
1780
1770
1760
1750
1740
1730
1720
1710
1700
(b)
Paslęk fm.
O3
L-1
VDOLfraction0 1
VLIMfraction0 1
VSANDfraction0 1
VILMD (m)
Time (ms) TopsfromKB
fraction0 1DTPm/s3000 6000
RHOB
K-1
g/cc1.5 3
3100
3125
3150
3175
3200
32252010
2000
1990
1980
1970
1960
1950
1940
(c)
Figure 14: Well logs representing sonic (DTP) and density logs
(RHOB) and lithological information for wells L-1, O-2, and K-1.
Pasłęk fm:the top of the Pasłęk Formation; Prabuty mudstone: O3.
Dashed black line approximates the linear character of velocity of
the PasłękFormation; dashed red line indicates the increase in
volumetric clay mineral content.
13Geofluids
-
Nevertheless, the top of the Ordovician similarly
manifestsitself by a rapid frequency increase (50Hz). The low
fre-quency anomaly that corresponds to the transition zone
hasdifferent morphology, and the FFT decomposition revealsmore
details into it. These differences are indicated by blackarrows in
Figure 10(b). Spatial comparison of the two fre-
quency attributes proves the continuity of the anomalywithin a
3D survey.
The CEEMD algorithm, in comparison with the previ-ously
presented, requires significantly more computationtime [22]. The
result of dominant frequency after theCEEMD for the same inline is
presented in Figure 11(b).
Vp (m/s)
VIL
(fra
ctio
n)
L-1
1
0.9
0.8
0.7
0.6
3700 3750 3800 3850 3900 3950 4000 4050 4100 4150 4200 4250 4300
4350 4400
2895.0
2890.5
2886.0
2881.5
2877.0
2872.5
2865.0
2863.5
2859.0
2854.5
2850.0
(a)
O-2
0.85
0.8
0.75
0.7
0.65
0.6
0.55
0.5
0.45
0.4
VIL
(fra
ctio
n)
Vp (m/s)370036003500 3800 3900 4000 4100 4200 4300 4400 4500
4600
2870
2864
2857
2850
2843
2837
2830
2823
2816
2810
2803
(b)
K-1
Vp (m/s)
VIL
(fra
ctio
n)
0.9
0.85
0.8
0.75
0.7
0.65
0.6
3750 3800 3850 3900 3950 4000 4050 4100 4150 4200 4250 4300 4350
4400 4450
3196.9
3192.3
3187.7
3183.0
3178.4
3173.7
3169.1
3164.4
3159.8
3155.1
3150.5
(c)
Figure 15: Cross plots showing relation for the Pasłęk Formation
between volumetric clay mineral content (VIL) and P wave velocity.
Depthis included as a colour scale. The data interval comes from
wells L-1, O-2, and K-1.
14 Geofluids
-
The results of the CEEMD algorithm are consistent withthe IF
values, and the low frequency anomaly is visible. Theanomaly is
more continuous than the result of the FFTdecomposition but reveals
similar features in terms of its spa-tial thickness. The frequency
values, however, are closer tothose indicated by instantaneous
frequency (compareFigures 9(b) and 11(b)).
The last decomposition algorithm that was incorporatedinto the
analysis was based on the CWT method. Its resultsare presented in
Figure 12.
The results of the CWT algorithm, although consistentwith the
other decomposition results, reveal slightly differentbehaviour.
The frequency values are similar to FFT and IF,but two
morphological objects can be visible. InFigure 12(b), there are
regions that can mislead the interpre-tation (marked with black
arrows—Figure 12(b), 1st arrowfrom left indicating low anomaly
overlapping with the topof Ordovician and 2nd arrow indicating
abrupt change inanomaly geometry) that exceed the range of the
Pasłęk For-mation and overlap with the top of Ordovician—the
Jantarformation. For this reason, CWT results might be
somehowmisguiding the automatic interpretation of the base of
thePasłęk Formation. Nonetheless, the top of the formation ismore
coherent and consistent in comparison with otheralgorithms
revealing the simillar morphology for the top ofthe formation.
With the results of the spectral analysis, it was possibleto
estimate the thickness of the Pasłęk Formation(Figure 13). It was
constructed by autopicking the topand bed of the low frequency
anomaly based on decompo-sition results. The resulting map is taken
as an averagevalue from the thickness estimated by FFT, IF,
andCEEMD algorithms. The CWT results were excluded fromthe
computation since in many places, the anomaly wassmeared out for
more than 150ms, the temporal distancemuch greater than a
documented thickness of the PasłękFormation. The map in Figure 13
shows temporal thicknessreaching a maximum of 60ms and diminishing
to almostzero (white region). The distribution of the low
frequencyanomaly exhibits the specific pattern and is not
random,e.g., there exist areas of higher and lower thicknesses
ofthe low frequency anomaly. There is a coincidence withthe
thickness of the Pasłęk Formation and its structuralposition. The
higher value of temporal thickness is localisedin lower structural
position, and more elevated areas areassociated with lower values
of thickness. Such a trendlinks the existence of lower frequency
anomaly to the geo-logical setting (i.e., the structural position
of the deposits).Hence, the presence of Wolf ramp manifested by the
fre-quency anomaly can be used as a guideline for
seismicinterpretation.
4.2. Discussion.We associate the low frequency anomaly withthe
Pasłęk Formation, which exhibits a linear change ofvelocity with
depth. In Figure 14, the sonic and density logstogether with
lithological models are presented. The well L-1 lays within the 3D
data; two others are situated outsidethe seismic data coverage. The
top of the Pasłęk Formationis marked dashed black line which
approximates the linear
character of velocity changes for the interval (as shown
inFigure 7(b), density value is constant). It can be observed
thatthe formation corresponds to the increased value of clay
min-eral (VIL) content (green area in Figure 14). Moreover,
thechange in clay mineral content also shows a specific
relatio-n—it increases with depth through the Pasłęk
Formation(Figure 14, red dashed line).
In Figure 15, we present the clay mineral content (frac-tion)
for the three wells. The depth of the sample is indi-cated by
colour. For the clay mineral content, a distinctivepattern can be
observed—the deeper part of the intervalcorresponds to the higher
clay mineral content, that is alsoassociated with lower velocities.
The velocity decreasingwith depth makes the Pasłęk Formation the
inverted veloc-ity layer. The relationship between the clay mineral
contentand velocity resembles the linear behaviour. For this
reason,we speculate that the velocity decrease observed in
thePasłęk Formation is associated with the increase in claymineral
content.
5. Conclusions
Given the above analysis, we can classify the Pasłęk Forma-tion
as an example of a transition zone. The interval is char-acterized
by a low frequency anomaly that was indicated byinstantaneous
frequency and by spectral decomposition.For the expected thickness
of interest, it was crucial to ana-lyze low frequency content of
the seismic data as the exis-tence of transition zone manifests
itself in the range oflower frequencies. For transition zone
interpretation, wepropose an application of various decomposition
algorithms,so as to compare the results and incorporate advantages
ofseveral decomposition methods.
The decrease in velocity for the Pasłęk Formation is asso-ciated
with the increased fraction of clay mineral content,and the
existence of a transition zone is governed by lithofa-cies changes
within the Pasłęk Formation.
With the application of spectral decomposition, it waspossible
to map the top and bed of the formation that other-wise were
difficult to be interpreted. With these results, themap showing the
thickness distribution of the interval wascreated. The thickness of
the formation aligns in a specificpattern and is not random, which
gives reason to believe thatthe distribution of the formation was
controlled by a geolog-ical factor; here, the factor is most likely
linked to the struc-tural position.
With the presented methodology and application of tran-sition
zone concept, it was possible to interpret the potentialshale play
reservoir. This enabled us to indicate the thicknessof the
potential shale play formation that is crucial forestimating the
reservoir volume.
Data Availability
Research data are not shared. The data owner is Polish Oiland
Gas Company that generously shared the data with theauthors for
scientific and didactic purposes.
15Geofluids
-
Conflicts of Interest
The authors declare that there is no conflict of
interestregarding the publication of this paper.
Acknowledgments
This research has been supported by AGH University ofScience and
Technology in Kraków (grant numbers11.11.140.645 and
16.16.140.315). The article is the result ofresearch conducted in
connection with a project: seismic testsand their application in
the detection of shale gas zones.Selection of optimal parameters
for acquisition and process-ing in order to reproduce the structure
and distribution ofpetrophysical and geomechanical parameters of
prospectiverocks was part of the program Blue Gas—Polish Shale
Gas;(BG1/GASLUPSEJSM/13). We would like to thank CGGfor their
provision of seismic interpretation software throughthe University
Software Grant Program. We would like tothank Polish Oil and Gas
Company for sharing the data forscientific and didactic purposes
and for permission for publi-cation of the results. Authors would
like to express apprecia-tion for two anonymous reviewers for
valuable commentsand insight. We thank our colleague, Gabriel
Ząbek, for hishelp in the preparation of the chosen figures.
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16 Geofluids
Seismic Signature of Transition Zone (Wolf Ramp) in Shale
Deposits with Application of Frequency Analysis1. Introduction2.
Materials2.1. Theory of a Transition Zone2.2. Motivation for
Application of Wolf Ramp Concept2.3. Modeling for Transition Zone
Recognition2.4. Geological Setting2.5. Potential Shale Gas
Prospects
3. Methods4. Results and Discussion4.1. Results of Spectral
Analysis4.2. Discussion
5. ConclusionsData AvailabilityConflicts of
InterestAcknowledgments
