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Advanced self-organizing map facies analysis with stratigraphic constraint Tao Zhao*, Fangyu Li, and Kurt J. Marfurt, University of Oklahoma
Summary
As a powerful and the most popular seismic facies analysis
method, self-organizing map (SOM) projects multiple
attributes into a lower dimensional (usually 2D) latent space.
Because of lacking geological time information, the seismic
facies classification results sometimes are problematic or
unreliable. In this study, we briefly introduce a stratigraphic
constraint derived from seismic decomposition method into
SOM facies analysis. After describing the principal method,
we show an example of an improved SOM using information
of sedimentary cycle, which is derived from variational
mode decomposition (VMD) on seismic amplitude data. On
an unconventional shale application, we observe that the
constrained SOM facies map shows layers that are easily
overlooked on traditional unconstrained SOM facies map.
Introduction
SOM is an excellent seismic facies analysis/classification
tool that captures the information residing in (multiple) input
seismic attributes by reorganizing data samples based on
their topological relation. Examples of the very first
applications of SOM on seismic facies analysis include
Strecker and Uden (2002), in which the authors used
multiattribute input and performed SOM classification
volumetrically using a 2D SOM latent space, and Coleou et
al. (2003) used both seismic amplitudes (waveform
classification) and seismic attributes as inputs for SOM. To
overcome the issue that the distance information in the input
attribute space is lost once projected into the 2D SOM latent
space, Zhao et al. (2016) adopted a distance-preserving step
in SOM, constraining the SOM facies to better reflect the
degree of diversity in input attribute space. However, till
now all the SOM applications are spatially (and temporally,
for time domain seismic data) unaware, because seismic data
are sorted into “attribute space” (each dimension is one
seismic attribute) before feeding into a classification
technique like SOM.
One of the side effects of such spatial unawareness is the
lack of explicitly defined geologic time involved when
performing SOM seismic facies analysis. That is to say, the
patterns of facies on an SOM map could only follow patterns
presented in input attributes. Adding information of
sedimentary cycle, which provides spatial (or temporal)
constraint on the vertical axis, may help define layers that
are otherwise not well defined on seismic attributes. Liu et
al. (2015) used empirical mode decomposition (EMD)
(Huang et al., 1998) to decompose the seismic signal into
different modes to analyze sedimentary cycle. However,
being a recursive model decomposition method, EMD is
sensitive to noise and sampling and therefore not so robust.
To overcome such issues, Dragomiretskiy and Zosso (2014)
proposed a novel mode decomposition method, VMD,
which decomposes a signal concurrently and is robust to
noise and sampling. Li et al. (2016) applied VMD method
on deriving a sedimentary cycle model from seismic
amplitude data.
In this study we follow the workflow described in Li et al.
(2016), adopting the VMD method to decompose the seismic
amplitude signal into a user-defined number of modes, and
select one of the modes as an indicator of the sedimentary
cycle by calibrating with well logs. By adding such
sedimentary cycle constraint in SOM facies analysis, we
identify some layers are better represented comparing to the
traditional unconstrained SOM facies analysis.
Methodology
In traditional SOM seismic facies analysis, the distance used
to find the best matching unit (BMU) for a given
multiattribute data sample vector is calculated using only
attribute values. As motioned above, there is no geological
time constraint, which sometimes leads to unreasonable
classification results.
In this study, we constrain this distance by adding a term
defined by the gradient of a mode calculated using VMD.
The modified distance metric is:
𝑑 = (1 − 𝛼) ∑‖𝐴𝑖 − 𝐴𝑃𝑉𝑖‖ + 𝛼‖𝑉𝑔𝑟𝑎𝑑 − 𝑉𝑃𝑉𝑔𝑟𝑎𝑑‖,
𝑁
𝑖=1
(1)
where 𝑑 is the weighted distance between a multiattribute
sample vector and a prototype vector; 𝑁 is the number of
attributes; 𝐴 and 𝐴𝑃𝑉 are the attribute values of a sample
vector and a prototype vector, respectively; 𝑉𝑔𝑟𝑎𝑑 and
𝑉𝑃𝑉𝑔𝑟𝑎𝑑 are the gradient of a mode from VMD for a sample
vector and a prototype vector, respectively; and 𝛼 is a weight
between 0 and 1. In practice, we find an 𝛼 of 0.6 – 0.7
provides reasonable result. The complete workflow of the
modified SOM facies analysis is shown in Figure 1.
Geologic Setting
We apply the proposed workflow on a seismic data set
acquired over the Fort Worth Basin, United States. In the
study area, interbedded limestone and shale layers are
presented, with the Upper and Lower Barnett Shales being
the dominant shale reservoirs. A general stratigraphic chart
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showing the shale reservoir formations in the Fort Worth
Basin is given in Figure 2.
Figure 1. Workflow of the proposed VMD constrained
SOM facies analysis.
Figure 2. General stratigraphy of the Ordovician to
Pennsylvanian section in the Fort Worth Basin through a
well near the study area (After Loucks and Ruppel, 2007).
Application
To constrain the SOM analysis using VMD derived mode,
we first use VMD to decompose the seismic signals into
three independent modes, which represents long, medium,
and short sedimentary cycles. Figure 3 shows the
decomposed three modes of a trace adjacent to well A. By
comparing the gradient of the three modes with the Gamma
Ray log on well A, we find the gradient of VMD 3 matches
the pattern of the Gamma Ray log the best (Figure 4), which
means the gradient of VMD 3 is an appropriate
representation of the sedimentary cycle at this area.
Therefore, we use the gradient of VMD 3 as the constraint
in the subsequent SOM analysis.
Figure 3. (a) Seismic amplitude from a trace adjacent to well
A. (b) VMD components of the trace above. Three
components are used to represent long, medium, and short
sedimentary cycles. (c) The gradient of VMD 3.
Figure 4. Comparison between the Gamma Ray log at well
A and the gradient of VMD 3 at an adjacent trace shown in
Figure 3.
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We use P-impedance, S-impedance, Mu/Lambda, and
Poisson’s Ratio as input attributes to feed into the SOM
algorithm. These input attributes are selected to represent the
variation in lithology caused by sedimentation. We use SOM
to project these four attributes into a 2D latent space with a
2D colorbar (Matos et al., 2009), which helps to define facies
that are not easily identified on these attributes. Figure 5
gives the SOM facies maps with and without VMD
constraint at t = 1.28 s. In this figure we observe the map
with VMD constraint has more details, but the meaning of
colors remains vague. To better compare the results, we take
vertical sections at AA’ (Figure 6) and BB’ (Figure 7), on
which different formations are better presented.
Figure 5. SOM facies maps generated (a) without VMD
constraint and (b) with VMD constraint at t = 1.28 s. A 2D
colorbar is used for visualization.
In Figure 6, we can clearly observe that different formations
are delineated with more distinct colors when a VMD
constraint is added. More specifically, a thin layer between
Marble Falls Limestone and Upper Barnett Limestone
presents in Figure 6b cannot be traced in Figure 6a (black
ovals in Figure 6). This thin layer behaves high Gamma Ray
on the well log at well A, while the Marble Falls Limestone
and Upper Barnett Limestone are of low Gamma Ray. Such
response on Gamma Ray log has verified the extra layer
identified on the SOM facies map with VMD constraint.
Figure 7 gives vertical sections of SOM facies maps without
and with VMD constraint at line BB’. Similar to Figure 6,
we can also identify a higher contrast of color in Figure 7b
comparing to Figure 7a, which means the facies are more
distinct. In the Upper Barnett Shale formation, a layer that is
not precisely defined in Figure 7a is now presented much
more clearly (black ovals), and we observe lateral variation
within this layer, represented by variation of colors. Figure
8 gives a close look at trace X1 and X1’, with overlaying trace
display. Comparing to trace X1, the difference between two
adjacent formations is more dramatic in X1’, which results
in a better separation between different layers. To further
understand the geologic meaning of the layer picked out by
SOM with VMD constraint, we use the VP/VS ratio at line
BB’ to look for evidence of this layer (Figure 9). There is
obviously a layer of high VP/VS ratio in the Upper Barnett
Shale formation, which corresponds to the layer identified in
Figure 7b, and the high VP/VS ratio correlates with the
blueish color facies. Such details are not presented in Figure
7a, where the VMD constraint is not used. It is common for
shale reservoir to have layering sub-structures, but without
the sedimentary circle constraint, the original SOM will miss
this thin layer, which is important for unconventional plays
characterization.
Conclusions and Future Work
In this study, we explored the feasibility of constraining the
SOM facies analysis using sedimentary cycle information.
The constrained SOM facies map provides more details, and
shows layers that are more likely being overlooked on
unconstrained SOM facies map. The sedimentary cycle is
estimated by decomposing seismic amplitude signal into a
finite number of modes using VMD. However, the
geological meaning of such modes is not well understood,
and these modes need to be carefully calibrated with well
logs. Furthermore, different layers with the same VMD
gradient are not distinguishable, and each seismic trace is
decomposed individually. Therefore, a spatial/temporal
constraint may further improve the SOM performance.
Acknowledgement
We thank Devon Energy for providing the seismic and well
log data. Financial support for this effort is provided by the
industry sponsors of the Attribute-Assisted Seismic
Processing and Interpretation (AASPI) consortium at the
University of Oklahoma. We thank colleagues for their
valuable input and suggestions. The prestack inversion was
performed using licenses to Hampson and Russell, provided
to the University of Oklahoma for research and education
courtesy of CGG.
a)
b)
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Figure 6. Vertical sections along line AA’ (location shown in Figure 5) through SOM facies maps generated (a) without VMD
constraint and (b) with VMD constraint. Note the layers are better separated in (b) at the Marble Falls Limestone and Upper Barnett
Limestone formations. Also the facies map in (b) presents more contrast in color which leads to an improved definition of different
layers. The blue curves are Gamma Ray logs at well A.
Figure 7. Vertical sections along line BB’ (location shown in Figure 5) through SOM facies maps generated (a) without VMD
constraint and (b) with VMD constraint. Note the formation highlighted by the black ovals is clearly presented in (b) but vague in
(a). Trace X1 and X1’ are discussed in Figure 8.
(a) (b)
(a) (b)
Figure 8. Trace display of the SOM facies at traces X1 and X1’. Note the
layer at t = 1.255 s is defined more clearly when a VMD constraint is
introduced in the SOM.
Figure 9. Vertical section along line BB’ (location
shown in Figure 5) through VP/VS ratio. The black
oval highlight a layer with high VP/VS ratio within
the Upper Barnett Shale. This layer corresponds to
the layer in blueish color identified in Figure 7b,
which is also marked with a black oval. In contrast,
this layer is not well defined in Figure 7a, in which
the VMD constraint is not used.
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EDITED REFERENCES Note: This reference list is a copyedited version of the reference list submitted by the author. Reference lists for the 2016
SEG Technical Program Expanded Abstracts have been copyedited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web.
REFERENCES Coléou, T., M. Poupon, and K. Azbel, 2003, Unsupervised seismic facies classification: A review and
comparison of techniques and implementation: The Leading Edge, 22, 942–953, http://dx.doi.org/10.1190/1.1623635.
de Matos, M. C., K. J. Marfurt, and P. R. S. Johann, 2009, Seismic color self-organizing maps: Presented at the 11th International Congress of the Brazilian Geophysical Society & EXPOGEF 2009, Expanded Abstracts, 914–917, http://dx.doi.org/10.1190/sbgf2009-198.
Dragomiretskiy, K. D. Z., and D. Zosso, 2014, Variational mode decomposition: IEEE Transactions on Signal Processing, 62, 531–544, http://dx.doi.org/10.1109/TSP.2013.2288675.
Huang, N. E., Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C. Yen, C. C. Tung, and H. H. Liu, 1998, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis: Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 454, 903–995, http://dx.doi.org/10.1098/rspa.1998.0193.
Li, F., T. Zhao, Y. Zhang, and K. J. Marfurt, 2016, VMD based sedimentary cycle division for unconventional facies analysis: Presented at the Unconventional Resources Technology Conference 2016, accepted.
Liu, Y., G. Yang, and W. Cao, 2015, The division of sedimentary cycle based on HHT: 85th Annual International Meeting, SEG, Expanded Abstracts, 1902–1906, http://dx.doi.org/10.1190/segam2015-5854651.1.
Loucks, G. R., and C. S. Ruppel, 2007, Mississippian Barnett Shale: Lithofacies and depositional setting of a deep-water shale-gas succession in the Fort Worth Basin, Texas: AAPG Bulletin, 91, 579–601, http://dx.doi.org/10.1306/11020606059.
Strecker, U., and R. Uden, 2002, Data mining of 3D poststack seismic attribute volumes using Kohonen self-organizing maps: The Leading Edge, 21, 1032–1037, http://dx.doi.org/10.1190/1.1518442.
Zhao, T., J. Zhang, F. Li, and K. J. Marfurt, 2016, Characterizing a turbidite system in Canterbury Basin, New Zealand, using seismic attributes and distance-preserving self-organizing maps: Interpretation, 4, SB79–SB89, http://dx.doi.org/10.1190/INT-2015-0094.1.
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