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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