NEUE ENERGIEN 2020 · the possible spatial directions to 109 and 193 respectively. The second goal of this project is the cascading use of seismic attributes. The third point of this

Energy Research Programme – 4th Invitation to Tender F e de r a l C l im a t e a n d E n e r gy F u nd - m a na g e d b y t h e A us t r i a n R es e a r c h P r om ot i o n A ge n cy FF G

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Energy Research Programme

Publishable Final Report

Programme control:

Climate and Energy Fund

Programme management:

Austrian Research Promotion Agency FFG

(Österreichische Forschungsförderungsgesellschaft mbH)

Final Report Created on

24/08/2020

Project: KrisT

Project Number: 865014


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Invitation to Tender 4th Invitation to Tender - Energy Research Programme

Start of Project 01/01/2018

End of Project 31/05/2020

Total project duration

(in months) 29 months

Project Holder

(Institution) Geo5 GmbH

Contact Person Christoph Eichkitz

Postal Address Roseggerstraße 17; 8700 Leoben

Phone +43 3842 / 47061

E-mail [email protected]

Website www.geo-5.at

mailto:[email protected]


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KrisT

Determination of fracture parameters using directional seismic texture attributes

to minimise the discovery risk

Authors:

Christoph Eichkitz

Marcellus Schreilechner

Martin Krainer

Sarah Schneider


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1 Table of Contents

1 Table of Contents ............................................................................................................................... 4

2 Introduction ........................................................................................................................................ 5

3 Presentation of Content ..................................................................................................................... 6

3.1 Method ....................................................................................................................................... 8

4 Results and Conclusions .................................................................................................................. 12

5 Outlook and Recommendations ....................................................................................................... 30

6 List of References ............................................................................................................................ 31

7 Contact details ................................................................................................................................. 34


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2 Introduction

Optimal planning of geothermal wells is a prerequisite for the cost-effective extraction and use of heat

and electricity from geothermal reservoirs. For an economical operation of geothermal projects, the

depth (temperature) and the composition of the geothermal reservoir (porosity and permeability) are of

immense importance. With the help of seismic surveys (2D and 3D) it is possible to map the general

geological structure of the subsurface and especially of the geothermal reservoir. For many geothermal

projects, the identification of fracture networks is crucial for the description of water conductivity

(permeability). With the help of seismic attributes such as coherence, curvature or ant track calculations,

areas of increased fracturing can be detected and thus fracture intensity distributions can be created.

However, this does not provide direct information about the strike and dip of fractures. In the FFG project

RiSeiTex (FFG project number 848799) the applicability of directional texture attributes based on the

Grey Level Co-Occurrence Matrix (GLCM) for the determination of fracture parameters was verified.

This research project has three main objectives. The first goal is to increase the resolution by extending

the possible spatial directions to 109 and 193 respectively. The second goal of this project is the

cascading use of seismic attributes. The third point of this project is the software optimization of the

algorithm to reduce the computing time. The results of the individual optimization steps were tested on

publicly available seismic data and compared with each other. This allowed an improved visualization of

areas with increased seismic variability, which in turn can correlate with the presence of fractures.


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3 Presentation of Content

A cost-effective use of geothermal heat or energy depends on the temperature and flow rate in the

geothermal reservoirs. A sufficient flow rate can almost only be achieved in fractured reservoirs (mostly

carbonates). Therefore, for geothermal projects it is above all necessary to describe underground

fracture networks as detailed as possible and to adapt the well path planning to these. The strike and

intensity of fractures can be described using existing boreholes with image log data. For the spatial

distribution of fractures, seismic attributes derived from surface geophysical investigations (reflection

seismics) can be used. In most cases post-stack data are used to describe fracture intensities (e.g.

Blumentritt et al., 2006; Desheng et al., 2010; Elebiju et al., 2011, Guo et al., 2011; Hunt et al., 2010;

Khromova et al., 2011; Mai et al., 2009; Narhari et al., 2009; Refunjol et al., 2010; Staples et al., 2010;

Yenugu et al., 2010). Seismic attributes that can be used for fracture description are either sensitive to

discontinuities in the reflectors (Coherence based attributes) or they are sensitive to the curvature of

reflectors (curvature-based attributes). A direct description of fracture acimuth and fracture dips is only

possible to a limited extent. With these attributes, only fracture zones and their intensity can be

estimated. Another form of input data for attribute calculations are pre-stack data (e.g. Dai et al., 2011;

Wang et al., 2013, 2014). With the help of this data it is possible to detect anisotropies in the data.

Basically, three different methods are used here to describe fractures. First, the P-Wave Azimuthal

Velocity Analysis (VVAZ) (Zheng, 2006), the P-Wave Azimuthal AVO Analysis (AVAZ) (Rüger, 1998)

and the Shear Wave Splitting Analysis (SWS) (Li, 2011). A combination of pre-stack and post-stack data

can be used for an improved description of fracture networks (e.g. Chen et al., 2014; Hunt et al., 2010).

However, pre-stack data is not always available for project processing. Therefore, the focus of this

project lies on the processing of post-stack data.

For the description of fracture networks in geothermal projects, Coherence analyses (Wolfgramm et al.,

2015), production data (Horne et al., 2012; Juliusson and Horne, 2010; Juliusson, 2012), neural

networks (Aminzadeh et al., 2010) or exploration analogies (Jafari and Babadagli, 2011) have so far

mostly been used.

Another type of post-stack data are seismic texture attributes. In seismic attribute analysis attributes

based on the Grey Level Co-Occurrence Matrix (GLCM) are mainly used.

Seismic texture attributes based on the Grey Level Co-Occurrence Matrix (GLCM) have so far mainly

been used for the interpretation of paleo channels and facies areas (e.g. Vinther et al., 1996; Gao, 1999,

2007, 2008a, 2008b, 2009, 2011; West et al., 2002; Chopra and Alexeev, 2005, 2006a, 2006b; Yenugu

et al., 2010; de Matos et al., 2011; Eichkitz et al., 2013). The aim of these interpretations was generally

the extraction of so-called geobodies and not the interpretation of directional parameters. In a work by

Gao (2003) the use of GLCM attributes for fracture interpretation is described. In this work, however, the

focus was on the interpretation of paleo channels and the interpretation of fractures is only mentioned.

For the detection of different facies areas within paleo channels, directional texture attributes have

already been successfully tested (e.g. Eichkitz & Amtmann et al., 2014; Eichkitz & de Groot et al., 2014;

Eichkitz et al., 2015). The results of this study show that in general anisotropies can be detected by

means of texture attributes (see Figure 1).


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Figure 1: Example for the calculation of direction dependent GLCM attributes for a 2D image. The randomly

generated image (a) is displayed with discrete numbers (b). For the calculation of the GLCM (c) the

adjacent pixel pairs are counted and entered into a 2D matrix. The pixel pairs of a 2D image can be counted

in horizontal (d), vertical (e), along the two diagonals (f and g), and in all directions simultaneously. Based

on the GLCM a probability matrix is calculated and this is then used to calculate a GLCM based attribute. In

this example it can be seen that the result of individual attributes changes depending on the direction

(Eichkitz et al., 2013).

In the exploratory project RiSeiTex (FFG project number 848799) the principle applicability of GLCM

based texture attributes for the detection of fracture networks was successfully tested. The workflow

available for the description of facies areas (Eichkitz et al., 2015) was adapted in a first part of the project

to make the description of fractures in geothermal reservoirs possible. These first tests showed that in

principle it is possible to describe fracture intensities, fracture strokes and fracture dips using GLCM

(Eichkitz et al., 2015; 2016; Schneider et al., 2015; 2016).


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Comparisons with other seismic attributes showed that GLCM-based attributes describe fracture dips in

much more detail and more meaningful than classical seismic attributes (Eichkitz et al., 2016). The KrisT

project focuses on three project objectives. The first goal is to increase the resolution by extending the

possible spatial directions to 109 and 193 respectively. The second goal of this research proposal is the

cascading use of seismic attributes. The third point of this research proposal is software-technical

optimisation of the algorithm to reduce the computing time.

3.1 Method

The Grey Level Co-Occurrence Matrix (GLCM) is a statistical method of describing texture properties.

This method is mainly used in the description of satellite images (e.g. Soh and Tsatsoulis, 1999; Franklin

et al., 2001; Maillard et al., 2005; Tsai et al., 2007) and computer tomography images (e.g. Kovalev et

al., 2001; Zizzari et al., 2011). In the field of seismic interpretation, GLCM-based attribute calculation is

hardly used compared to classical attributes such as coherence, curvature, spectral decomposition or

inversion. In the last 15-20 years, however, the GLCM method has also been used in seismic

interpretation. For use with seismic data, the GLCM must be calculated in three dimensions. The

previous methods (Vinther et al., 1996; Gao, 1999, 2003, 2007, 2008a, 2008b, 2009, 2011; West et al.,

2002; Chopra and Alexeev, 2005, 2006a, 2006b; Yenugu et al., 2010; de Matos et al., 2011) use the

two-dimensional calculation of GLCM attributes in a 3D analysis window. Eichkitz et al. (2013, 2014) use

a full 3D algorithm to calculate GLCM in all possible spatial directions.

The GLCM is a measure of how often different combinations of grey levels occur in neighbouring pixels.

For the two-dimensional case this calculation would be done in 4 spatial directions. For the 3D case the

calculation would normally be done for directly neighbouring pixels, this would be in 13 spatial directions

(see Figure 2).

Figure 2: Adjacent pixel pairs in a 3D data set are arranged in 13 spatial directions. (Eichkitz et al., 2013)

Based on the GLCM, various attributes can be calculated. Haralick et al (1973) describe 14 different

GLCM attributes. In the meantime, further GLCM based attributes have been developed (Soh &

Tsatsoulis, 1999), so that 24 attribute calculations are already known.

To improve the calculation of GLCM attributes, the calculation should be done along the structural dip of

data. For this purpose, so-called steering cubes must be calculated before the actual GLCM calculation.

In these Steering Cubes, dip information in inline and crossline direction is stored for each data point. By

integrating the steering information into the GLCM calculation, the analysis window is changed. This

means that the analysis window is not a horizontal window, but adapts to the structural dip of the data

(see Figure 3).


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Figure 3: The standard calculation window for the calculation is a rectangle (a). The structural dip of the

reflectors is not considered in this calculation. To optimise the calculation of GLCM attributes, the

calculation can include the structural dip of the reflectors in the calculation. In this case the analysis

window is adjusted to the dip and azimuth of the reflectors (b).

For the calculation of fracture intensities from directional GLCM based attributes, a workflow (see Figure

4) has been further developed, which was previously used to describe facies changes in paleo channels

(Eichkitz et al., 2014). For this purpose, individual GLCM-based attributes are first calculated in 13

different spatial directions. These are then compared with each other and from this comparison an

estimation of fracture intensity, strike and dip of the fractures is made. Anisotropy describes the

directional dependence of each attribute. These seismic anisotropies can be caused by spatial variations

of the sediments, the presence of fractures and fault zones and differences in pore fillings. In

geophysics, anisotropy usually refers to the dependence of velocity on direction or angle (e.g. Crampin

1981, 1985; Lynn & Thomsen, 1990; Willis et al., 1986, Martin & Davis, 1987; Thomsen, 1986; Alkhalifah

& Tsvankin, 1995).


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Figure 4: Basic workflow for the calculation of anisotropies in the subsurface. In a first step GLCM based

attributes are measured in all spatial directions. Afterwards the maximum value, the minimum value and

the directions in which maximum and minimum values occur are determined for each sample point. Since

the same value very rarely occurs in all directions during the calculations, it is necessary to filter the

results. For this purpose the ratio of maximum and minimum values is determined. Based on this ratio,

sample points with a low ratio are set to isotropic (Eichkitz et al., 2014).

For a better understanding of the method, the effect of the directional calculation of GLCM attributes and

the determination of anisotropy on a synthetic model is shown (see Figure 5). It can be seen here that

individual calculations of GLCM attributes hardly differ, but direct comparisons per data point still cause

variations.


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Figure 5: Synthetic example for the calculation of a GLCM-based energy attribute in different directions

and comparison of the results. Calculations in single directions or the combination of several directions

give similar results. However, by comparing the individual results, a different result is obtained with a

focus on an area where the spatial variability of the data is greatest.


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The research project KrisT was basically divided into five work packages, whereby work package 1 is the

project management and this work package includes the whole area of dissemination. Work packages 2-

4 reflect the objectives of the research project. These are:

• Adaptation of the existing workflow to increase the resolution. In the exploratory project RiSeiTex,

the resolution of fracture dips and strike was improved from 45° to 22.5°. Compared to image log

data, however, this resolution is still insufficient. Therefore, the first project goal is to increase the

resolution. Here, the algorithm was adapted so that GLCM attributes can now be calculated in

109 spatial directions (11.25°) or in 193 spatial directions (5.625°).

• Integration of other seismic attributes. Cascade calculations allow other seismic attributes to be

used as input for the calculation of fracture parameters based on texture attributes. In the given

research project, the focus was mainly on structural attributes such as coherence. In addition,

seismic input data was converted into seismic data with a focused frequency spectrum using

spectral decomposition and GLCM attributes were calculated on this data.

• Optimisation of computing time: The calculations in the RiSeiTex exploratory project were carried

out for relatively small 3D seismic data. Today, however, many 3D seismic data are already over

1000 km² in size. With the existing algorithm, computing times of several days can be expected.

For a later use of this technology it is necessary to minimize this time. In this research project we

therefore tried to minimise the computing time using different approaches.

4 Results and Conclusions

Aims of the research project were the extension of the existing workflow for the determination of seismic

variability in more spatial directions, the cascade calculation of GLCM-based attributes and the

optimisation of the algorithm to perform the calculations faster.

The calculation of GLCM attributes in 3D is done using the following equation:

In this equation, dx, dy, dz define the distance between the neighbouring data points, usually taking a

constant value of 1. This would describe directly adjacent data points, which are arranged in 13 spatial

directions. By increasing the values for dx, dy and dz, the number of spatial directions also increases.

For a constant distance of 2 you get 49 spatial directions, for a distance of 3 you get 109 spatial

directions and for a distance of 4 you get 193 spatial directions. This increase in spatial directions is also

accompanied by an improvement in resolution. Thus 13 spatial directions can be used to describe

changes of the seismic fascies with 45° accuracy, for 49 directions it would be 22.5°, for 109 directions

11.25° and for 193 directions 5.625° (see Figure 6).


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Figure 6: Effect of the distances used for dx, dy and dx and the resulting number of possible directions. (a)

For a distance of 1, the direct neighbours are compared, resulting in 13 possible directions. (b) For a

distance of 2, the direct neighbours are skipped, resulting in 49 possible directions. (c) For a distance of 3,

two layers are skipped, resulting in 109 possible directions. (d) Currently the highest tested distance is 4,

skipping 3 layers and giving us 193 possible directions.

In principle, this approach improves the lateral resolution. However, a larger distance between the pixel

pairs is also required for this. Thus, there is the danger of overlooking small-scale changes in the seismic

facies. Conversely, higher directional numbers can also mean an improvement in the visualisation of

large-scale structures. Figure 7 shows the effect of calculating the anisotropy with different numbers of

directions. In this example, a calculation with 13 spatial directions mainly visualises areas with small-

scale changes. An increase in the number of directions results in a larger area with change of the

seismic facies.

Figure 7: Estimation of the lateral seismic variability using GLCM based energy. If the calculation is

performed in 13 spatial directions, only a few areas are highlighted. An extension of the spatial directions

also produces more areas with increased variability. This is related to the size of the structures shown.

In principle, this method has the advantage that you can highlight structures of different sizes. For

example, small-scale structures can represent karstification, while larger structures can correspond to

fracture areas and very large structures can correspond to facies changes or fault zones. Purely by

calculating the anisotropy, however, it is not yet possible to make any statements about its cause.

Therefore, a correlation with bore information is necessary.


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Figure 8: Influence of the size of the analysis window on the calculation of the GLCM-based anisotropy.

In the context of the further development of the algorithm for the calculation of more spatial directions, a

parameter for the calculation of GLCM-based anisotropy became more and more important, which was

hardly considered in the calculations so far. Besides the number of grey levels, the used analysis

window has a great influence on the GLCM calculation. The analysis window for 2D data is defined by a

number of tracks and a number of vertical samples. For 3D data the analysis window must be defined by

an inline area, a crossline area and the number of vertical samples. Gao (2007) points out that typically a

vertical analysis window should be taken from the size of the average wavelength. For seismic data with

an average dominant frequency of 36 Hz, this would mean a vertical window size of 30 ms, giving 15

samples (data points) at a sampling rate of 2 ms. Tests with different analysis windows (see Figure 8)

showed that depending on the size of the analysis window, different features are expressed or

suppressed. Small analysis windows such as [3,3,7] can only highlight larger structures, but not smaller


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elements such as those in the west (red arrows in Figure 8). When the vertical analysis window is

enlarged, this small element is also visualised. The analysis windows [3,3,13] and [3,3,15] show an

increase in blur and a reduction in resolution, with noise reduction in the surrounding area. The

amplitude values also decrease with larger vertical window sizes. With the size of the horizontal analysis

window, it can generally be seen that smaller horizontal analysis windows produce sharper images. De

Martino et al (2003) showed that window size accounts for 90 percent of the variability in the results of

the classification. The size of the analysis window must be redefined for each data set or question, which

is a very time-consuming process. For this reason, we tried to develop an automated determination of

the vertical analysis window. For this purpose, a semi-variogram analysis is carried out to determine the

optimal window size. The effect of the semi-variogram analysis was tested on two different data sets. On

the one hand on the Hector 3D seismic, New Zealand, and on the other hand on the Teapot Dome 3D

seismic, USA. In the first example, the semi-variogram was calculated for constant time intervals, namely

240 ms, 1000 ms, 2400 ms and 3000 ms. In addition, five different greyscale transformation methods are

used to investigate their effect on the semi-variogram analysis (see Figure 9). Interestingly, the results of

the semi-variogram analysis are independent of the type of greyscale transformation, but are strongly

influenced by the respective time interval. At a shallow time interval of 240 ms the five different greyscale

transformations lead to a very fast increase of the semi-variance values, the highest values being

reached at a vertical analysis window of ±3. After that the semi-variance values start to decrease again.

On the lowest time interval of 3000 ms the different transformation methods lead to similar curves, but in

this case the increase of the semi-variance is flatter with a maximum for a vertical analysis window of ±5.

The comparison of semi-variograms for different time levels clearly shows the depth or time

dependencies of the semi-variogram analysis. At shallower time intervals - where higher frequencies

dominate - the optimal vertical analysis window is rather small. With increasing depth, the higher

frequencies are suppressed and thus the semi-variogram analysis suggests larger vertical analysis

windows. A very interesting observation can be made for the Hector 3D seismic. At a time level of 2400

ms the optimal analysis window reaches a maximum of ±6, below that the optimal analysis window

decreases to ±5. This could be related to the very high amplitude values at this time level.


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Figure 9: Semi-Variogram analysis for the Hector 3D data set. (a) Semi-variograms for different greyscale

transformations on a constant time interval of 240 ms (b) Semi-variograms for different greyscale

transformations on a constant time interval of 3000 ms. (c) Semi-variograms for different time intervals

each with linear greyscale transformations.

Figure 10: Semi-variogram analysis for the Teapot Dome data set. (a) Semi-variograms for different

greyscale transformations for the interpreted Frontier Horizon. (b) Semi-variograms for different greyscale

transformations for the interpreted Tenseleep B horizon. (c) Semi-variograms for different interpreted

horizons each with linear greyscale transformations.


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The second example comes from the Teapot Dome seismic, USA, where interpreted horizons are used

for semi-variogram analysis instead of constant time planes (see Figure 10). Again, the calculation along

a single interpreted horizon using different greyscale transformation methods leads to similar semi-

variograms. For the shallow horizon "Frontier" an optimal vertical analysis window of ±6 is determined.

The same optimal vertical analysis window can be determined for the deeper Tensleep B formation, but

the semi-variograms differ from those of the Frontier Horizon. In particular, the comparison of different

horizons shows a bell-shaped semi-variogram for the shallower horizons, which then begin to flatten out

at deeper horizons. These observations show that the semi-variogram calculation to determine the

optimal analysis windows is more or less independent of the greyscale transformation method. However,

it is very important to perform the semi-variogram analysis in several depth levels and to divide the later

attribute calculation into corresponding packages.

Another focus of this research programme was the calculation of GLCM based attributes from alternative

input data. Normally, amplitude cubes are used as input for the calculation of GLCM post-stack

amplitude cubes. In this research project other data like conventional seismic attributes and the results of

a spectral decomposition were used as input data.

In a first step, conventional seismic attributes such as Coherence, Curvature, RMS Amplitude,

Instantaneous Phase, Instantaneous Frequency or Sweentness were calculated and then used as input

data for the GLCM workflow. In principle, the developed workflow also works on this data, but the quality

of the results does not meet the previous expectations. Since most attributes such as coherence or

curvature (see Figure 11) already focus on a few areas, GLCM attributes can also visualise only the

same areas based on this data. The environment of these areas is then completely negated in the

GLCM calculation. Thus, GLCM attributes based on these attributes hardly bring new insights and act

rather counterproductively.

Figure 11: Example of cascade calculation of anisotropy parameters. In the first column the seismic

amplitude cube was used directly. In column 2 the anisotropy direction was calculated from a Coherence


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attribute. In column 3 the Most Negative Curvature and in column 4 the Most Positive Curvature was used

for the calculation. In contrast to the direct calculation from an amplitude cube, the cascade calculation

emphasises individual areas which already appear prominent in the initial attributes.

The situation is different with attribute cubes based on a spectral decomposition. Spectral decomposition

divides amplitude cubes into data with a limited frequency spectrum. This makes it possible to better

visualise structures with defined frequency ranges. In this research project the individual frequency

ranges were used as input for the anisotropy workflow. Since these input data are very similar to a

classical amplitude cube, the results of the GLCM calculation are also very similar. Here the complete

area of a seismic data set is mapped and not, as with the other attributes, already focused on certain

areas. Figure 12 to Figure 15 show the results of the anisotropy calculation based on limited frequency

spectra for the levels "Tensleep B" and "Alcova Limestone" from the Teapot Dome data set, USA. In

direct comparison to the results with the complete amplitude cube, a very similar picture can be seen.

However, the individual frequency ranges focus on different structures. For example, the lower

frequencies of 10 Hz tend to show fewer areas of increased anisotropy, and with increasing frequency,

anisotropy values generally become higher. Therefore, it is possible to visualise single structural

elements better with this method. For a precise description of these individual areas, however,

information from drillings is necessary. Especially for the description of fissure areas this method is a

valuable support, because it can be assumed that fissures are rather to be assigned to the higher

frequency areas.


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Figure 12: Result of the calculation of the anisotropy at level "Tensleep B" for (a) the amplitude cube and

for (b) - (g) individual frequency ranges. The GLCM based energy was calculated in 13 spatial directions.

Figure 13: Result of the calculation of the anisotropy at level "Tensleep B" for (a) the amplitude cube and

for (b) - (g) individual frequency ranges. The GLCM based energy was calculated in 49 spatial directions.


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Figure 14: Result of the calculation of the anisotropy at "Alcova Limestone" level for (a) the amplitude cube

and for (b) - (g) individual frequency ranges. The GLCM based energy was calculated in 13 spatial

directions.

Figure 15: Result of the calculation of the anisotropy at "Alcova Limestone" level for (a) the amplitude cube

and for (b) - (g) individual frequency ranges. The GLCM based energy was calculated in 49 spatial

directions.


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All non-trivial software goes through phases of optimisation and modernisation. If necessary,

functionalities are also added to it. Due to the size of seismic datasets, the non-functional aspect of

performance optimisation also plays a decisive role in this project. In the following, these phases of

software and algorithm development within the scope of this project are described in more detail. The

performance of the algorithm depends mainly on the number of grey levels (see Figure 16), the number

of directions used, and the analysis window used.

Figure 16: The size of the greyscale matrix increases with the square of the number of greyscales

In the first version of the implementation of the calculation algorithm, the main focus was on the

functionality and correctness of the program. In terms of performance, the programming language C++

was chosen, which was particularly suitable for time-critical applications due to its proximity to the

machine and the resulting performance advantage over many other programming languages (Aruoba,

Fernández-Villaverde, 2014).

Originally, only 13 spatial directions were taken into account. This made it possible to follow a procedural

approach for a first implementation. For each reference point, the corresponding seismic amplitude

values within a sub-cube were determined for each spatial direction and the grey scale value pairs were

calculated from these values. Structures containing these greyscale values and their co-occurrence were

stored in a single linked list. This list was then used to calculate the respective attribute value for this

reference point. The calculation of all attribute values for each reference point of the seismic Input Cube

finally represents the Output Cube.

In view of the planned extension of the algorithm to 49 and subsequently to 109 and 193 spatial

directions, it soon became clear that the approach chosen in the first version could not be pursued

further. An initial problem analysis yielded the following results, among others:

• Poor expandability

o With only 13 spatial directions, the procedural approach is still quite acceptable. However,

this is no longer practicable even with a first extension of the algorithm to 49 spatial

directions and requires a modular structure of the program.

• Code duplicates

o The code for calculating the greyscale values and updating the single-linked list is

identical for all room directions. The resulting code duplicates can be eliminated.


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• C++ Version

o With the simply linked list based on dynamically generated pointers, a C++ programming

style is applied which should be avoided in modern versions of a C++ program (Meyers,

2014).

• Multiple access to seismic amplitude values

o Seismic amplitude values are determined for each spatial direction, which are also

required for the calculation for other spatial directions. These values are located for a

certain reference point in a defined area of the seismic cube. Since each access also

requires computing time it is obvious to optimise this time critical part of the algorithm.

This leads to the matrix optimisation, which is explained in the next section.

Each calculation run to determine an attribute value for a reference point requires a certain amount of

seismic amplitude values from a sub-cube, the size of which can vary according to the default settings.

These settings relate to the size of the selected inline/crossline window and the vertical (time/depth)

window. With a 3x3x11 Sub-Cube this corresponds to 99 values, a 9x9x11 Sub-Cube already contains

891 values. The seismic amplitude values are determined by a function and therefore require computing

time.

Since the algorithm uses these values for each spatial direction, it is obvious to make this sub-cube

available in the form of an efficient 3D matrix, the values of which only have to be determined once with

a function, in order to subsequently reduce the calculation time through fast memory access.

Several options are available for implementation in C++, including:

• Simply linked list, access to the data using pointer

o A simply linked list is already used in the first version for the greyscale values/co-

occurrence structure and is characterised by fast memory access. However, this method

is highly error-prone, since on the one hand the length of the list is not known at runtime,

and on the other hand one can also access undefined memory areas, which can lead to

unexpected results up to a program crash.

• Static (multidimensional) array, access to data via index operator

o A static, multidimensional array is a field with a certain size and any number of

dimensions. Data access is via an index operator. This approach offers the advantage of

most directly mapping the 3-dimensional sub-cube in the code. However, this is at the

expense of flexibility, since the array has a fixed size and this must also be defined with

constant expressions. However, since the size of the sub-cube is only known at program

runtime, this approach proves to be impractical.

• Container class oft he C++ standard library

o The C++ standard library provides several container classes. These can be categorised

into sequential and associative containers. Sequential containers provide access to (half-

open) sequences of elements, associative containers provide associative search based

on a key (Stroustrup, 2013).


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Since a search based on keys is not necessary for matrix optimisation, only sequential containers of the

C++ standard library will be discussed in detail below:

• Vector

o A coherently assigned sequence of elements of a certain type.

• List

o A double linked list of elements of one type. This option is useful when you need to insert

or delete elements without moving existing elements.

• Forward-list

o A simply linked list of elements of one type. Ideal for empty and very short sequences.

• Deque

o A double-ended series of elements of one type. This is a mixture of vector and list, but

slower for most applications.

• Array

o A field with a fixed size of a certain number of elements of a certain type. Very similar to a

static array.

Due to the different properties of the containers and the requirements on the algorithm, vector and array

are particularly suitable. Vector is a dynamic array and is therefore able to dynamically adjust the

number of elements. All containers have in common that for each container corresponding iterator

classes are defined. Iterators allow a pointer-like access to the elements of a container. Additionally,

there are predefined algorithms that can be applied to the vector, such as search, replace or insert. All

these algorithms have been extensively tested and well defined and are part of the ISO standard itself.

Strictly speaking, Array is the ideal candidate, since the sub-cube has a certain size at runtime and

therefore a dynamic enlargement of the container is actually not necessary. Nevertheless, Vector was

chosen as container for the matrix optimization for the following reasons:

• "The standard library vector is very flexible and efficient. Use it as your standard container".

(Stroustrup, 2018)

• Possible efficiency advantages of the array over the vector are practically eliminated by memory

reservation during definition.

• A possible later functional extension of the algorithm, which requires a size adjustment of the

container at runtime, is guaranteed by the flexibility of the vector.

Due to the structure of a vector, it is a sequential container, the data of the sub-cube must be read in a

defined sequence. Thus, the 3D Sub-Cube is displayed one-dimensionally. An auxiliary function

determines the correct value of the matrix via the position of the inline/crossline window and the sample

of the time/depth window.

This increase in efficiency with regard to access to seismic amplitude values has led to a significant

reduction in computing time (see Figure 17).


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Figure 17: Calculation times for a typical data set with a classic 2D matrix and with the first approach of a

linked list depending on the number of grey levels.

The extension of the space directions to 109 and 193 space directions respectively produced interesting

results, especially in the area of analysing fault systems or facial changes. However, the larger analysis

windows of 7x7 and 9x9 required for this purpose also require higher computing times, which can hardly

be reduced by the already optimised matrix operations.

For this reason, a new approach was pursued to reduce the computing time, the so-called focused

variant. This is also applicable for 49 spatial directions and brings in relation to the non-focussed

algorithm the more calculation time savings, the more spatial directions one considers.

For each spatial direction, the non-focused algorithm runs through the previously created matrix with the

seismic values of a sub-cube to determine the grey value matrix. This matrix is then used to calculate the

corresponding attribute. Especially for 109 or 193 spatial directions, this means considerably more

calculation steps and thus considerably more calculation time.

The focused variant of the algorithm uses the fact that a calculated spatial direction with a resolution of

45° (13 spatial directions) is highly likely to cover the area that a calculation with higher resolution (22.5°,

11.25° and 5.625°) would produce. For this reason, the focused algorithm first calculates the spatial

direction with the lowest resolution. Based on this value, only those spatial directions with higher

resolution are subsequently examined that are closest to the original direction (up to 9 in each case),

thus gradually increasing the resolution (see Figure 18).


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Figure 18: Possible directions for the calculation of GLCM based attributes with a sample spacing of (a) 1,

(b) 2, (c) 3 and (d) 4 By pre-defining certain directions, the number of directions to be calculated and thus

the calculation time can be reduced considerably. For a distance of (f) 2 the number of directions is halved.

For a distance of (e) 3 the number of directions is approximately one third of the number of directions and

for a distance of (h) 4 the number of directions is approximately one fifth of the number of directions

compared to the normal method.

In the following, the calculation of the focused algorithm is shown using an example workflow on the

basis of 109 spatial directions:

1. Determination of the spatial direction for 13 spatial directions

a. Result e.g.: Azimuth 45, Dip 0

2. Based on this result, the spatial direction is determined for 49 spatial directions, but only

considering the following directions

a. Azimuth: 22,5 / Dip: 0

b. Azimuth: 22,5 / Dip: 22,5

c. Azimuth: 22,5 / Dip: 157,5

d. Azimuth: 45 / Dip: 0

e. Azimuth: 45 / Dip: 22,5

f. Azimuth: 45 / Dip: 157,5

g. Azimuth: 67,5 / Dip: 0

h. Azimuth: 67,5 / Dip: 22,5


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i. Azimuth: 67,5 / Dip: 157,5

j. Result e.g.: Azimuth: 45 / Dip: 22,5

3. Based on this result, the spatial direction is determined for 109 spatial directions, now only for

these directions:

a. Azimuth: 30 / Dip: 15

b. Azimuth: 30 / Dip: 30

c. Azimuth: 45 / Dip: 15

d. Azimuth: 45 / Dip: 30

e. Azimuth: 60 / Dip: 15

f. Azimuth: 60 / Dip: 30

Result for 109 spatial directions gives a value between Azimuth: 30 / Dip: 15 and Azimuth: 60 / Dip: 30

From these calculations the maximum deviations of azimuth and dip for 49, 109 and 193 spatial

directions can also be determined based on 13 spatial directions:

• 49 spatial directions: Maximum 22,5°

• 109 spatial directions: Maximum 30°

• 193 spatial directions: Maximum 33,75°

This method results in considerable savings in computing time, which are all the more significant the

higher the resolution is (see Figure 19).

Figure 19: Computing times for the calculation of the anisotropy for all directions or the adapted method

with focused calculation.

In principle, almost any programming language can be used for the developed algorithm. The used

programming language C++ is particularly suitable for time-critical applications due to its proximity to the

machine and the resulting performance advantage over many other programming languages.


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Like most programming languages, C++ is also subject to changes, most of which serve modernisation

and stability as well as performance. One of the biggest changes of the programming language existing

since 1985 took place with the version C++11, which introduced many new features over the standard

library, increased type safety and with the "Zero-Overhead" principle also increased performance. A

fundamental performance problem that still existed with the previous version C++03 was expensive and

unnecessary so-called "deep copies", which can implicitly occur when objects are passed as values.

Another no less important factor for any programme is its maintainability. In the first version of the

calculation algorithm, pointer arithmetic was still used throughout. While the use of pointers still allows

extremely efficient memory accesses, their use in modern versions of C++ has to be refrained from for

several reasons:

• The danger of memory leaks increases because every pointer created with the keyword "new"

must be explicitly released again.

• The efficiency of the processor cache suffers if a data structure refers to many memory blocks

that are far apart in the address space.

• Pointers can reference invalid memory locations, which can lead to incorrect results or even

program crashes.

Under the leadership of the inventor of the programming language C++, Bjarne Stroustrup, and Herb

Sutter, chairman of the C++ ISO working group, the initiative "C++ Core Guidelines" was launched. The

main goal of the guidelines is to create rules and "best practices" to write type- and resource-safe C++

efficiently and consistently. The Core Guidelines were announced in the opening speech at CPPCon

2015.

The final optimisation step in terms of programming was to apply these rules to the programme,

including:

• „Smart pointer“ instead of „raw pointer“, to avoid memory leaks.

• C++ standard vectors instead of chained pointers with indefinite length.

• "noexcept" specification for functions to enable compiler optimisations.

• Use of the C++ standard library. These algorithms are already extensively tested and well defined

and are part of the ISO standard itself.

• "constexpr" for values and function returns which can be evaluated at compile time.

• By default, declare all functions, parameters and objects as "const". This prevents so-called "race

conditions".

• Low level code is not necessarily faster than high level code. The reason for this is that low-level

code sometimes prevents optimisations of the compiler.

• Simple code often optimises better than handmade, complex code.

• Minimising the number of allocations and memory releases.

Figure 20 to Figure 23 show the results of the calculation of different GLCM attributes in all spatial

directions or in the focused spatial directions for the Tensleep B Horizon side by side. The aim of this

comparison is to examine whether the optimised workflow achieves similar results or not. In general, it

can be said that the results based on different workflows are largely similar. A higher number of


Page 28 von 34

directions often leads to images with a generally higher anisotropy factor, on the other hand these results

often appear smoothed. With the method of focussed directions, it is first of all possible to reduce the

calculation time considerably. In addition, this new focused workflow leads in most cases to very similar

results as the standard workflow and, moreover, it often even increases the resolution of the output

image.

Figure 20: Calculation of GLCM based dissimilarity at Tensleep B level using classical calculation and

focused method.


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Figure 21: Calculation of the GLCM based energy on level Tensleep B using classical calculation and

focused method.

Figure 22: Calculation of the GLCM based homogeneity at Tensleep B level by means of classical

calculation and focused method.


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Figure 23: Calculation of the GLCM based contrast on level Tensleep B by classical calculation and

focused method.

5 Outlook and Recommendations

In this research project the calculation of GLCM attributes in more than 49 spatial directions was

successfully implemented. Due to the higher number of spatial directions, it is possible to increase the

lateral resolution on the one hand and on the other hand, different large structures can be visualised

more easily. A further increase of the spatial directions with the currently used methods is rather

unproductive, because the distances between the sample points become larger with a higher number of

directions. In the future it might be possible to reduce the inline and crossline distance in a 3D seismic

data set by means of 5D interpolation and thus increase the resolution.

The cascade calculation of GLCM based attributes is only of limited use. A calculation of GLCM

attributes based on other seismic attributes did not provide any improvement for the visualization of

fissures. These calculations rather limited the meaningfulness of the anisotropy estimation, which is why

this approach of calculation will be used rather little in the future. In contrast, the calculation of cascading

attributes using spectral decomposition yielded good results. With the help of this method, structures of

different sizes can be perfectly visualised. However, for the exact identification of the structures a

comparison with geophysical borehole measurements is necessary. In connection with spectral

decomposition, the use of a "spectral GLCM" could be of particular interest for future research. Similar to

a "Spectral Coherence", only the real parts of the seismic traces could be taken and the GLCM


Page 31 von 34

calculation could be performed on them. Before calculating the attributes, it would be important to add

the individual spectral elements in a greyscale matrix. This would allow a sharper visualisation of

structural elements. The disadvantage of this method, however, would again be an increase in

computing time.

The calculation of anisotropy using GLCM attributes is generally a computationally intensive process. By

optimising the individual code parts, it is possible to reduce the computing time to a reasonable extent.

For the higher spatial direction numbers, especially the calculation with a focussed algorithm has proved

to be very successful. The calculation times could be reduced to a fifth in some cases and the resulting

attributes provide similar results to the complete calculation. However, the reduction of the calculation

time will also be the main focus of attention for future projects, as currently several hours of calculation

time are still required for large data sets.

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7 Contact details

Project Manager DI Christoph Eichkitz

Geo5 GmbH

Roseggerstraße 17, 8700 Leoben

Tel: 03842/47061

[email protected]

www.geo-5.at
mailto:[email protected]://www.geo-5.at/

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NEUE ENERGIEN 2020 · the possible spatial directions to 109 and 193 respectively. The second goal of this project is the cascading use of seismic attributes. The third point of this