Variogram Analysis Simplified: Part-4: Variogram Signatures & Its Importance

Variograms serve as essential tools in geostatistics, particularly in fields like Oil & Gas exploration, where understanding spatial relationships is critical. Each pattern revealed by a variogram provides valuable insight into the underlying geological processes, helping to describe the continuity, variability, and structure of subsurface features. By examining these patterns, such as anisotropy, trends, nugget effects, and periodicity, we can better interpret geological formations and make more informed decisions in reservoir modelling. This article will delve into these key patterns in detail, emphasizing how they reflect different geological conditions and how they can be modelled to enhance the accuracy of geostatistical predictions.

There are several signatures but few key elementary signatures were as shown below;

For detailed insight on various other aspects of Variogram please refer to the previous articles mentioned below.

Variogram Analysis Simplified Part-1. Variogram calculation and fitting a variogram model

Variogram Analysis Simplified: Part-2: Variogram Parameters & How they affect the result

Variogram Analysis Simplified: Part-3: Unlock the secrets of spatial patterns with Directional Variogram Analysis

In this article, we will explore the key characteristics exhibited by variograms across various geological scenarios and highlight their significance in spatial analysis.

Several key characteristics of variograms were explained below,

1. Geometric Anisotropy

• Characteristics: This occurs when the range of spatial correlation varies with direction but the sill (the variance) remains constant.
• Importance: Geometric anisotropy indicates that the geological feature being studied is more extended or correlated in one direction than another, which can be due to geological processes like sediment deposition.
• Action: Incorporate anisotropy in the variogram model by fitting different ranges for different directions. This helps in more accurate modeling of the spatial structure.

2. Zonal Anisotropy

• Characteristics: In this case, both the range and sill vary with direction. This often indicates more complex geological structures where different processes dominate in different directions.
• Importance: Zonal anisotropy can signal the presence of different geological layers or structures that have varying properties in different directions.
• Action: Model this by allowing both the sill and range to vary with direction. This can be done by fitting different variograms for different directions.

3. Mixed Anisotropy

• Characteristics: Mixed anisotropy is a combination of both geometric and zonal anisotropy. It occurs when the spatial structure of the data shows different ranges and sills in different directions. This can happen when the geological features have varying scales and intensities of correlation depending on the direction.
• Importance: Mixed anisotropy is significant in complex geological environments where multiple processes influence the spatial distribution of properties. It often indicates that different geological layers or features interact with each other in ways that affect the spatial correlation differently in each direction.
• Action: To model mixed anisotropy, you need to fit variograms in different directions with both the range and sill varying. This typically involves using a combination of variogram models that can account for the different directional influences. Mixed anisotropy can be challenging to model accurately, so it's important to carefully analyze the data and consider using advanced modeling techniques such as anisotropic kriging or directional variograms.

Mixed anisotropy is especially relevant in reservoirs where the depositional environment or tectonic activity has resulted in varying degrees of continuity in different directions. Accurately capturing this anisotropy is crucial for reliable reservoir characterization and resource estimation.

4. Hole-Effect/Cyclic Patterns

• Characteristics: This pattern shows periodic rises and falls in the variogram, indicating cyclic or repeating structures at certain intervals.The patterns show repetitive variogram structures. These can arise from regular geological formations like alternating sedimentary layers.
• Importance: The hole effect is typical in data with periodicity, such as layered formations, bedding planes, or cyclic sedimentation.Recognizing cyclic patterns helps in understanding the depositional environment, which may exhibit cyclicity
• Action: Identify the periodicity and include a hole-effect model in the variogram. This will better capture the repeating spatial structure. Use cyclic or periodic models in the variogram to account for these patterns, ensuring that the model captures the inherent periodicity of the data.

5. Nugget Effect

Semivariograms for different surface structures and patterns as above,

a. Pure nugget effect. The variance is not spatially structured, random or with non-dissolvable variance.

b. Large-scale heterogeneity. Patches are few, large, continuous and large scale.

c.?Small-scale heterogeneity. Many small patches, sharply discontinuous, ‘salt and pepper’ effect.

d.?Nested heterogeneity. Different scales of patchiness exist because different factors influence heterogeneity at different scales (according to Ettema and Wardle 2002)

• Characteristics:The nugget effect refers to a variogram that starts with a non-zero value at very small distances, indicating measurement error or micro-scale variability.
• Importance: A significant nugget effect suggests that there is variability at scales smaller than the sampling distance, which might be due to fine-scale heterogeneity or errors.
• Action: Include a nugget effect in the variogram model to account for this small-scale variability, which will lead to more realistic geostatistical predictions. Else you can take decission to ignore the data from your analysis.

6. Nested Structures

• Characteristics: This occurs when the variogram is best modeled by the sum of two or more structures (e.g., spherical, exponential).
• Importance: Nested structures indicate the presence of multiple scales of variability in the data, such as large-scale trends and smaller-scale features.
• Action: Fit a nested variogram model to capture the multi-scale spatial structure. This approach ensures that both small and large-scale features are accurately represented.

7. Non-Stationarity/Trend Effect

• Characteristics: Trends in the variogram indicate non-stationarity, where the mean of the data changes across the field. Non-stationarity is indicated by a variogram that does not stabilize.
• Importance: Trends can be caused by large-scale geological features like a sloping bed or a change in lithology. specific example can be Porosity continuously increases with depth.
• Action: Detrend the data before variogram analysis. This can be done by fitting and removing the trend to ensure that the variogram reflects only the spatial correlation.

Other signatures also discussed during variogram analysis are as follows;

8. Long-Range Correlation (Drift)

• Characteristics: A variogram that increases without reaching a sill indicates long-range correlation or drift.
• Importance: Long-range correlations suggest large-scale geological features that extend beyond the sampled area.
• Action: Consider using a trend model or a variogram that doesn't reach a sill (e.g., linear or power variograms). This can help in modelling the long-range continuity observed in the data.

9. Short-Range Correlation

• Characteristics: When the variogram quickly reaches its sill, it indicates that the correlation is strong only over short distances.
• Importance: Short-range correlation suggests that the geological feature changes rapidly over short distances, common in heterogeneous formations.
• Action: Use a variogram model with a short range, and consider increasing the sampling density if more detail is required.

Example Scenarios:

Presented below are several geological scenarios along with the corresponding variogram behaviors they exhibit.

Below is another example of cyclicity, trends, geometric anisotropy, and zonal anisotropy with different depositional environment scenarios.

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Please feel free to cite this article as:

Mahapatra, Mahabir Prasad (2024), Variogram Analysis Simplified: Part-4: Variogram Signatures & Its Importance https://www.dhirubhai.net/pulse/variogram-analysis-simplified-part-4variogram-its-mahabir-prasad-9srof

References:

• Computational system for geostatistical analysis
• Modeling of zonal anisotropic variograms
• https://www.supergeotek.com/Spatial_Statistical_ENG_HTML/isotropy_and_anisotropy.htm
• The whole story on the hole effect
• Monitoring and assessing of landscape heterogeneity at different scales
• Factorial kriging analysis: Geostatistical filtering applied to reservoir characterization
• https://geostatisticslessons.com/lessons/The Sill of the Variogram
• An evaluation of potential sampling locations in a reservoir with emphasis on conserved spatial correlation structure
• Methodology for Improved Variogram Interpretation and Modeling for Petroleum Reservoir Characterization
• Citation in Applied Geostatistics https://claytonvdeutsch.com

Recommended Reads:

• An In-depth Look at the Four Key Aspects of Variography - Snowden Optiro
• Variograms (geostatisticslessons.com)
• Variogram Dreaming ... | LinkedIn
• Practical Geostatistics by Isobel Clark
• Geostatistical Models and Methods (nku.edu)
• Experimental Variogram Tolerance Parameters (geostatisticslessons.com)
• Variogram Models (seequent.com)
• Experimental Variography and Variogram Models (seequent.com)
• Empirical semivariograms for different directions—ArcMap | Documentation (arcgis.com)
• [PDF] Methodology for Variogram Interpretation and Modeling for Improved Reservoir Characterization | Semantic Scholar
• The Variogram Basics: A visual introduction to one of the most useful geostatistical concepts | CSEG RECORDER
• Quantification of Soil Surface Roughness Evolution under Simulated Rainfall (researchgate.net)
• Defining lithic patterns within river-dominated delta deposits for geostatistical simulation | Petroleum Geoscience (www.lyellcollection.org)

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