View source for OR/21/006 Lithology determination using log cut-off values

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{{OR/21/006}}

==Introduction==
The geophysical log response of different rock types generally occurs within a defined range of values that (partly) reflects the bulk chemical composition of the rock framework and cementing materials. Table 1 shows a selection of typical log values for some common rock types taken from the more complete listing of Rider (2000). Although the range of log response values for a particular rock type are often large and there are frequently substantial overlaps in response between different rock types, it is often possible to compute a continuous lithology log in a semi- automated way by using defined ranges on one or more geophysical logs. The ranges are defined by one or more ‘cut-off’ values.

<center>
{| class="wikitable"
<span id="Table 1"></span>
|+ Table 1&nbsp;&nbsp;&nbsp;&nbsp;Typical logging-tool response values for a selection of common rock types (after Rider, 2000).
| ! scope="col" style="width: 200px;" | '''Rock type (matrix only)'''
| ! scope="col" style="width: 150px;" | '''Gamma-ray (API)'''
| ! scope="col" style="width: 200px;" | '''Resistivity (ohm m<sup>2</sup>/m)'''
| ! scope="col" style="width: 225px;" | '''Sonic transit time (µs/ft)'''
|-
| Halite
| 0
| <10<sup>4</sup>–10<sup>14</sup>
| 66.7–67
|-
| Anhydrite
| 0–12
| 10<sup>4</sup>–10<sup>10</sup>
| 50
|-
| Limestone
| 18–100
| 80–6&nbsp;x&nbsp;10<sup>3</sup>
| 47.6–53
|-
| Sandstone
| 18–160
| Up to 1000
| 53–100
|-
| Mudstone
| 24–1000
| 0.5–1000
| 60–170
|}
</center>

Figure 14 provides a simple example where a cut-off value of 30 API on a gamma-ray curve could be used to subdivide halite-rich sedimentary rocks (with a low gamma-ray response) from those that are predominantly mudstone. The cut-off value creates a continuous lithological log using a method that does not require any manual digitising.   ]]
 
[[Image:OR21006fig14.jpg|thumb|center|500px|  '''Figure 14'''&nbsp;&nbsp;&nbsp;&nbsp;Illustration of how a log cut off value on a gamma-ray curve can be used to automatically subdivide a sequence of halite-rich strata (H) from halite-poor mudstones (M) in the Mercia Mudstone Group of the Winterborne Kingston borehole.   ]]

==Required input data==
Cut-off methods can be undertaken on almost any geophysical log data, from a single curve which may have been digitised from a vintage paper record to a modern suite of digital logs. While the input logs should ideally pass the quality control checks listed in Table 2 this is often not possible and, with due care, does not necessarily preclude the application of cut-off lithological classification. Most projects undertaken in BGS unavoidably combine log data that has been acquired across many decades, was run to meet the needs of many different geoscience sectors (e.g. water, oil, coal), is of vastly varying quality and quantity, and may have been received and archived with little supporting metadata.

<center>
{| class="wikitable"
<span id="Table 2"></span>
|+ Table 2&nbsp;&nbsp;&nbsp;&nbsp;Quality checklist for geophysical log data in<br>order to avoid working with erroneous data.
| ! scope="col" style="width: 500px;" | Mud resistivity properties (Rm, Rmf) and corresponding temperature reported
| ! scope="col" style="width: 50px;" | ✔
|-
| Proper logging scales chosen and reported for all logs
| ✔
|-
| Caliper log does not show large variations
| ✔
|-
| Resistivity curves do not read less than zero
| ✔
|}
</center>

The risks and uncertainties associated with cut-off analysis using sub-optimal input data can be greatly reduced by starting projects with as much background geological information as possible. This should include information on the expected number of lithologies, the likely proportion of each lithology within the stratigraphic interval of interest, their typical mineralogy (with particular regard to the presence of radiogenic minerals such as glauconite) and the expected range of bed thickness and other parameters of the stratal architecture. The source of this information might be from the well itself in the form of cuttings descriptions, short cored intervals or sidewall cores, or from image logs (optical, acoustic or resistivity). Additional information on the geological formation under consideration might come from regional understanding gained from outcrop descriptions and adjacent boreholes. Finally, a general understanding of the depositional system under investigation can help control and verify the types, stacking order and bed thickness of lithologies that are being generated by the applied cut-offs.

==Normalisation of well log data==
Normalisation of well log data is a routine process within petrophysical workflows and is used to correct for inconsistencies between wells in the distribution of values recorded by a log for a particular lithology (Shier, 2004<ref name="Shier 2004">SHIER, D E. 2004. Well Log Normalization: Methods and Guidelines. ''Petrophysics'', 45.3: 268–280.</ref>). These variations can arise for many different reasons such as incorrect tool calibrations, varying tool vintage and changes in downhole environmental conditions between wells.

Some form of normalisation will be required in nearly all cases where cut-off analysis is attempted as a batch process. Exceptions might occur where a cluster of similarly drilled and constructed wells have been logged by one service company who have applied a consistent set of corrections and calibration procedures to the log data.

The normalisation process is a re-scaling or re-calibration procedure so that all logs in the set under consideration are consistent. A defined set of cut-off values in one well should therefore generate the same lithological classification in another. Normalization is commonly applied to gamma-ray logs, but can also be applied to all logs that sample bulk rock properties such as neutron porosity, bulk density, sonic and spontaneous potential logs. Resistivity logs, which are heavily affected by dynamic fluid properties, are generally not normalized unless there is a sufficient reason to do so (Shier, 2004<ref name="Shier 2004"></ref>).

There are a number of different approaches to log normalisation—Normalisation might be carried out by using a simple linear shift of the log curve. This applies particularly where data has been recorded in different units.

𝐶𝑢𝑟𝑣𝑒<sub>𝑛𝑜𝑟𝑚</sub> = 𝐶𝑢𝑟𝑣𝑒 + 𝑆ℎ𝑖𝑓𝑡

In unity-based normalisation curves are rescaled to the minimum and maximum values, bringing all the values within the range [0,1]. The output values are dimensionless and any reference to the original absolute magnitude of the log response is lost.
 

𝐶𝑢𝑟𝑣𝑒<sub>𝑛𝑜𝑟𝑚</sub> = (    𝐶𝑢𝑟𝑣𝑒𝑉𝑎𝑙𝑢𝑒 − 𝐶𝑢𝑟𝑣𝑒𝑉𝑎𝑙𝑢𝑒<sub>𝑚𝑖𝑛</sub>     )<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;𝐶𝑢𝑟𝑣𝑒𝑉𝑎𝑙𝑢𝑒<sub>𝑚𝑎𝑥</sub> − 𝐶𝑢𝑟𝑣𝑒𝑉𝑎𝑙𝑢𝑒<sub>𝑚𝑖𝑛</sub>
 
An alternative approach involves selecting a reference well (Ref) from within the dataset under consideration. Curves values from other wells (Curve) are then stretched and squeezed to match the minimum and maximum values of the corresponding curve in the reference well. This approach is frequently applied to gamma-ray data (Shier, 2004).
 

𝐶𝑢𝑟𝑣𝑒𝑛𝑜𝑟𝑚
 

= 𝑅𝑒𝑓𝑚𝑖𝑛
 

+ (𝑅𝑒𝑓𝑚𝑎𝑥
 

− 𝑅𝑒𝑓𝑚𝑖𝑛
 
) ∗ (   𝐶𝑢𝑟𝑣𝑒𝑉𝑎𝑙𝑢𝑒 − 𝐶𝑢𝑟𝑣𝑒𝑉𝑎𝑙𝑢𝑒𝑚𝑖𝑛     )
𝐶𝑢𝑟𝑣𝑒𝑉𝑎𝑙𝑢𝑒𝑚𝑎𝑥 − 𝐶𝑢𝑟𝑣𝑒𝑉𝑎𝑙𝑢𝑒𝑚𝑖𝑛
 
Anomalous outliers in curve values will adversely impact the outcome of normalisation processes using minimum and maximum values. For this reason it is common practise to use percentiles in the frequency distribution (e.g. 5th and 95th) in place of minimum and maximum values. A quick check on the descriptive statistics of the log data under consideration prior to normalisation will establish whether this is necessary.
In addition to normalising curve data between wells, the types of approach outlined above can also be useful to correct data within a single well. For example, normalising a gamma-ray curve that over some of its length has an attenuated signal due to being run through steel casing (Quatero et al. 2014).
Finally it should be noted that an alternative to normalisation is to simply avoid batch processing and work on a well-by-well basis, generating a bespoke set of cut-off criteria for each well. This may sometimes be the most efficient approach and has the advantage of preserving the integrity (including all of the inherent errors) of the original log data. There is always a risk that normalising log data will remove or alter real geological signal and it should be approached carefully.

3.4	METHOD
Applying cut-off values to a well log is a relatively simple process and most geophysical log handing software has built in functionality to define cut-offs and output a derived lithological log. Figure 15 illustrates the facies calculator in SKUA-GOCAD 2019 as an example. Lithological classifications are achieved in four main steps.
 
1.	Well selection. Wells can be selected and worked on either individually or in batches of any size.
2.	Well Region. Where the well length is greater than stratigraphic interval of interest it is generally advantageous to work within a corresponding sub-selection of the log data. Creating and working within pre-defined well ‘regions’ (in the terminology of SKUA-GOCAD ) avoids the need to fragment and subsample the original continuous log dataset.
3.	Classification. A pre-defined table is selected which lists the lithologies or sedimentary facies that will be generated by the cut-offs. Each facies is assigned a numerical value and a colour or pattern fill. This table can be edited and augmented as the project proceeds.
4.	Input properties. One or more logs are selected that will be used in the analysis. The logs can be either primary measurements or logs that have been derived and modified from these primary measurements (e.g. normalised curves or shale volume Vshale).


Figure 15. Facies calculator in SKUA-GOCAD 2019

5.	Cut off values and assigned lithology. In the final step lithologies that have been pre- defined in the classification table are assigned to the available permutations of log type and cut- off value. Clicking ‘apply’ will generate a continuous lithological log based on these input data for the input wells.

3.5	SELECTING CUT-OFF VALUES
Selecting appropriate cut-off values is clearly the most critical step in this classification approach. There is no singular robust statistical method for determining cut-offs because of the infinite number of ways in which geophysical tools imperfectly sample and respond to the complexities of real-world geology. Cut-offs are often defined both empirically and heuristically to achieve an end-product that is imperfect but deemed geologically plausible. The process
 
generally involves the determination of clusters within the dataset which are then mapped to specific lithologies using both the absolute magnitude of the responses (e.g. Table 1) but also soft supporting information such as cuttings descriptions and broader geological knowledge. The outcome of a cut-off analysis might also vary with the purpose of the study. For example, in an aquifer study the cut-offs might be deliberately biased toward the recognition of potential flow barriers such as mudstones, even if this overestimates reality. In addition to analysing geophysical logs within conventional downhole tracks (e.g. (Figure 16A) the most commonly used tools for the initial recognition of lithology clusters are frequency distribution histograms and multivariate scatter-plots. There are numerous statistical tools that can be used to enhance the recognition of clusters within these basic types of plot (Ma, 2011; 2019). Cases are considered below of lithology determination based on a single log and using multiple logs.

3.5.1	Case 1: Using a single log type
Where only one lithology log is available (quite often the gamma-ray log) an exploratory analysis of the frequency distribution histogram can help in identifying populations and potential cut-off values (Figure 16B). It is often necessary to experiment with bin sizes to reveal the populations within the histogram. Once the populations are identified a somewhat arbitrary and artificial ‘wall’ or cut-off is selected and used to generate the continuous lithology log. The effectiveness of the cut-off is usually judged against supporting lithological information such as core or cuttings descriptions.




Figure 16. A lithology log (with a simple two-fold classification) created for a short section of Carboniferous Millstone Grit using a gamma-ray log. A histogram highlights the bimodal distribution created by interbedded sandstone and mudstone. The histogram shows distinct modes at 40API and 90API. A cut-off value of 70 API produces the lithology log shown in A. Note that the cut-off is a rather arbitrarily placed ‘wall’ in the lithofacies-component histogram.

In many cases, frequency distribution histograms of log values will not display distinct populations but are single mode histograms with a skewed long tail. This can occur even where the geology consists of two well-defined rock types, such as the Triassic St Bees Sandstone Formation illustrated below which is predominantly sandstone but also contains subordinate mudstone (Figure 17).
 
 

Figure 17. (A) Gamma-ray log of the Triassic St Bees Sandstone in NW England (B) histogram of the gamma-ray values (C) Outcrop of the St Bees Sandstones showing thinly interbedded sandstones and mudstones (D) gamma-derived lithology log.

Gamma-ray spikes related to thin interbedded mudstones are clearly seen on the gamma-ray log (Figure 17A) but they do not form a distinct population on the unimodal skewed histogram (Figure 17B). This is a common feature of geological units that contain thin beds because the logging tool will record a signal that is a mixture of the formation properties within the tool's vertical range of investigation. For example the zone of investigation of gamma-ray tool records signals from a hemispherical zone that is typically around 0.9 m across vertically. Coupled with continuous downhole logging-tool travel, thinly interbedded mudstones such as those illustrated in Figure 17C will always produce a convoluted or ‘mixed-lithology’ signal mid-range between sandstone and mudstone end members. This drowns the presence of a distinct peak in the histogram for thinly bedded mudstones. The vertical resolution will vary according to the type of tool (Figure 18) as well as other factors, in particular logging speed.

Figure 18. Common logs ranked from lowest to highest vertical resolution as follows. The absolute resolution of a given log varies depending on the tool, the sampling rate, logging speed, and processing methods.
 
While efforts can be made to deconvolve the long tail of the histogram into additional populations (Ma 2019) the selection of a cut-off value is generally based on supporting information from core and cuttings and on a regional understanding of the typical bulk proportion and bed thickness of mudstone within the St Bees Sandstone Formation.

3.5.2	Case 2: Using multiple log types
Using two or more log types will often produce a clearer separation of lithofacies from geophysical log datasets. There are no fixed rules on what logs can be combined but some advocate against combining logs that are highly correlated because they do not bring significant additional information into the lithofacies classification process (Ma, 2019). The main limiting factor in many projects undertaken in BGS using data archives assembled over many decades and derived from many heterogeneous sources are the low number of wells with comparable datasets of similar curve types and log quality..
Two logs can be readily plotted on a 2D scatter-plot. Figure 19 illustrates a cross-plot of sonic and gamma-ray for the Mercia Mudstone and Penarth Group in the Winterborne Kingston borehole in South Dorset (see Figure 22). While there are substantial overlaps, a number of high-density points clusters points toward the existence of at least four distinct lithologies in the stratigraphic interval.


Figure 19. Cross-plot of gamma-ray and sonic logs for the Mercia Mudstone Group of the Winterborne Kingston Borehole (see Fig. 7) reveals four high density (darker red) clusters more effectively than logs plotted as individual distributions.

Additional lithological resolution can be achieved by colouring the points with a third property such as density. Figure 20 shows how this can be used to distinguish anhydrite (which has a relatively high density) within the scatter plot.
 
 

Figure 20. (A) Histogram of density log data for the Mercia Mudstone and Penarth Groups of the Winterborne Kingston borehole. The typical densities for a range of rock materials are shown on the plot. Cross-plot of sonic and gamma-ray logs with points coloured up by the density log. This reveals a cluster of high density anhydrite which was not apparent before including the additional log information on the 2D cross-plot.

An alternative method of cross-plotting three properties is to use a 3D scatter plot (Figure 21). A fourth property can be used to colour up the points, or as shown in Figure 21 this can be used to highlight the derived lithological clusters. Such 3D plots can however become difficult to interpret. Any addition of further properties requires the application of techniques such as
 
principal component analysis which reduces dimensional data into a low dimensional sub-space that can be visualized in 2–3 dimensions.


Figure 21. 3D scatter plot of density, sonic and gamma-ray for the Mercia Mudstone Group of the Winterborne Kingston borehole with the points coloured by derived lithology information.

Once the optimal combination of logs has been established for the stratigraphic interval under consideration a table of cut-off values can be created and the analysis run (Figure 22). As in most cases of cut-off analysis the approach is highly iterative. Cut-off values can be adjusted and the lithological log re-created in a highly interactive way until there is a close match between the lithology profile and what should be expected from additional evidence such as cuttings and general stratigraphic understanding.
 
 

Figure 22. Resultant lithology log (central track, see A for key to colours).

3.6	THE IMPORTANCE OF WORKING WITHIN WELL REGIONS
The main difficulty of using simple cut-off analysis is discriminating lithologies when there is large overlap in their log properties. Figure 23 illustrates an example from the Winterborne Kingston borehole in South Dorset where the dolomitic siltstones and mudstones of the Blue Anchor Formation show a remarkably similar log response to the Sherwood Sandstone at greater burial depth. While effort could be expended to discriminate these rock types by introducing additional logs or by applying more sophisticated clustering techniques a simple solution is to restrict the analysis to a shorter well region that excludes the overlapping rock types.
 
 

Figure 24. Gamma-ray and sonic log from Triassic strata in the Winterborne Kingston Borehole in South Dorset. The interbedded mudstones and dolomitic siltstones of the Blue Anchor Formation show a large overlap in their gamma-ray and sonic log response with the interbedded sandstones and mudstones of the Sherwood Sandstone at greater depth. Rather than attempting to discriminate lithofacies by introducing more log data it is often simpler and more efficient to work in smaller well regions e.g. B rather than A.


[[Category:OR/21/006 Derivation of lithofacies from geophysical logs: a review of methods from manual picking to machine learning | 03]]