Curve Normalization

Purpose

Curves for the same measurement in different wells do not always agree, even in the same rock. Tools from different vendors and generations, calibration drift, mud and borehole differences and processing changes all move the curves. A petrophysical model that uses one set of parameters across a field (a clean and clay gamma-ray value, a shale resistivity, a matrix density) needs the curves to be on a common scale first, or the same parameter means different things in different wells. Normalization is the correction that puts the curves of several wells on the scale of a Key well or of agreed target values.

Position in the workflow

Upstream. Normalization needs curves that already have consistent names, units and depths: see Curve Aliasing and Mnemonics and Log Curve Cleanup. It also needs bad hole removed or repaired, as in Washout Identification and Repair, because a washout inside the reference interval will move the percentile picks.

Downstream. Every parameter that was picked on a multi-well basis depends on it: clay volume end-points, shale density and resistivity, matrix and fluid parameters, cutoffs and zone parameters used across a field. Normalized curves are also the input to any cross-well statistics, regional maps and machine-learning models.

Error propagation. A normalization error is systematic: it shifts every sample of a well in the same direction. A 10 gAPI error in a gamma ray end-point, for example, changes the clay volume of every sample by a similar amount (see Clay Volume). An error in a reference interval is much worse than an error in the interval chosen for a parameter, because it is inherited by every later calculation in that well.

Key concepts

Why normalize. The aim is to remove differences between wells that come from the logging system and not from the rock, so that the same rock reads the same in every well.

Key well and reference interval. The Key well is the well taken as the standard. A Normalization reference interval is a zone that is expected to have the same distribution in every well, normally a thick, laterally uniform shale or other consistent unit. Normalization compares the distributions of a curve in that interval.

Picks. A pick is a percentile of the curve in the reference interval: low (Source low pick), middle (Source middle pick) and high (Source high pick). Percentiles are used in place of the minimum and maximum so that spikes and bad hole do not set the scale.

Shift, scale and shift-and-scale. A shift adds a constant, a scale multiplies by a factor, and a two-point map does both by matching a low and a high pick. See Shift, Scale, and Shift-and-Scale.

Fixed targets. Where there is no trusted key well, a curve is mapped onto targets chosen by the analyst: Normalization to a Fixed Range or Value.

Resistivity is different. It spans decades and its errors are multiplicative, so it is normalized in log space, and in many projects not at all. See Resistivity Normalization.

What not to normalize. Normalization removes a difference between wells. If the difference is real, normalization damages the data. Do not normalize across a real geological change (a different facies, a change in formation, a gas or hydrocarbon-bearing interval); do not use a reference interval that is not the same rock in both wells; and be careful with porosity-type curves from calibrated tools. Density, neutron and sonic tools are calibrated to physical standards, and a difference between wells is more often a real difference in rock, borehole or environmental correction than a calibration offset. Gamma ray, SP and resistivity are the usual targets.

Method selection guide

Method	Inputs	Use when	Strengths	Weaknesses
No normalization	None	The curves come from the same tool type and processing, are calibrated, and agree in a reference interval	Nothing to defend; no risk of removing real signal	Disagreements that are real calibration problems remain
Shift (additive)	Key-well and source median in a reference interval	The distributions in the reference interval have the same shape but are displaced	One parameter; does not change spread	Wrong when the spread also differs; moves clean-rock values out of range
Two-point shift and scale	Low and high picks of both wells	The second well is a stretched or compressed version of the key well (typical of gamma ray)	Fixes offset and spread; the workhorse	Needs a reference interval that spans low and high values; extrapolates at the ends
Three-point piecewise	Low, middle and high picks	A non-linear relation between the wells is demonstrated	Matches three points	Kink at the middle pick; fits noise in the picks
Fixed range or value	Picks of one well, analyst targets	There is no key well, or a downstream step needs a particular scale	Does not depend on one well being right	Targets are an assumption; erases real differences between wells
Percentile picks	Curve in a reference interval	With every method above, to read the picks	Robust to spikes and bad hole	Needs a thick, uniform interval
Resistivity, log space	Percentile picks in log10	The wells differ by a multiplicative factor in a water-wet reference interval	Respects the log-normal distribution and multiplicative error	Easy to over-apply; wrong in hydrocarbon zones or with different tool types

Decision guidance

If a trusted key well exists, normalize to it. If it does not, build a composite from the best wells before turning to fixed targets.
Start with a shift. Move to a two-point map only if the histograms show a difference of spread and not just of position.
Gamma ray is the most commonly normalized curve. SP and resistivity are next. Density, neutron and sonic should usually be corrected for environment and checked against known matrix and fluid values before any normalization is considered.
Prefer the percentile picks of a thick shale to those of a thin or mixed interval.
If the effect of the normalization on the result is smaller than the uncertainty of the later parameter, leave the curve alone.

Shared parameter picking

Reference interval. Pick one for each curve type that is the same unit in all the wells and is thick, uniform and free of bad hole. For a gamma ray this is usually a regional shale; a resistivity reference needs to be water-wet. The same interval should be used for all methods on one curve. Make it per formation if the field has several distinct unit changes.

Percentile levels. The same three levels (low, middle, high) are used by every method: typically the 5th, 50th and 95th percentile, as discussed on Histogram and Percentile-Based Picks. Using different levels for different methods on the same curve makes results hard to compare.

Key-well values. The key-well picks (Reference low value, Reference middle value, Reference high value) are computed once and used for every other well. Do not recompute them from a well that has already been normalized.

Fixed targets. If fixed targets are used, record their source. They are parameters of the project, not properties of the curve.

Recommended default approach

Absent other information, a careful generalist would:

Finish unit conversion, depth checks, spike removal and bad-hole handling first, then pick.
Choose a thick, uniform shale as the reference interval and one well with the best data as the key well.
Overlay the histograms of the gamma ray in the reference interval for every well. Normalize only the wells where the histograms clearly differ.
Use a two-point shift and scale on the 5th and 95th percentiles for the gamma ray, and a shift on the 50th percentile if the spread agrees.
Treat resistivity separately, in log10, with a shift on the median and only where there is a documented reason.
Leave density, neutron and sonic alone unless a specific calibration problem is documented.
Re-check the histograms and a second interval that was not used for picking, and record the picks and the map for each well.

Combining methods

Normalization methods are applied one at a time to a curve, not combined. Apply a single map per curve, computed from the original data, and keep the original curve. Normalizing a normalized curve compounds maps and hides the origin of the result. Where one well needs more than one map (a change of tool partway down the hole), compute a separate map for each section and splice the results, as in Curve Splicing and Merging. A sequence that is acceptable is a shift for the offset followed by a check, and only then a two-point map if the spread still disagrees; the second map is computed from the original data in one step, not stacked on the shifted curve.

QC of results

A good result:

has histograms in the reference interval that overlay the key well's, including at percentiles that were not used for the picks,
matches in a second, independent interval,
has a small, physically plausible shift or slope for each well,
leaves clean rock and shale end-points at believable values (no negative porosity, no gamma ray outside the physical range), and
leaves reservoir intervals unforced, with real differences between wells preserved.

Signs of a bad result: a very large shift, a slope far from 1, a mismatch in the second interval, and normalized curves that look like they come from the same well in every zone.

Common pitfalls

Normalizing across a real geological change, so that real difference between wells is erased.
Using a reference interval with different rock in the two wells.
Picking the end-points from the minimum and maximum, or from an interval with spikes or bad hole.
Using a thin interval, or one with a trend, so that the picks depend on the interval chosen.
Normalizing resistivity in linear space, or in a hydrocarbon interval.
Normalizing density, neutron and sonic to hide a problem that should be fixed with an environmental correction or a tool-type choice.
Normalizing a curve twice.
Forcing every well onto one range and then reading the result as a field-wide property.
Losing track of what was done: no record of the picks, the interval and the map.

Going Deeper

Well-log normalization is an old problem, discussed in the logging literature since at least the early 1970s, and one that grew in importance as multi-well and field-wide studies replaced single-well interpretation. The simple one- and two-parameter maps are the ones in everyday use. Quantile matching, histogram matching and regression against a regional standard are the more flexible alternatives, and they have the same hazard: the more flexible the map, the more of the real geology it removes. A recurring recommendation is to normalize as little as possible, to document every correction, and to prefer fixing the cause of a disagreement (a tool-type difference, an environmental correction, a depth shift) to equalizing its symptom.