Gamma ray log and natural gamma ray spectrometry

Quick refresher

Almost all the natural gamma radiation of rocks comes from potassium-40 and from the decay series of uranium-238 and thorium-232. (A decay series is a chain of radioactive steps that ends in a stable isotope.) Each source emits photons with its own energies.
Potassium and thorium are tied mainly to clay minerals, micas and feldspars. Uranium is tied to organic matter and phosphates. That is why the gamma ray log usually reads high in shales and low in clean sandstones, limestones, anhydrite and salt.
The reading is proportional to the mass concentration of the radioactive elements, and we measure it in API units. The depth of investigation is only the first tens of centimetres of rock. The vertical resolution (the thinnest bed the tool shows clearly) is about half a metre.
The gamma ray index $I_{GR}$ shows where the reading lies between the clean-formation baseline and the shale baseline. We work out shale volume from it (Determining shale volume).
A high gamma ray reading is not yet shale. Feldspars, micas, glauconite (a green, potassium-rich mineral), uranium and the potassium in the mud also give high readings. To check, use spectrometry, other methods and core (rock samples cut from the well).
Spectrometry separates potassium, uranium and thorium. The uranium-free gamma ray (CGR) shows shale volume better, and the Th/K ratio hints at the type of clay minerals.

Key relationships

GR = \dfrac{\sum_i \rho_i V_i A_i}{\rho_b}

the reading is the sum of the contributions of the radioactive minerals, weighted by mass

I_{GR} = \dfrac{GR - GR_{cl}}{GR_{sh} - GR_{cl}}

gamma ray index (the double-difference parameter)

GR \approx 16\,\mathrm{K} + 8\,\mathrm{U} + 4\,\mathrm{Th}

roughly: GR in API, potassium in %, uranium and thorium in g/t

CGR \approx 16\,\mathrm{K} + 4\,\mathrm{Th}

gamma ray without the uranium component

Common pitfalls

Taking the highest peak of the log as the shale baseline. That peak is often a shale rich in uranium, not a typical shale.
Calling a bed shaly only because the gamma ray reading is high, without checking spectrometry and methods that rely on different physics.
Comparing the absolute gamma ray values of different wells without normalising them (bringing them to a common scale). Tools, hole sizes, muds and casing all shift the scale.
Forgetting potassium chloride in the mud. It raises the readings, especially opposite washouts (places where the hole is wider than the drill bit).

After this lesson you can

explain where the natural radioactivity of rocks comes from and why shales are usually “hotter” (more radioactive) than sandstones and carbonates
describe how a gamma ray tool detects the radiation, what API units mean, and which properties of the rock and the borehole affect the readings
use the gamma ray log for lithology, correlation and depth matching, and calculate the gamma ray index from the clean-formation and shale baselines
recognise the pitfalls of the gamma ray log: radioactive sandstones, uranium in carbonates and sandstones, “cold” (weakly radioactive) shales, and potassium in the mud
explain how spectrometry measures potassium, uranium and thorium separately, and use the uranium-free gamma ray log and the ratios of the elements in interpretation

Natural radioactivity of rocks

Gamma rays are high-energy photons of electromagnetic radiation. The nuclei of certain isotopes emit them when they decay. (An isotope is a form of an element. Radioactive decay is the slow change of an unstable nucleus into another one.) We measure the photon energy in megaelectronvolts (MeV). In sedimentary rocks, almost all the natural gamma radiation comes from three sources. Their half-lives (the time in which half of the atoms decay) are billions of years, so since the rocks formed the amount of these sources has hardly changed.

Natural sources of gamma radiation

Source: Potassium-40 (about 0.012% of natural potassium)
Half-life: ≈ 1.25 billion years
Characteristic line: 1.46 MeV, the only one
Where it occurs: potassium feldspars, micas, illite, glauconite, potash salts

Source: Uranium-238 series
Half-life: ≈ 4.5 billion years
Characteristic line: 1.76 MeV (bismuth-214) among many others
Where it occurs: organic matter, phosphates, some carbonates; uranium is carried by groundwater

Source: Thorium-232 series
Half-life: ≈ 14 billion years
Characteristic line: 2.62 MeV (thallium-208) among many others
Where it occurs: clay minerals, heavy minerals (monazite, zircon), volcanic ash

Source	Half-life	Characteristic line	Where it occurs
Potassium-40 (about 0.012% of natural potassium)	≈ 1.25 billion years	1.46 MeV, the only one	potassium feldspars, micas, illite, glauconite, potash salts
Uranium-238 series	≈ 4.5 billion years	1.76 MeV (bismuth-214) among many others	organic matter, phosphates, some carbonates; uranium is carried by groundwater
Thorium-232 series	≈ 14 billion years	2.62 MeV (thallium-208) among many others	clay minerals, heavy minerals (monazite, zircon), volcanic ash

Uranium and thorium decay to stable lead through long chains of daughter isotopes (the products of each decay step). So their spectra contain many lines, and the characteristic lines belong to the daughter isotopes. Potassium-40 emits a 1.46 MeV photon in about one decay in nine. The other decays happen without gamma radiation.

Why shales are “hotter” than sandstones. Clay minerals form when feldspars and micas weather (break down at the surface). Illite, a common clay mineral, holds potassium in its crystal structure. Fine clay particles have an enormous surface, and it attracts thorium and uranium (adsorbs them). Thin marine muds are often rich in organic matter, which pulls uranium out of the water. Clean quartz sand and clean limestone contain almost none of these elements, because quartz and calcite are not radioactive. So in a siliciclastic section (one made of sand, silt and clay grains) a high gamma ray reading usually means shale, and a low one means clean sandstone. The word “usually” matters here. The exceptions are discussed below.

The three elements behave differently in nature, and this helps in interpretation. Thorium hardly dissolves in water, so it travels only inside mineral particles. Uranium dissolves in oxygen-rich (oxidising) waters. It drops out of the water where there is little oxygen (a reducing environment): in organic matter, in phosphates and along the paths of groundwater. Potassium is part of the silicate minerals (feldspars, micas, illite) and of the salts that crystallise from brines.

How a gamma ray tool works

On the way to the tool, a photon from the rock hits the electrons of atoms and loses some of its energy at each hit. This is Compton scattering. In the end, an atom absorbs the weakened photon (photoelectric absorption). So the tool gets radiation only from the nearest layer of rock. The depth of investigation (how far into the rock the tool can “see”) of the gamma ray log is roughly 15–30 cm. Its vertical resolution (the thinnest bed it shows clearly) is about half a metre.

The detector is a scintillation counter. It has a crystal, usually sodium iodide, in which each absorbed photon makes a flash of light. A photomultiplier tube turns the flashes into electrical pulses. The first tools used Geiger–Müller counters (gas-filled tubes that give a pulse when a photon passes through). Scintillation counters are far more efficient, so the detector can be short and the resolution better. Almost every wireline tool string includes a gamma ray tool. (A wireline tool string is the set of tools lowered into the well on a cable.) So does the assembly for logging while drilling (LWD), where the tools are part of the drill string (Open-hole logging: why, how and when).

Gamma ray reading and the content of radioactive minerals

GR = \frac{\sum_i \rho_i\,V_i\,A_i}{\rho_b}

where:

$GR$ gamma ray log reading after borehole corrections, API
$\rho_i$ density of the $i$ -th radioactive mineral, g/cm³
$V_i$ volume fraction of this mineral in the rock, fraction
$A_i$ radioactivity per unit mass of the mineral: the reading that the pure mineral would give, API
$\rho_b$ bulk density of the rock, g/cm³

Units: API; densities in any units, the same for all terms

Holds when

Corrections for the hole diameter, the mud and the casing have already been applied.
The contributions of the minerals are independent and add up.
The bed is uniform within the volume the tool sees and thicker than the tool's vertical resolution.

The ratio $\rho_i V_i/\rho_b$ is the mass fraction of the mineral. The tool responds to the mass concentration of the radioactive elements, not to the volume concentration. Suppose two rocks hold the same amount of these elements per unit volume. The less dense rock will show a somewhat higher gamma ray reading, because it absorbs the radiation less strongly (more detail in the advanced section).

The API gamma ray unit is named after the American Petroleum Institute. A reference model fixes it. In Houston, people built a model of a formation out of concrete, with zones of low and high radioactivity. By definition, the difference between the readings in these two zones is 200 API units. Before use, each tool is calibrated against a field standard that is tied to this model, so the logs of different tools can be compared. Before this scale existed, readings were given in micrograms of radium equivalent per tonne of rock. In Russian-language practice they were also given in microroentgens per hour (µR/h). In interpretation we still move to a relative quantity: the index between the clean-formation and shale baselines.

Typical gamma ray readings

Rock: Rock salt, anhydrite
GR, API (approximate): less than 10–15
Comment: almost no potassium, uranium or thorium

Rock: Clean limestones and dolomites
GR, API (approximate): 10–25
Comment: higher if the rock contains uranium

Rock: Clean quartz sandstones
GR, API (approximate): 15–35
Comment: higher with feldspars, micas, glauconite

Rock: Coals
GR, API (approximate): usually less than 30
Comment: sometimes enriched in uranium

Rock: Shales and claystones
GR, API (approximate): 80–150
Comment: depends on the composition of the clay minerals

Rock: Organic-rich shales
GR, API (approximate): 150 or more
Comment: uranium bound to organic matter

Rock: Potash salts (sylvite, carnallite)
GR, API (approximate): hundreds
Comment: potassium is the main component of the mineral

Rock	GR, API (approximate)	Comment
Rock salt, anhydrite	less than 10–15	almost no potassium, uranium or thorium
Clean limestones and dolomites	10–25	higher if the rock contains uranium
Clean quartz sandstones	15–35	higher with feldspars, micas, glauconite
Coals	usually less than 30	sometimes enriched in uranium
Shales and claystones	80–150	depends on the composition of the clay minerals
Organic-rich shales	150 or more	uranium bound to organic matter
Potash salts (sylvite, carnallite)	hundreds	potassium is the main component of the mineral

These numbers only give a rough idea. Every area and every tool has its own values, so we read the gamma ray log relative to the clean-formation and shale baselines of the same section.

The readings also depend on the borehole. The mud and the casing absorb part of the radiation. So the reading is lower in a wide hole, in a heavy mud with barite, or behind casing. (Barite is a heavy mineral added to make the mud heavier.) In each case the reading is lower than opposite the same rock in a narrow hole. Some muds contain potassium chloride (KCl, a common additive that stops clays from swelling). Then the mud itself gives off radiation, and the reading rises, especially opposite washouts. We correct for all this with charts made for the particular tool (Interpretation charts: how to read them).

Radioactive decay is a random process. So the number of photons the tool counts varies even opposite a uniform bed. The small spikes on a gamma ray curve are often statistical noise, not geology. The slower the logging speed, the smaller the scatter, but slow logging costs rig time. Averaging over depth also reduces the scatter, but it smooths out thin beds (more detail in the advanced section).

What the gamma ray log is used for

Lithology and the reservoir–non-reservoir boundary. A reservoir is rock that can hold and yield oil or gas. In a siliciclastic section, high values are shales and low values are sandstones. In a carbonate section (limestones and dolomites), the clean rocks give low values and their shaly varieties give higher ones. Salt and anhydrite show the lowest values, and potash salts the highest.
Correlation. The shape of the gamma ray curve repeats in neighbouring wells. So we use it to correlate the sections of wells (Well correlation). We also use it to match the depths of the records from different runs, of the LWD data and of the core.
Tie-in through casing. The gamma ray log works in a cased hole. Before perforating, we record it together with a casing collar locator (a tool that finds the joints between the casing pipes). Then we match it with the open-hole gamma ray log. This puts the perforations exactly opposite the bed.
Shale volume. We calculate the gamma ray index from the position of the reading between the clean-formation and shale baselines. From the index we find the shale volume (Determining shale volume).
Depositional environments (the settings where the sediments were laid down). The shape of the curve within a package of beds is called the log motif. It shows how the shale volume changed and, in siliciclastic rocks, often also the grain size. A “bell” (the reading increases upward) means the grains get finer upward, as in channel deposits. A “funnel” (the reading decreases upward) means they get coarser upward, as in mouth bars (sand bars at the mouth of a river channel). A “cylinder” is an even package with sharp boundaries. This is a hint for the geologist, not a diagnosis (Facies, facies successions and sedimentary logs).
Source rocks (the rocks that generate oil and gas). High uranium in shales often points to a lot of organic matter (Source rocks, maturation and migration).

Gamma ray index

I_{GR} = \frac{GR - GR_{cl}}{GR_{sh} - GR_{cl}}

where:

$GR$ gamma ray reading in the interval of interest, API
$GR_{cl}$ clean-formation baseline (clean line): the typical reading of a clean sandstone or carbonate of the same section, API
$GR_{sh}$ shale baseline (shale line): the typical reading of thick shale packages, API

Units: any consistent gamma ray units; the index is dimensionless

Holds when

The radioactivity of the bed is created only by shaly material.
The shales in the bed are the same as in the reference shale packages, and the clean part is the same as in the reference clean bed.
The baselines are chosen in the same hole, on the same record and close in depth.

The index shows how far along the radioactivity scale the reading has moved from clean rock towards shale. It is not equal to shale volume. The topic Determining shale volume explains how to go from the index to the volume fraction of shale. In Russian-language practice the same quantity is called the double-difference parameter $\Delta J_\gamma$ .

For example, take a clean-sandstone baseline of 25 API and a shale baseline of 125 API. A reading of 75 API then gives an index of 0.5: the bed is halfway from clean rock to shale. How much shale it contains by volume depends on the rocks, and core is used to check it.

When the gamma ray log misleads

The gamma ray log measures radioactivity, not shale volume. The link between them holds as long as only shales are radioactive. Here are the main cases where this is not so.

Pitfalls of the gamma ray log

Situation: Arkosic (feldspar-rich) and micaceous (mica-rich) sandstones, glauconitic sands
What the gamma ray log shows: high gamma ray reading in a clean reservoir
How to recognise it: a lot of potassium and little thorium on the spectrometry; normal porosity and signs of permeability from other methods; core

Situation: Uranium in carbonates and sandstones: organic matter, phosphates, stylolites (thin, jagged seams where the rock has dissolved under pressure), fractures, uranium deposited from formation waters
What the gamma ray log shows: gamma ray peaks in a clean rock
How to recognise it: uranium shows on the spectrometry and the uranium-free gamma ray is low; the neutron and density logs show no signs of shale

Situation: Heavy minerals (monazite, zircon) in sands
What the gamma ray log shows: high gamma ray reading because of thorium
How to recognise it: a lot of thorium and little potassium; usually in thin layers

Situation: “Cold” shales (kaolinitic, poor in potassium)
What the gamma ray log shows: low gamma ray reading in a shaly rock, so shale volume is underestimated
How to recognise it: the neutron and density logs, the spontaneous potential (SP) log and core disagree with it

Situation: Potassium chloride in the mud
What the gamma ray log shows: a general rise of the gamma ray reading, especially in washouts
How to recognise it: compare with the caliper log (it measures the hole diameter) and apply corrections; spectrometry shows potassium in clean beds too

Situation	What the gamma ray log shows	How to recognise it
Arkosic (feldspar-rich) and micaceous (mica-rich) sandstones, glauconitic sands	high gamma ray reading in a clean reservoir	a lot of potassium and little thorium on the spectrometry; normal porosity and signs of permeability from other methods; core
Uranium in carbonates and sandstones: organic matter, phosphates, stylolites (thin, jagged seams where the rock has dissolved under pressure), fractures, uranium deposited from formation waters	gamma ray peaks in a clean rock	uranium shows on the spectrometry and the uranium-free gamma ray is low; the neutron and density logs show no signs of shale
Heavy minerals (monazite, zircon) in sands	high gamma ray reading because of thorium	a lot of thorium and little potassium; usually in thin layers
“Cold” shales (kaolinitic, poor in potassium)	low gamma ray reading in a shaly rock, so shale volume is underestimated	the neutron and density logs, the spontaneous potential (SP) log and core disagree with it
Potassium chloride in the mud	a general rise of the gamma ray reading, especially in washouts	compare with the caliper log (it measures the hole diameter) and apply corrections; spectrometry shows potassium in clean beds too

The rule: check any conclusion about shale volume from the gamma ray log with at least one method that works on different physics (SP, the neutron and density logs, spectrometry), or with core.

Spectrometry: potassium, uranium and thorium separately

An ordinary gamma ray log counts all photons together and does not know where they came from. Spectral gamma ray logging separates them by energy. The tool is a scintillation detector pressed against the borehole wall. It records an energy spectrum, which shows how many photons arrived in each energy interval. On the way to the detector, the photons scatter and lose energy. So instead of sharp lines, the tool sees blurred peaks on top of a continuous “tail” of scattered photons.

We divide the spectrum into several energy windows (ranges of photon energy). The high-energy windows cover the characteristic peaks: 1.46 MeV for potassium, 1.76 MeV for uranium (from bismuth-214) and 2.62 MeV for thorium (from thallium-208). Calibration (testing the tool on known samples) gives the response of the tool to each element. Then we solve a set of equations using the number of counts in all the windows. This gives the content of potassium (in %) and of uranium and thorium (in g/t, that is, parts per million, ppm).

The main difficulty is statistics. There are few high-energy photons, so the contents come out noisy, especially for uranium. To reduce the noise, we also use the many counts in the low-energy windows. We log more slowly than for an ordinary gamma ray log, smooth the curves over depth, and save the original spectra so that they can be processed again.

Total gamma ray from the potassium, uranium and thorium contents (approximate)

GR \approx 16\,\mathrm{K} + 8\,\mathrm{U} + 4\,\mathrm{Th}

where:

$GR$ total gamma ray (SGR), API
$\mathrm{K}$ potassium content, % (by mass)
$\mathrm{U},\ \mathrm{Th}$ uranium and thorium content, g/t (ppm)

Units: GR in API; potassium in mass per cent, uranium and thorium in g/t

Holds when

The coefficients are approximate and depend on the tool and its calibration.
Radioactive equilibrium holds in the uranium and thorium series.
Borehole corrections have been applied.

1% of potassium gives about as much as 2 g/t of uranium or 4 g/t of thorium. If we drop the uranium term, we get the computed gamma ray (CGR): $CGR \approx 16\,\mathrm{K} + 4\,\mathrm{Th}$ . Uranium moves easily in water and is often unrelated to shales, so CGR shows shale volume more reliably.

Worked exampleShaly dolomite or uranium?

Given (assumed data)

Clean limestone (clean-formation baseline): $\mathrm{K} = 0.1$ %, $\mathrm{U} = 0.8$ g/t, $\mathrm{Th} = 0.6$ g/t
Shale (shale baseline): $\mathrm{K} = 3.0$ %, $\mathrm{U} = 3.0$ g/t, $\mathrm{Th} = 11$ g/t
Dolomite under study: $\mathrm{K} = 0.4$ %, $\mathrm{U} = 8.5$ g/t, $\mathrm{Th} = 2.0$ g/t

Solution

Total gamma ray: dolomite $16\cdot 0.4 + 8\cdot 8.5 + 4\cdot 2.0 = 82.4$ API; limestone 10.4 API, shale 116 API.
Index from the total gamma ray: $(82.4 - 10.4)/(116 - 10.4) = 0.68$ . The dolomite looks strongly shaly.
Uranium-free gamma ray: dolomite $16\cdot 0.4 + 4\cdot 2.0 = 14.4$ API; limestone 4.0 API, shale 92 API.
Index from CGR: $(14.4 - 4.0)/(92 - 4.0) = 0.12$ . The share of uranium in the radiation of the dolomite is 83%.

Answer: The index is 0.68 from the total gamma ray and 0.12 from the uranium-free gamma ray. The dolomite is practically clean, and uranium causes the high gamma ray reading.

What it means. If we judged the interval from the total gamma ray alone, we would call it shaly and might exclude it from the reservoir. Before doing that, we check methods that work on different physics. Suppose we use the dolomite matrix (the mineral frame of the rock) in the porosity calculation. A clean porous dolomite will then give a similar porosity on the neutron and density logs, without the separation between the curves that is typical of shales. The coefficients 16, 8 and 4 are approximate. So this calculation is good for comparison only, and the working SGR and CGR curves come from the spectrometry processing. The data in this example are assumed for illustration.

CalculatedCalculated curves of the total gamma ray (SGR), the uranium-free gamma ray (CGR), potassium and thorium in an assumed section. They come from the approximate relationship

GR \approx 16\,\mathrm{K} + 8\,\mathrm{U} + 4\,\mathrm{Th}

. The shale and the dolomite are the ones from the example above. The shading between SGR and CGR is the contribution of uranium.

Ratios of the elements help with lithology:

Th/K: the type of clay and potassium-bearing minerals. A high ratio (almost no potassium and a lot of thorium) is typical of kaolinite. A middle ratio is typical of smectites and mixed-layer clays (clays whose crystals alternate between two clay types). A low ratio points to illite and micas, and the lowest to potassium feldspars. This is how we tell an arkosic sandstone with a high gamma ray reading from a shaly one: it has a lot of potassium and little thorium (Lithology from the photoelectric factor and spectral gamma ray).
Th/U: the depositional environment. Thorium does not dissolve, but uranium dissolves in oxygen-rich (oxidising) waters and drops out in a reducing environment (one with little oxygen). A ratio below about 2 is typical of marine shales rich in organic matter. A ratio above about 7 is typical of continental (land) oxidising environments.
Uranium on its own is a sign of organic matter, phosphates, fractures and stylolites in carbonates.

Terms and symbols

Gamma ray photon: A packet of electromagnetic radiation that a nucleus emits when it decays. We measure its energy in MeV.
API unit: The unit of the gamma ray scale. It is 1/200 of the difference between the readings in the zones of high and low radioactivity of the reference formation model.
Clean-formation baseline and shale baseline, $GR_{cl}$ and $GR_{sh}$: The typical gamma ray readings of reference clean beds and reference shaly beds of the same section.
Gamma ray index, $I_{GR}$: The position of the reading between the clean-formation and shale baselines. In Russian-language practice it is called the double-difference parameter $\Delta J_\gamma$ .
SGR and CGR: The total gamma ray from spectrometry, and the gamma ray without the uranium component.
Secular radioactive equilibrium: The state of a decay series in which the proportions of all the daughter isotopes stay constant. Uranium and thorium spectrometry rests on it.

Common mistakes and misconceptions

Wrong

“A high gamma ray reading means shale.”

In fact

A high gamma ray reading means that the rock contains a lot of potassium, uranium or thorium. The source may be feldspars, micas, glauconite, organic matter, phosphates or a mud with KCl. Other methods must confirm the shale volume.

Wrong

“The shale baseline is the maximum of the gamma ray log.”

In fact

The maximum often comes from uranium-rich shales or from single anomalies. We draw the shale baseline through the typical thick shale packages close to the interval of interest.

Wrong

“The gamma ray log in a cased hole is useless.”

In fact

Behind casing the readings are lower, but the shape of the curve stays the same. We use it to tie in the perforations and to compare records made in different years.

Wrong

“Spectrometry gives the exact uranium content at every point.”

In fact

There are few high-energy photons, and uranium is the noisiest curve. We read it from average values over intervals, together with other data.

In depth: advanced detail

Why the reading depends on the density of the rock

The number of photons that reach the detector from the rock depends on two things. It is proportional to the source strength per unit volume. It is inversely proportional to how strongly the rock absorbs the photons. In the energy range where Compton scattering dominates, the absorption (attenuation) is proportional to the number of electrons per unit volume. That means it is practically proportional to the density of the rock, because in ordinary rock-forming minerals the ratio of the number of electrons to the mass is almost the same. So the density cancels out. The reading is then proportional to the radioactivity per unit mass, that is, to the mass concentration of potassium, uranium and thorium.

An example: two beds hold the same amount of potassium in a cubic metre, but one has a density of 2.2 g/cm³ and the other 2.6 g/cm³. The mass concentration in the first bed is $2.6/2.2 \approx 1.18$ times higher, so its gamma ray reading will be about 18% higher. Now take a typical contrast between the densities of a porous sandstone and a shale (2.25 and 2.50 g/cm³). The difference is then about 11%. The effect is noticeable, but the topic Determining shale volume shows that it is not the main reason why the gamma ray reading and shale volume are not linearly related.

Counting statistics and logging speed

Decays happen at random. The number of counts recorded during the counting time follows the Poisson distribution (the usual pattern for random events counted over a fixed time). Its standard deviation (a measure of the scatter) equals the square root of the number itself. The relative error falls slowly: to halve it, we need four times as many counts.

Statistical error of a sample

\frac{\sigma_N}{N} = \frac{1}{\sqrt{N}}, \qquad N = n\,\frac{\Delta z}{v}

where:

$N$ number of counts per sample, —
$\sigma_N$ standard deviation of this number, —
$n$ count rate opposite the given bed, counts per second
$\Delta z$ sampling interval in depth, m
$v$ logging speed, m/s

Units: SI; for a logging speed in m/h, $N = 3600\,n\,\Delta z/v$

Holds when

The count rate is constant within a sample (a uniform bed).
The background radiation and the dead time of the detector (the short pause after each count, when it cannot count) are ignored.
The samples are independent, with no filtering over depth.

There are three ways to reduce the error: log more slowly, use a larger detector (which increases $n$ ), or average neighbouring samples. The last way makes the vertical resolution worse. This is why spectrometry, where the high-energy windows have few counts, is logged more slowly than an ordinary gamma ray log.

Worked exampleCurve noise at different logging speeds

Given (assumed data)

Count rate in a spectrum window: 25 counts per second
Sampling interval: 0.15 m
Logging speed: 540 m/h and 270 m/h

Solution

At 540 m/h, each sample takes $0.15\cdot 3600/540 = 1.0$ seconds. The number of counts is $N = 25$ , and the error is $1/\sqrt{N} \approx 20$ %.
At 270 m/h, the time and the number of counts are twice as large: $N = 50$ . The error is 14%.
Averaging four neighbouring samples at 270 m/h gives $N = 200$ and an error of 7.1%. But the averaging window is now 0.6 m.

Answer: The error falls from 20 to 14% at half the speed, and to 7.1% with averaging over 0.6 m. The averaging costs vertical resolution.

What it means. Fluctuations of 15–20% from one sample to the next in such a window are statistics, not geology. That is why we read a noisy uranium curve from average values over intervals, not from single peaks. The data in this example are assumed for illustration.

Connections to other topics

Open-hole logging: why, how and when — how and when logs are recorded, and why the gamma ray log is part of every tool string.
Determining shale volume — how to turn the gamma ray index into shale volume and check it with other methods.
Borehole environment: invaded zone and mudcake — how the borehole and the mud affect the readings of the tools.
Well correlation — matching the sections of wells by their characteristic packages of beds on the gamma ray log.
Lithology from the photoelectric factor and spectral gamma ray — mineral composition from spectrometry and the photoelectric factor.
Spontaneous potential (SP) log — the second passive method of identifying shales and permeable beds.
Source rocks, maturation and migration — source rocks, which often stand out as uranium anomalies.

Check yourself

1
Which source gives the single gamma ray line with an energy of 1.46 MeV?
1. A.The thorium-232 series
2. B.The uranium-238 series
3. C.Potassium-40
4. D.Bismuth-214
Show the answer
Correct answer: C. Potassium-40
Potassium-40 emits photons of one energy only, 1.46 MeV. The uranium and thorium series give many lines. The characteristic ones are 1.76 MeV (bismuth-214, uranium series) and 2.62 MeV (thallium-208, thorium series).
2
A clean dolomite reads about 85 API on the gamma ray log, the same as the neighbouring shales. Spectrometry gives potassium 0.3%, thorium 1.5 g/t and uranium 9 g/t. How should we interpret this?
1. A.The tool is faulty
2. B.The radiation is mainly from uranium, so the rock is clean on the uranium-free gamma ray; check the porosity with other methods
3. C.The effect of potassium chloride in the mud
4. D.The dolomite is shaly and should be excluded from the reservoir
Show the answer
Correct answer: B. The radiation is mainly from uranium, so the rock is clean on the uranium-free gamma ray; check the porosity with other methods
The uranium-free gamma ray is $\approx 16\cdot 0.3 + 4\cdot 1.5 \approx 11$ API, while the uranium term is $8\cdot 9 = 72$ API, which is almost all of the radiation. The rock has little potassium and thorium, the elements that are typical of shales. KCl in the mud would show up as a rise in potassium, not in uranium.
3
Why does a less dense rock show a higher gamma ray reading when the content of radioactive elements per unit volume is the same?
Show the answer
The reading is proportional to the source strength divided by the absorption, and the absorption of gamma rays is proportional to density. So the gamma ray log reflects the radioactivity per unit mass. With the same radioactivity per unit volume, a light rock has a higher mass concentration and absorbs less radiation.
4
A well is drilled with a potassium chloride mud. Opposite a sandstone with a washout the gamma ray reading rose sharply. How can you check whether this is shale or an effect of the mud?
Show the answer
Compare it with the caliper log. If the rise in the gamma ray reading matches the washout, the mud is the cause, because a washout puts more radiating fluid next to the tool. Spectrometry will show a rise in potassium only, with no rise in thorium. The SP log will show no signs of shale in the sandstone. Where the hole is in good enough condition, the neutron and density logs will show none either. After corrections for the mud and the hole diameter, the anomaly should disappear.
5
Which ratio from spectrometry points to kaolinitic shales?
1. A.Low Th/K
2. B.Zero thorium content
3. C.High Th/K
4. D.High U/Th
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Correct answer: C. High Th/K
Kaolinite has almost no potassium but holds on to thorium, so its Th/K ratio is high. A low Th/K is typical of illite, micas and especially potassium feldspars.

Updated: 30 September 2026