Evaluation of Potash Grade with Gamma-ray Logs 

By Philip H. Nelson1

1

Denver, Colorado 

Open-File Report 2007–1292 

U.S. Department of the Interior 

U.S. Geological Survey
U.S. Department of the Interior 

DIRK KEMPTHORNE, Secretary 

U.S. Geological Survey 

Mark D. Myers, Director 

U.S. Geological Survey, Reston, Virginia 2007 

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Suggested citation: 

Nelson, Philip H., 2007, Evaluation of potash grade with gamma-ray logs: U.S. 

Geological Survey Open-File Report 2007-1292, 14 p. 

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Abstract 

Potassium is an emitter of gamma-ray radiation, consequently deposits of potash 

can be detected and evaluated using gamma-ray logs. A method originally designed to 

evaluate uranium deposits in boreholes can also be applied to potash deposits. The 

method equates the depth-integral of a gamma-ray log to the grade-thickness product of a 

potash-bearing bed or series of beds. The average grade of a bed is then determined by 

dividing by the overall bed thickness, which can also be obtained from the gamma-ray 

log. The method was tested using gamma-ray logs and potash assays from boreholes 

near Carlsbad, New Mexico. 

Introduction 

The radioactive isotope K-40 forms 0.01% by weight of natural potassium and 

emits a sufficient level of gamma rays to be detectable in the subsurface. Because 

potassium is one of only three geologically common elements that emit gamma rays, the 

best approach to the estimation of potash grade in boreholes is through the use of the 

gamma-ray log. The gamma-ray response to a “formation” comprised of pure potassiumbearing minerals was computed by Edmundson and Raymer (1979) and included in a 

tabulation by Hearst and others (2000), as shown in table 1: 

Table 1. Gamma-ray responses to potassium-bearing minerals. From 

Edmundson and Raymer (1979). 

Mineral Chemical composition K (wt percent) API units 

Sylvite KCl 52.4 747 

Carnallite KMgCl3●6H2O 14.1 200 

Langbeinite K2SO4Mg2(SO4)2 18.8 268 

Polyhalite K2SO4Mg(SO4)(Ca(SO4))2●2H2O 13.0 185 

The measured gamma-ray flux in a potash zone varies with mineral concentration. 

Peak gamma-ray values in 16 potash zones in wells drilled in southeastern New Mexico 

range from 120 to 270 API units (Lewis, 2006). 

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The estimation of radioactive concentration from gamma-ray logs was of great 

interest in the assessment of uranium reserves and a technical procedure for doing so was 

developed in the late 1950s in work sponsored by the Atomic Energy Commission. 

Borehole calibration facilities containing known concentrations of potassium, uranium, 

and thorium were established at various sites in the western United States (Steele and 

George, 1986). The procedure for estimating the grade of radioactive material is directly 

applicable to potash, as described below. 

Method of Obtaining the Grade-Thickness Product from Gamma-Ray Logs 

Gamma-rays emitted by a thin bed of radioactive material penetrate adjacent beds 

as well as the radioactive bed itself. Consequently, a logging tool measuring gamma-ray 

activity in a borehole penetrating a sequence of thin radioactive beds will measure not 

only the radiation of the nearest bed but also that of adjacent beds. These “tails” of 

radiation pose a problem in estimating the amount of radioactive material in a bed, 

because radiation encountered in a borehole will be the sum of radiation emitted by the 

radioactive material at that depth plus the sum of the “tails” from all adjacent beds. As a 

consequence, a plot of gamma-ray activity γ (measured in a borehole) versus the 

concentration of in situ radioactivity (measured as grade G from core material) can 

exhibit considerable scatter, reducing the utility of the form G = mγ + b, where m and b

are empirical constants. (The determination of true grade from a simple linear relation is 

valid only if the gamma-ray detector is positioned in the center of a thick bed with 

uniform radioactivity, where “thick” means greater than 3 ft (Scott, 1963).) 

Scott and others (1961) showed experimentally and theoretically that the gradethickness product of a radioactive bed is proportional to the area under the gamma-ray 

curve, 

 GT = KA (1) 

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where: 

G is the grade or average concentration of a radioactive element by weight in a bed 

(weight percent U3O8 in the original experimental work), 

T is the thickness (feet) of the bed, 

K is the proportionality factor (weight percent U3O8 / γ-ray response unit), and 

A is the integral of the γ-ray response with respect to depth (the area under the γ-ray 

curve) and is referred to here as the “gamma-ray-thickness”. 

In practice, A is evaluated by summing the γ-ray response with respect to depth 

(Fink, 1978), 

 A = Σ wi γi for i = 1,...N (2) 

where wi is the thickness of the ith interval and γi is its gamma-ray response. The sum 

extends over an interval sufficient to capture the response of the logging tool to the bed 

(or the sum can be truncated near the bed boundaries and a “tail factor” can be applied 

(Scott and others, 1961)). If the γ-ray response is digitized at regular intervals w, then 

 A = w Σ γi for i = 1,...N (3) 

A common value for w is 0.5 ft. In oil and gas well logging, γ-ray response is measured 

in “API units”, a unit established in a calibration facility in Houston, Texas, in which case 

the units of A are API-feet. If a logging tool is not calibrated in API units, the response is 

generally in counts per second (cps), and the units of A are cps-feet. 

Scott and others (1961) noted that “although the method has been applied 

specifically to uranium deposits, the principles upon which it is based are generally 

applicable to deposits of other elements which either emit gamma rays or are 

quantitatively related to gamma-ray emitters.” There is a caveat to this statement, 

however. Uranium-rich beds produce high count rates, so the background count rate is 

negligible. In potash-rich beds, count rates are lower and the background may not be 

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negligible. To remove background, the value of γi in equations 2 and 3 should be 

determined after subtracting out the gamma-ray baseline, which typically ranges from 10 

to 20 API units. 

A Test of the Grade-Thickness Method for Potash 

To test the grade-thickness approach, I used two data sets from the Carlsbad, New 

Mexico area supplied by Jim Lewis, Chief Geologist of Intrepid Mining, LLC. The first 

data set includes a total of 72 depth intervals in 7 wells, within which there were 16 

potash zones with K2O analyses and accompanying gamma-ray values. Data from six 

contiguous depth intervals in one zone from well AEC-008 are given in Table 2 to 

illustrate the nature of the data set. 

Table 2. K2O analyses and gamma-ray values in potash zone 10C in well AEC008. 

Top 

(depth 

in feet) 

Base 

(depth 

in feet) 

Thickness 

(feet) 

K2O 

Grade 

(wt %) 

Gradethickness 

(wt %-ft) 

Gammaray (API) Gammaraythickness 

(API-ft) 

Correction 

factor 

Corrected 

Gamma-ray 

(API) 

Corrected 

Gammaraythickness 

(API-ft) 

1,589.1 1,589.7 0.6 4.26 2.56 119 71.4 1.12 133 80.0 

1,589.7 1,591.7 2.0 17.68 35.36 151 302.0 1.12 169 338.2 

1,591.7 1,592.2 0.5 16.18 8.09 183 91.5 1.12 205 102.5 

1,592.2 1,594.5 2.3 21.23 48.83 196 450.8 1.12 220 504.9 

1,594.5 1,594.7 0.2 12.87 2.57 94 18.8 1.12 105 21.1 

1,594.7 1,595.5 0.8 4.59 3.67 57 45.6 1.12 64 51.1 

Sum 101.08 980.1 1097.7 

Figure 1 shows the gamma-ray response plotted against K2O grade; the plot 

contains 72 points from the first data set, including the six points from well AEC-008 

listed in table 2. The plot (fig. 1) shows a general increase in gamma-ray responses as 

K2O grade increases, although as the K2O grade decreases to zero, the gamma-ray 

response does not drop to zero, but instead ranges from 20 to around 100. This plot (fig. 

1) indicates that an attempt to estimate grade in thin intervals from a simple relation G = 

kγ will result in overestimates of grade at low count rates. 

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Figure 1. Plot of gamma-ray responses versus K2O grade in potash zones in 7 wells near 

Carlsbad, New Mexico (data set 1). 

Potash analyses were done over varying thickness intervals, so to determine the 

gamma-ray-thickness sum A, equation 2 was applied to these data instead of equation 3. 

For zone 10C in the AEC-008 well, the K2O grade-thickness, obtained by summing the 

product of the thickness and K2O grade in table 2, is 101.1 weight percent-ft, and the 

value of A for the uncorrected gamma-ray log is 980.1 API-ft. This value of A and the 

values of A for 15 other potash zones are plotted against the K2O grade-thickness in 

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figure 2. The gamma-ray thickness product A increases as the K2O grade-thickness 

increases, although with some scatter along the trend. The gamma-ray-thickness 

response appears to approach zero as the K2O grade-thickness approaches zero. 

Figure 2. Plot of gamma-ray-thickness versus K2O grade-thickness in potash zones in 7 

wells near Carlsbad, New Mexico (data set 1). 

The second data set used in this study incorporates gamma-ray logs and K2O 

analyses from the P-series of wells, in which the gamma-ray log was recorded in cps 

rather than API units. This data set includes 100 depth intervals in 29 potash zones in 11 

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wells. A plot of all 100 pairs of gamma-ray values and K2O analyses (fig. 3) shows a 

general increase of gamma-ray response as K2O grade increases, with more scatter than 

exhibited in figure 1. When the grade-thickness computation is done, the scatter is 

greatly reduced and the resulting data points from the 29 zones show better correlation 

between gamma-ray-thickness and K2O grade-thickness (fig. 4). 

Figure 3. Plot of gamma-ray responses versus K2O grade in potash zones in 11 wells 

near Carlsbad, New Mexico (data set 2). 

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Figure 4. Plot of gamma-ray-thickness versus K2O grade-thickness in potash zones in 11 

wells near Carlsbad, New Mexico (data set 2). 

One might wonder why the slopes differ between figures 1 and 2, inasmuch as the 

data in figure 2, displaying the grade-thickness and gamma-ray-thickness averages, are 

closely related to the data of figure 1, displaying the individual measurements. (Note that 

both figs. 1 and 2 have ratios of 10:1 for the y-axis:x-axis.) The same question applies to 

figures 3 and 4. Inspection of table 2 supplies an explanation for this dilemma. At the 

upper edge of zone 10C, K2O is 4.26%, a factor of 4 less than the 17.68% value of the 

underlying layer, yet the gamma-ray value only dropped from 151 to 119 API units, 

because gamma-rays have propagated upwards as well as laterally and because gamma10
ray detectors have a finite length. As a result, unexpectedly high gamma-ray values are 

recorded within layers having low values of K2O. This effect accounts for the high 

gamma-ray values at low K2O values in figures 1 and 3. The opposite effect occurs at 

high values of K2O, where the contribution of adjacent layers with lesser potash content 

can produce lower gamma-ray response. By taking the effect of adjacent layers into 

account, the grade-thickness computation provides a more robust estimate of K2O content 

than do estimates on a foot-by-foot basis. 

These two examples illustrated in figs. 1-2 and 3-4 represent a preliminary 

demonstration of the grade-thickness calculation for potash rather than a complete one, 

because the tails of the gamma-ray log above and below the ore zones were ignored and 

because the gamma-ray baseline value should be removed before computing the sum. 

The calculations should be repeated with digitization of the gamma-ray log on equal 

(half-foot) increments, with inclusion of the tails, and with removal of the gamma-ray 

baseline. With these steps, the scatter in figures 2 and 4 should be further reduced and 

the K-factor can be determined. 

Determination of Average Grade 

Once the grade-thickness is determined for a single potash zone, the average 

grade for that zone is determined simply by dividing by the zone thickness. The 

thickness is the distance between the elevations at which the gamma-ray response 

declines to one-half its maximum value. 

Sources of Error in Using the Grade-Thickness Computation 

Errors in using the grade-thickness computational method, such as those listed 

below, deserve consideration. However, the method does eliminate some sources of error 

that would be encountered in using a method based upon least-squares analysis. 

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1. Depth misalignment. Logging depths differ from driller’s depths, so the depth 

mismatch must be resolved when comparing chemical analysis to well log data. 

Consideration of the chemical data for an entire bed along with the total gamma-ray 

anomaly, as is done with the grade-thickness method, reduces the error in depth 

matching. 

2. Excessive logging speed. Too fast a logging speed reduces the count rate and thereby 

reduces the grade-thickness estimate. 

3. Gamma-ray attenuation caused by cement, casing, mud weight. The correction factors 

for the gamma-ray logs (1.12, table 2) were obtained in a manner described by Lewis 

(2006). The value of A for the corrected gamma-ray log is 980.1*1.12 = 1097.7 API-ft 

for well AEC-008. When the values of A for all wells were plotted in a manner identical 

to that of figure 1, the scatter worsened (not shown), indicating that correcting the data 

for borehole conditions can create more problems than it solves. 

4. Washouts. Extreme washouts of potash zones are expected to reduce the gamma-ray 

count, and therefore reduce the grade-thickness estimate. This problem is alleviated by 

use of the grade-thickness method if only a portion of the potash zone is washed out. 

5. Thin beds. Beds having less than a minimum thickness will produce a gamma-ray 

signature that is determined by the detector size and logging speed, although the gammaray-thickness A of the gamma-ray response is not altered (Woodhouse, 1994). Because 

only the maximum thickness, Tmax, can be determined for a thin bed, the estimate of 

average grade, Gest = (GT)/Tmax, will therefore be a minimum estimate. 

6. Use of drilling muds containing potassium. Potassium-based muds will raise the 

overall count rate and increase the gamma-ray baseline level. Accounting for the 

baseline in the grade-thickness method removes this source of error. 

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7. Errors in calibration of gamma-ray logs If an offset has been introduced, then the 

grade-thickness method will not be affected. However, if the API value is off by a 

constant multiplicative factor, then the grade-thickness evaluation will be proportionately 

in error. 

8. Presence of uranium and thorium. Both uranium and thorium emit gamma-rays and if 

present would raise the count rate of a total-count gamma-ray tool. The levels of uranium 

and thorium in potash zones can be established from core or by logging some test wells 

with spectral gamma-ray logging tools. 

Summary 

The grade-thickness method is recommended as the best procedure for calculating 

potash grade from well logs. Overall accuracy cannot be assessed until calculations more 

thorough than used in this review are carried out. 

References Cited 

Edmundson, H. and Raymer, L.L., 1979, Radioactive logging parameters for common 

minerals, The Log Analyst, v. 20, no. 5, p. 38-47. 

Fink, J.B., 1978, On K-factors and gamma log calculations: Geophysics, v. 43, no. 7, p. 

1546-1550. 

Hearst, J. R, Nelson, P.H., and Paillet, F.L., 2000, Well logging for physical properties: 

John Wiley and Sons, London, 483 p. 

Lewis, J.P., 2006, Evaluation of potash content in the Conoco Phillips Peakview II well, 

Eddy County, New Mexico: Intrepid Mining LLC, Denver, Colorado, 10 p. 

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Scott, J.H., Dodd, P.H., Droullard, R.F., and Mudra, P.J., 1961, Quantitative 

interpretation of gamma-ray logs: Geophysics, v. 26, no. 2, pp. 182-191. 

Scott, J.H., 1963, Computer analysis of gamma-ray logs: Geophysics, v. 28, no. 3, p. 

457-465. 

Steele, W.D. and D.C. George, 1986, Field calibration facilities for environmental 

measurement of radium, thorium, and potassium: Report GJ/TMC-01, UC-70A, 

Bendix Field Engineering Corporation, Grand Junction, Colorado, 73 p. 

Woodhouse, R., 1994, The quality of the gamma ray log thin-bed response: The Log 

Analyst, v. 35, no. 5, p. 26-27.