Correlation of Sonic Travel Time to the Uniaxial Compressive 

Strength of U.S. Coal Measure Rocks 

David C. Oyler, Research Engineer
 

Christopher Mark, Principal Research Engineer
 

Gregory M. Molinda, Lead Research Scientist 

NIOSH-Pittsburgh Research Laboratory 

Pittsburgh, PA
 

ABSTRACT 

Sonic travel time logging of exploration boreholes is routinely 

used in Australia to obtain estimates of coal mine roof rock 

strength. Because sonic velocity logs are relatively inexpensive 

and easy to obtain during exploration, the technique has provided 

Australian underground coal mines with an abundance of strength 

data for use in all aspects of ground control design. However, the 

technique depends upon reliable correlations between the 

unconfined compressive strength (UCS) and the sonic velocity. 

This paper describes research recently conducted by the National 

Institute for Occupational Safety and Health (NIOSH) aimed at 

developing a correlation for use by the U.S. mining industry. At 

three coreholes in Illinois, Pennsylvania, and southern West 

Virginia, sonic velocity logs were compared with point load tests 

for a broad range of coal measure rock types. For the entire data 

set, the relationship between UCS and sonic travel time is 

expressed by the following equation, where UCS is in psi and t is 

the travel time of the P-wave in microsec/ft. 

UCS = 468,000 x e-0.054t (1) 

The r-squared value for this equation is 0.87, indicating that a 

strong correlation between sonic travel time and UCS can be 

achieved with this technique. The paper also addresses the steps 

that are necessary to ensure that high-quality sonic logs are 

obtained for use in estimating UCS. 

ACKNOWLEDGEMENTS 

The authors would like to thank Collin Henke of Patriot Coal, 

Murali Gadde of Peabody Energy, and Brian Schaeffer of 

Foundation Coal for providing drill core for testing and access to 

drill sites. 

INTRODUCTION AND BACKGROUND 

Sonic logging has been routinely used for many years in 

Australia to obtain estimates of coal mine roof rock strength for 

use in roof support design (McNally, 1987 and 1990). The 

estimates are obtained through measurements of the travel time of 

the compressional or P wave, determined by running sonic 

geophysical logs in coreholes, which are then correlated with 

uniaxial compressive strength measurements made on core samples 

from the same holes. In McNally’s classic original study, 

conducted in 1987, sonic velocity logs and drill core were obtained 

from 16 mines throughout the Australian coalfields. The overall 

correlation equation McNally obtained from least-squares 

regression was: 

UCS = 143,000 x e-0.035t (2) 

where UCS is in psi and t is the travel time of the P-wave in 

microsec/ft. Figure 1 shows a typical data set collected by 

McNally, in this case from the German Creek Formation (McNally, 

1987). 

Today, most Australian mines employ mine-specific 

correlations in preference to the generic McNally equation 

(Hatherly, 2002; Larkin, 2000 and Ward and Riley, 2000). These 

correlations allow for continuous mapping of the roof rock UCS in 

each borehole (Gordon, 2000 and Guo et al., 2000). Once an 

acceptable correlation has been developed for a mine or mining 

district, mine planners have easy access to a wealth of rock 

strength data for use in mine design. The sonic velocity data can 

be obtained from logs of either cored holes or rotary drilled holes. 

In actual practice, the amount of coring and core testing are 

probably reduced, but not eliminated, even after acceptable 

correlations are developed. 

For example, at the Crinum Mine in Queensland, a sonic 

velocity-to-UCS correlation was established during initial mine 

exploration by running sonic logs and testing 150 core samples. 

Sonic logs were obtained from all subsequent exploration holes, 

and the correlations were applied to the bolted horizon and 

contoured over the workings. After several panels, it became clear 

that areas of difficult ground corresponded closely with regions of 

low sonic velocity and estimated UCS<1500 psi. Currently, 

boreholes are drilled every 450 ft along each gateroad, and the 

derived UCS values are contoured as part of the hazard plan 

(figure 2). These contour plots are used to select bolting densities 

and the location of secondary support (Payne, 2008). 

Current Australian research (Hatherly and Medhurst, 2000; 

Hatherly, 2002; Medhurst and Hatherly, 2005; Hatherly, et al., 

2007) is focused on employing the full suite of geophysical logs, 

including density, sonic, gamma ray and neutron logs to develop a 
more complete strata characterization. This work has resulted in 

the development of the Geophysical Strata Rating (GSR), which 

has been calibrated by comparison with the CMRR, but is derived 

solely from geophysical log data (Hatherly, 2006). 

 In contrast to the Australian situation, only limited research 

has been conducted in the U.S. in this area (see, for example 

Feddock, et al., 2003). The goal of the NIOSH research reported in 

this paper was to demonstrate that the logging tools and techniques 

available in the US could be used to obtain a McNally-type 

correlation with a coefficient of determination (r2

) of similar 

magnitude to that commonly considered acceptable in Australian 

practice (r2 ≥ 0.7). A secondary objective was to report on the best 

practices for obtaining quality sonic logs for use in estimating UCS. 

25,000
 

20,000 German Creek data 

from McNally
 

UCS = 213,000e-0.038t
 

R2 = 0.87
 

UCS, psi15,000 

10,000 

5,000 

0 

60 70 80 90 100 110 

Travel time, microsec/ft 

120 130 140 

Figure 1. Sonic travel time versus UCS data from the Australian German Creek seam. Data after McNally (1987). 

Roof Section View Boreholes (0 - 40 ft) 

40 

20 

0 

Coal Seam 

Depth, ft 

Figure 2. Contour plot of UCS of the immediate roof above a gateroad at the Crinum mine, Queensland, Australia (Payne, 2008). 

UCS data computed from sonic travel time log data, with black representing the weakest roof and light gray to white the strongest 

roof. Vertical scale 0 to 40 ft. Plot width approximately 8,000 ft (after Payne, 2008). 

SONIC LOGGING TOOLS 

Sonic logging tools contain one or more transmitters which 

generate high frequency (generally 20 to 24 kHz) sound waves, 

which then travel through fluid in the borehole and the formation, 

and are received by two or more detectors (figure 3). The 

difference in arrival times of the sonic wave train received by two 

detectors is then used to determine the sonic velocity. Generally 

sonic data are displayed in travel time per foot, with typical travel 

times for sedimentary rocks ranging from 40 to 140 microsec/ft. 

Sonic travel times for sedimentary rocks are generally bounded by 

the P wave travel times in quartz (sandstone matrix), calcite 

(limestone matrix) and water which are respectively, 55.6, 45.5 and 

190 microsec/ft (Schlumberger, 1991). Travel times for coal and 

shales are not necessarily limited by the quartz and calcite travel 

times (although they may be influenced if they contain these 

minerals), but still generally fall within the 40 to 140 microsec/ft 

travel time range. 
 If the signal from a sonic receiver is graphed versus time, it 

appears as a more-or-less sinusoidal wave. The waveform includes 

both compressional (P) and shear (S) waves, but the velocity 

usually displayed on logs is determined from the first arrival, 

which is the compressional wave, the fastest component of the 

waveform. Sonic logging tools collect a large quantity of data, 

only a small portion of which is actually required to determine the 

P wave velocity. There are two generally accepted ways to display 

the sonic waveform; which is frequently displayed on the logs. 

The most common display technique is described as a variable 

density display, while the other is an actual sonic waveform. 

However, the variable density display is also sometimes described 

as a waveform display. 

 The sonic logging tools currently available fall into two broad 

groupings, larger diameter tools designed for oil and gas logging 

and smaller diameter tools designed for minerals logging. The 

tools used for logging oil and gas wells are generally compensated, 

that is they generally have two transmitters and 4 receivers and the 

data received can be used to correct for tool misalignment in the 

hole. They frequently have a spacing between the receivers of 2 ft, 

which improves their depth of investigation, but reduces their 

vertical resolution. Minerals logging tools frequently have only 

one transmitter and two receivers and are not compensated. The 

receiver spacings available in the U.S. are usually 1 ft, although 

tools with multiple spacings and slightly shorter spacings (20 cm 

or 8 inches) exist and are frequently used in Australia. Although 

data sampling intervals can vary, the sonic data collected for this 

paper were all sampled at 0.1 ft intervals. The large quantities of 

data which must be transmitted uphole by sonic tools probably 

make sampling intervals shorter than 0.1 ft impractical, but not 

impossible, if the need was obvious. On the other, hand more 

frequent sampling does not improve the vertical resolution, which 

is probably a more serious problem in ground control applications. 

 Finally, it is important to note that since the logging tool 

measures the sound wave’s travel time between two receivers, the 

velocity it records is actually the average velocity of all the rock 

layers contained within that 1- or 2-ft interval. UCS test specimens, 

on the other hand, are only several inches long. Figure 3 illustrates 

this averaging of the travel time. The figure shows a single 

transmitter, two-receiver tool positioned with the tool measure 

point centered on the contact between a thick uniform shale and 

sandstone. Each measurement reads the time required for the P 

wave to travel from C to D. If we assume that the travel times in 

the shale and sandstone are, respectively, 100 microsec/ft and 60 

microsec/ft, then, at the position shown, the tool reading would be 

80 microsec/ft. As the tool moves uphole, the reading decreases 

until the lower receiver enters the sandstone, at which point the 

tool reading is 60 microsec/ft. This “averaging” that is inherent in 

the design of the tool has several important implications that are 

discussed below. 

C 

T
 

R 

D 

R 

Figure 3. Single transmitter, two-receiver sonic tool geometry 

showing the path of the sound wave. The difference between 

the travel times from the transmitter (T) to the far and near 

receivers (R) is the travel time. The tool vertical resolution is 

the distance C to D. 

CORRELATING SONIC AND POINT LOAD UCS DATA 

 While simple in concept, successful correlation of sonic 

velocity to UCS measurements requires careful attention to many 

details of the logging process. 

Depth Correlation and Correction 

 Before accurate correlations of sonic and point load derived 

UCS data can be obtained, the depths of the core and sonic logs 

must be in agreement. Typically it can be expected that the 

driller’s and logger’s depths will not necessarily agree without 

adjustment of one set of depths. As long ago as 1987, McNally 

reported on several of the potential sources of error in correlating 

sonic logs to core strength data. McNally identified five possible 

sources of depth errors: 

• Loss of core; 

• Core stumps left in the hole and assigned to a later run; 

• Core swelling (primarily making correction of other error 

sources more difficult); 

• Use of different depth reference points by the driller and 

logger, and; 

• Ordinary errors in measurement and transcription by the 

driller or core logger. 

 When correlating core and log depths, it can be useful to 

begin by placing all of the geophysical logs run on a single depth 

scale. Typically, a density log with natural gamma ray and caliper 

is the standard coal log. The sonic log is usually recorded on a 

separate run with a second natural gamma ray log, and the two 

gamma ray logs are used to correlate the density, gamma ray, and 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

caliper logs to the sonic travel time curve. The geophysical log 

depths usually agree, but there can sometimes be small differences 

of depth between the two logs. Thin limestones, coalbeds and 

clean (low radioactivity) sandstones make good markers for 

matching core and geophysical log depths. Comparison of the 

thickness of the intervals as determined by the density, sonic and 

gamma ray logs to the length of core of a uniform lithology of 

known properties (for instance a limestone of low porosity which 

would be expected to have low radioactivity), can also help in 

making depth corrections. Thin coals are especially helpful in this 

respect. It is usually the case that depth discrepancies between the 

logs and core will be relatively consistent, and will change slowly 

with depth. This is especially likely to be the case if the 

discrepancies are derived from errors in the logger’s measuring 

wheel. Arithmetic errors, transcription errors and loss of core are 

more likely to be caused by the driller and jumps in the depth 

discrepancies can be expected at the depths where the errors took 

place. 

Vertical Resolution Differences Between Log and Test 

Specimens 

McNally also pointed out that since test specimens are 

typically much shorter than sonic log receiver spacings, it is 

possible to exactly correlate the core and log depths and still obtain 

a poor correlation between the rock strength and sonic log travel 

time, due to averaging by the sonic log of rocks of greatly differing 

velocities. In our study the samples tested ranged in length from 

0.05 to 0.2 ft, generally averaging 0.125 ft in length. The receiver 

spacing on the Century 9321 tool that was used to run all three 

sonic logs obtained for this NIOSH study is approximately 1.1 ft. 

To obtain travel times from the 9321 tool comparable to point load 

strengths, sonic data must be collected from zones of uniform 

properties greater than 1.1 ft in length and not closer than 0.5 ft 

from a bed boundary. Rock units containing thin beds of 

alternating properties, such as thin interbedded shales and 

sandstones are likely to show poor agreement between the strength 

of individual samples and the sonic log travel time even when 

those samples have been taken far from the bed boundaries. Where 

possible such zones should be avoided when attempting to 

correlate UCS and travel time data. 

Analysis of the data from all three coreholes suggests three 

alternative techniques for handling the differences in vertical 

resolution between logs and core samples. 

1.	 Select sonic travel readings only from homogeneous zones 

of thickness greater than twice the sonic tool receiver 

spacing and test specimens from as close to the center of 

those sonic readings as possible. 

2.	 Perform multiple point load tests in each suitable rock unit 

meeting condition 1 and determine the average UCS for 

the 1-ft zone centered on the location of the sonic velocity 

measurement. 

3.	 If sufficient point load tests are available, compute a 

moving average UCS of 1-ft intervals of the borehole and 

correlate those to the sonic readings. This technique 

actually best mirrors the sonic travel time log itself, which 

essentially averages the travel times of all the rocks that 

the sonic pulse encounters as it travels from the near 

receiver to the far receiver. 

Techniques 1 and 2 are not mutually exclusive and to some 

extent form a logical progression. Technique 3 requires testing of 

thin beds and near bed boundaries and much more testing; it is 

incompatible with technique 1. Tests run near bed boundaries and 

in thin beds probably will not improve the correlation until 

sufficient tests have been conducted to obtain good moving 

averages; so technique 3 requires a decision about the number of 

tests to run and the resources to be committed to the testing process. 

Technique 3 is much more time consuming, but can provide a very 

detailed picture of rock strength in a zone of particular interest, 

such as the immediate roof of a coal seam. 

In the work conducted for this project, technique 1 was 

originally used on the data from all three coreholes, but the results 

of applying technique 2 to the West Virginia and Pennsylvania 

core data suggest that it can provide more reliable correlations. 

Technique 3 was used on the Illinois core, where only 24 ft of core 

was available. The results obtained from each of the three 

techniques will be described in the “Discussion and Results” 

section. 

Sonic Log Errors 

Another source of error is from errors in the measured sonic 

travel times. Sonic tools are designed to detect the arrival of the 

first signal of the wavetrain, which is roughly a series of sinusoidal 

waves at the tool’s operating frequency. The peaks arrive at 

intervals of approximately 42 microsec. The detectors measure the 

amplitude of the arriving signal and the time of the arrival is 

recorded when a threshold signal amplitude is detected. For tools 

containing two receivers the difference between the arrival times at 

the two receivers, is computed and presented as the travel time. If 

the amplitude of the first arrival is too small to trigger the detector, 

however, it is possible for the detector to trigger on the second, or a 

later arrival. If this happens to only one of the detectors, it can 

cause travel time shifts in 42 microsec steps. This type of error is 

usually referred to as a cycle skip. Typically the far detector is 

affected and the shift is toward longer travel times, but cycle 

skipping by the near receiver (less likely, but still possible) can 

lead to reduced travel times. Cycle skipping can be caused by 

eccentering of the tool (the axis of the tool and hole not being 

parallel), and decentralization of the tool in the hole, both of which 

lead to destructive interference of the sonic signal and reduction of 

the signal amplitude. Other causes of cycle skipping include 

incorrect tool gain settings, gas flowing into the hole (causing both 

attenuation of signal and increased travel times) and attenuation 

across joints or fractures. The presence of joints and fractures can 

sometimes be detected through observation of cycle skipping, 

although the sources of cycle skips are usually not identified. 

Noise from the tool or centralizers scraping on the wall of the hole 

can create high frequency noise which can cause early triggering of 

either detector. Again, this can lead to either increased or 

decreased travel times, depending upon which detector is affected. 

Better centralizers and lower logging speeds can sometimes reduce 

the problem, but errors caused by noise are probably more difficult 

to diagnose than cycle skipping. Noise and attenuation of the 

signal can also cause errors in detection of the first arrival which 

can lead to travel time errors. These can be of lower magnitude 

than errors caused by cycle skipping. Since attenuation is more 

likely to affect the far detector, attenuation errors usually cause 

longer travel times. 

Because cycle skips are so distinctive, they are easier to 

identify than errors due to attenuation or noise. Because the sonic 

tool averages the travel time of an interval of rock equal in length 

to the receiver spacing, most changes in travel time are gradual and 

smooth, even when the tool is traveling through the boundaries of 
 

 

 

 

 

 

 

 

 

 

 

 

formations of drastically different sonic velocities. Cycle skipping 

usually causes distinctive sharp changes in travel time that are of 

greater magnitude and take place more quickly than legitimate 

changes in travel time. Errors caused by attenuation or noise can 

be more difficult to identify on a log, but one good method of 

identifying them, and for checking the tool calibration, is to run the 

log in fluid filled steel casing (when available). A properly 

calibrated sonic log should read 57 microsec/ft in steel casing (of 

any diameter), and the travel time should be constant (except at 

casing joints). 

Because of the analog nature of the sonic wavetrain (even 

though the data are probably transmitted up hole digitally), the data 

may be processed by adjusting the gain factors of one or more 

amplifiers or pre-amplifiers. Proper setting of these gain factors is 

important to obtaining an accurate log. Where the logging 

engineer is not familiar with the proper settings, or where 

conditions are unusual, it may be worthwhile to make logging runs 

(despite additional cost) at several gain settings to determine the 

optimum settings. Generally it is probably easier to determine the 

proper gain settings by examining logs of several gain settings 

side-by-side, so it may make sense to either run the entire log at 

several gain settings or to run short portions of the log at different 

settings, then print the test runs and examine them for the correct 

setting to run the final log. In this project several gain checks were 

made on all three holes, but the best settings in all three cases were 

eventually found to be the logging company’s standard settings. 

Confirmation of this fact was considered to be worth the extra 

logging costs. 

Water Loss from Previously Mined Coalbeds 

A problem not discussed by NcNally is the loss of water in the 

hole due to the effects of subsidence or from mined coalbeds above 

the seam of interest. Water loss does not cause measurement errors, 

but it does prevent the measurement of travel time data in intervals 

above the water level. This is a common problem in southern West 

Virginia and eastern Kentucky, but it can occur in all U.S. coal 

fields. Potential damage to boreholes can also force mining 

companies to run density logs through pipe to avoid the risk of 

losing a gamma ray source in a corehole. Although not the subject 

of this paper, density logs run through drill pipe cannot be 

accurately calibrated. While it does not affect sonic velocity logs, 

the practice of running density logs through pipe would make it 

difficult to use some of the advanced geophysical techniques for 

determining roof rock properties currently being developed in 

Australia (Hatherly et al., 2007). 

There are several possible solutions to the problem of fluid 

loss, depending upon the severity of the loss. If the loss rate is not 

severe and the water level is high enough, it may be acceptable to 

simply log less of the hole. It may also be possible to add fluid 

during the logging operation to maintain an acceptable fluid level. 

If the rate of fluid loss is greater, it may be necessary to use drilling 

mud to reduce the rate to manageable levels. Finally, in extreme 

cases it may be necessary to case off the zones of fluid loss. This 

adds the expense of running additional casing in the hole and may 

also require the use of multiple core rigs and larger bit sizes. In 

some cases, where reducing fluid loss rates may require running 

casing through mineable coal seams, this may not be acceptable. 

In these cases it may be more cost effective to abandon the use of 

sonic data and continue laboratory testing of core samples. 

DISCUSSION AND RESULTS 

NIOSH collected data from three coreholes, one located in 

Fayette County, Illinois, one in Wyoming County, West Virginia 

and the third located in Greene County, Pennsylvania. In all three 

cases the sonic logs core were run by Geological Logging Systems, 

a Division of Marshall Miller & Associates 1

, using a Century 

Geophysical Corp model 9321 sonic tool. The 9321 is an 

uncompensated sonic tool with one transmitter and two receivers, 

and is typical of the sonic tools available for minerals industry use. 

1

Mention of company name or product does not constitute endorsement by 

the National Institute of Occupational Safety and Health. 

Although the UCS data were not restricted to any one source, 

all of the UCS data collected for this paper were obtained from 

cores provided to NIOSH by cooperating mining companies and 

point load tested by NIOSH personnel. The point load data were 

obtained using a point load tester manufactured by GCTS (Tempe, 

AZ). The GCTS tester consists of a hand pump, a hydraulic 

cylinder and two 60° cone shaped platens to break the samples. It 

incorporates a pressure transducer and potentiometric position 

transducer, along with hardware and software to allow recording of 

sample loading and deformation by a laptop computer. Sample 

deformation was measured for all of the samples tested for this 

report and all strength calculations were made using the sample 

heights at the time of failure. 

The testing and calculations followed the procedures outlined 

in the International Society for Rock Mechanics (ISRM) 

recommended method for determination of point load strengths 

(ISRM, 1985). The equation proposed by Rusnak and Mark 

(2000), which was based upon approximately 10,000 PLT and 

UCS tests of coal measure rock, was used to convert point load 

data to UCS, where Is50 is determined from the point load test 

using the standard ISRM procedures. 

UCS = 21 x Is50 (3) 

The GCTS hardware and software were upgraded after the 

Illinois corehole with an increased sensitivity pressure transducer, 

longer stroke position sensor and a higher resolution analog to 

digital data card. The upgrades were primarily needed to allow 

more accurate estimates of the strength of very weak rocks, such as 

those commonly found in the Illinois corehole and to measure the 

dimensions of larger diameter core samples, such as the 3-in 

diameter core from the Illinois corehole. Most of the samples from 

the West Virginia and Pennsylvania coreholes were not as weak as 

those encountered in the Illinois rocks and the cores in both cases 

were nominally 2 inches in diameter. 

Figures 4, 5 and 6 show sonic travel time, in microsec/ft 

graphed versus uniaxial compressive strength, as determined from 

point load data, for the Illinois, West Virginia and Pennsylvania 

coreholes, respectively. In all three cases the graph points 

represent individual point load tests correlated to the closest 

individual sonic travel time measurement. The coefficients of 

determination (r2

) for the Illinois, West Virginia and Pennsylvania 

data were 0.34, 0.63 and 0.77 and the number of samples were 121, 

127 and 139, respectively. The samples from the Pennsylvania 

corehole were divided by rock type into three groups, limestones, 

sandstones and shales and claystones, as shown in figure 6. There 

were few siltstones in the corehole, although there were many 

zones of interbedded thin shales and sandstones. These zones were 
 

 

avoided because of the anticipated difficulty in correlating the UCS 

values of short homogeneous samples with the log responses of a 

foot of heterogeneous rock. 

In the case of the West Virginia and Pennsylvania coreholes 

sufficient core was available to attempt to follow technique 1, 

although in some cases rock from thin zones or samples from near 

bed boundaries were tested. UCS, psi 

40,000 

35,000 

30,000 

25,000 

20,000 

15,000 

10,000 

5,000 

0 

IL corehole data 

UCS = 250,000e-0.052t 

R2 = 0.34 N=121 

40 50 60 70 80 90 100 110 120 130 140 

Travel time, microsec/ft 

Figure 4. Illinois core sonic travel time versus UCS, with best fit relationship. Data points represent individual sample point load tests 

and sonic travel time measurements. 

40,000
 

35,000
 

30,000
 

UCS, psi 25,000 

20,000 

15,000 

10,000 

5,000 

0 

WV corehole data 

UCS = 715,000e-0.061x 

R2 = 0.63 N=127 

40 50 60 70 80 90 100 110 120 130 140 

Travel time, microsec/ft 

Figure 5. West Virginia core sonic travel time versus UCS, with best fit relationship. Data points represent individual sample point 

load tests and sonic travel time measurements. 

In the Illinois case, only 24 ft of core were available for 

testing and the available range of rock strengths and sonic 

velocities was limited (the travel times ranged from 76 to 129 

microsec/ft and the UCS values from 80 to 9,800 psi). The limited 

amount of available core from this site did, however, allow for 

more complete testing of the core. Ultimately 122 tests were 

conducted in the 24 ft; roughly one test per 2.5 in. Since much of 

the rock tested was thinly bedded, and since each sonic travel time 

measurement essentially averages the strength of a 1- ft-long 

interval of the rock in the hole, it was anticipated that a point-by-
 

 

point comparison of the UCS to the sonic travel time would result 

in a poor correlation. 

The Illinois data were also graphed using a 5 point moving 

average (technique 3). Instead of a single point load reading 

representing an average interval of 2.5 in and the sonic log 

averaging the travel time of a roughly 13 in interval, the averaged 

point load readings approximate the average response of 9.3 in of 

rock. However, the actual intervals between tests varied 

considerably, with a standard deviation of 4.3 in. The use of the 

moving average increased the coefficient of determination (r2

) for 

the Illinois data from 0.34 to 0.54. This improvement was 

primarily due to the averaging of UCS sample properties across 

bed boundaries by the use of the moving average, which produces 

in the UCS data the same effect the 1-ft vertical resolution of the 

sonic tool has on the travel time measurements. Due to the 

averaging the number of samples in the regression was reduced 

from 121 to 117. 

The West Virginia and Pennsylvania data were averaged 

using technique 2. Where multiple point load tests had been 

performed within a single rock unit, the UCS estimates were 

averaged and new regressions computed using the averaged UCS 

estimates. The original testing procedure was not specifically 

designed with technique 2 in mind and although the results showed 

some improvement in the correlations, the results were probably 

not optimized. The improvement in the r2

 value in the West 

Virginia case was from 0.63 to 0.71, while the Pennsylvania r2 

value changed minimally from 0.77 to 0.78. The number of 

samples in the regressions was reduced, as a result of the averaging, 

to 106 and 93 for the West Virginia and Pennsylvania regressions, 

respectively. 

The large difference between the improvement in the West 

Virginia and Pennsylvania data (less than 0.01 versus 0.08), most 

likely indicates the range of improvement to be expected from 

using technique 2, but other factors might have been influential. 

The most likely factor was the initial range of the data, which was 

much wider for the Pennsylvania data (the travel times ranged from 

46 to 118 microsec/ft for the Pennsylvania data, but only from 49 

to 90 microsec/ft for the West Virginia data). In general a wider 

range of travel times will improve the r2

. It is likely the 

Pennsylvania case was already closer to the optimum correlation 

prior to averaging, and the West Virginia core had more room for 

improvement. The selection of tests averaged might also have had 

an effect, but this seems less likely, since more tests were averaged 

from the Pennsylvania cores and no particular effort was made in 

either case to optimize the selection of test zones for improving the 

correlation. The decision to average the data was not made in 

either case until after all of the testing was completed. The low 

coefficient of determination (r2

) for the Illinois data also appears to 

be partly due to the narrow range of the data, between 76 and 130 

microsec/ft. Had a wider range of rock strengths been present, 

particularly including higher strength (low travel time) rocks, the 

initial r2

 probably would have been larger. 

UCS, psi

40,000
 

35,000
 

30,000
 

25,000
 

20,000
 

15,000
 

10,000
 

5,000 

0 

40 50 60 70 80 90 100 110 120 130 140 

Travel time, microsec/ft 

PA corehole data 

UCS = 212,000e-0.043t 

R2 = 0.77 N=139 

Limestone 

Shale or Claystone 

Sandstone 

Least squares fit 

Figure 6. Pennsylvania core sonic travel time versus UCS, with best fit relationship. Data points represent individual sample point 

load tests and sonic travel time measurements. Lithology indicated for each sample. 

The large number of tests of the Illinois core allowed the sonic 

log and UCS data to be plotted versus depth and compared as 

shown in Figure 7. The sonic log has been inverted in Figure 7 and 

presented as a velocity curve in ft/sec, and the UCS data have been 

graphed using data averaged using a 5-point moving average. The 

UCS scale has also been adjusted to overlay the two curves in the 

weak shale intervals. A thin limestone, centered at 599 ft, was 

used to correlate the two curves. The curves agree fairly well 

except between 588.5 to 592.5 ft where the UCS data suggest a 

weaker rock than does the sonic velocity curve. 

Figure 8 summarizes all of the test data collected in a single 

graph using the 5 point moving average data from the Illinois 

corehole and including the averaged data points for the West 

Virginia and Pennsylvania coreholes. The general Australian 

McNally equation (McNally, 1987), converted from MPa to psi, 

has been added for comparison. The averaged data from all three 

coreholes have also been combined and a regression equation for 

the combined data included on the graph. Although the individual 

r

2

 values for the Illinois, West Virginia and Pennsylvania coreholes 
are 0.54, 0.71 and 0.78, respectively, the r2

 for the combined data 

set is 0.87. The equation for the combined data set: 

UCS = 468,000e-0.054t (4)

is similar in shape and range to the Australian equations, which 

further supports its validity. It appears that both the geological 

conditions and the available geophysical logging technology in the 

U.S. are suitable for developing and using the sonic travel time 

versus unconfined compressive strength correlations, much as the 

Australian mining industry has already done. 

14,000 

9,000 

Velocity Log (Inverted sonic log) 

UCS (5 PT Avg) 

578 580 582 584 586 588 590 592 594 596 598 600 

Depth, ft 

13,000 

12,000 

11,000 

UCS, psi ( 5 PT moving average) 

7,000 

5,000 

Velocity, ft/sec 10,000 

3,000 

9,000 

1,000 

8,000
 

7,000
 -1,000 

Figure 7. Sonic log of the Illinois core interval with the travel time log inverted and plotted as a velocity curve (ft/sec). The 5 point 

moving average UCS data (from point load tests) have been plotted with the scales chosen to overlay the curves in shale and give the 

curves similar sensitivities. 

UCS = 143,000e-0.035t

40,000 

IL, WV & PA data 

UCS = 468,000e-0.054t 

R2 = 0.87 N=316 

IL corehole data 

WV corehole data 

PA corehole data 

Combined IL, WV & PA data 

McNally Equation 

40 50 60 70 80 90 100 110 120 130 140 

Travel time, microsec/ft 

250 

200 

35,000 

30,000 

25,000 

20,000 

15,000 

UCS, psi 

UCS, MPa

150 

100 

10,000 

50 

5,000 

0 0 

Figure 8. Best fit relationship for the entire data set of the Illinois, West Virginia and Pennsylvania core data. The original 

Australian McNally equation (in psi units) is shown for comparison.
 

CONCLUSIONS 

The study demonstrated that sonic travel time logs can be 

used to estimate the UCS of U.S. coal measure rocks. The results 

were consistent across three distinct data sets, representing three 
 

 

 

 

 

 

separate coal provinces and representing the broad range of rock 

encountered in the eastern and midwestern coal fields. 

The ability to use sonic logs to estimate rock strength provides 

the U.S. coal industry with a powerful new tool for improving 

ground control design. The UCS is essential to provide effective 

roof support selection, gate entry design, and many other aspects of 

ground control. Widespread use of sonic logs during the 

exploration phase could vastly increase the quantity of 

geotechnical data that is available for mine design. 

The study also suggests that high-quality sonic logs are 

essential if the technique is to be successful. Careful attention to 

the details of the logging process, including use of appropriate 

logging tools, making accurate depth correlations and eliminating 

logging errors, such as “cycle skips”, can all help to improve the 

correlations. 

Disclaimer 

The findings and conclusions in this paper have not been 

formally disseminated by the National Institute for Occupational 

Safety and Health and should not be construed to represent any 

agency determination or policy. 

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