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Three-dimensional time-lapse velocity tomography

of an underground longwall panel

Kray Luxbachera , Erik Westmana, Mario a Karfakis

a

Department of Mining & Minerals Engineering, Virginia Tech., Blacksburg, VA 24061-0239, USA 

Peter Swansonb,

b

Spokane Research Laboratory, National Institute for Occupational Safety and Health, Spokane, WA 99207, USA 

Abstract

Three-dimensional velocity tomograms were generated to image the stress redistribution around an underground coal longwall panel

to produce a better understanding of the mechanisms that lead to ground failure, especially rockbursts. Mining-induced microseismic

events provided passive sources for the three-dimensional velocity tomography. Surface-mounted geophones monitored microseismic

activity for 18 days. Eighteen tomograms were generated and high-velocity regions correlated with high abutment stresses predicted by

numerical modeling. Additionally, the high-velocity regions were observed to redistribute as the longwall face retreated, indicating that

velocity tomography may be an appropriate technology for monitoring stress redistribution in underground mines.

Keywords: Rockbursts; Longwall; Coal; Tomography; Velocity; Stress

1. Introduction

Roof characterization and control pose significant

challenges to the underground mining industry. Approximately one-third of fatalities reported in underground

mines in the United States between 2001 and 2005 were the

result of fall of roof, rib, or face [1]. In addition to

accounting for a significant portion of fatal accidents, these

incidents also result in a considerable portion of lost time

injuries, translating into substantial losses in production.

Some of the most unpredictable and violent types of roof

failure are rockbursts, often referred to in coal mines as

bumps or bounces. Rockbursts are sudden and violent

failures of overstressed rock that can cause expulsion of

material and airblasts. Rockbursts not only pose a danger

to miners due to flying material, but they can cause

ventilation changes, and may also propagate dust and gas

into the air, creating a potentially explosive environment

[2]. Rockbursts and bumps generally occur in mines that

have at least 300 m (about 1000 ft) of cover and are either

overlain or underlain by a massive and competent geologic

formation [2,3].

Velocity tomography is a technology that can be used to

ascertain the relative state of stress and the redistribution

of stress in a rock mass. Velocity tomography relies on the

transmission of seismic waves, specifically p-waves,

through a rock mass. The velocity of the wave is

determined, and the mass is divided into voxels, or cubes,

with a velocity calculated for each cube. The sharpness of

the image is dependent on the size of the voxel. The voxel

size must be optimized to insure that all voxels are

traversed by a sufficient number of rays.

Velocity tomography is useful for inferring stress

redistribution. During the pre-failure regime, the p-wave

velocity usually increases linearly with stress at lower stress

levels, and then plateaus at higher stress levels. This

increase of p-wave velocity with stress is attributed to the

closure of cracks and pore space [4–8]. With increasing

levels of structural damage, the p-wave velocity can drop to

values less than observed in the initial state.

In order to implement velocity tomography, a source

must be selected for the seismic waves. Sources may be

active or passive. Active sources, such as hammer strikes,
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blasts, or cutting equipment are advantageous because they

allow for consistent and predictable seismic raypath

distribution. However, active sources are not always

feasible for relatively long time-lapse studies, since they

usually require the presence of a person to initiate the

source and record the time and location. Passive sources

allow for remote, continuous monitoring of a rock mass.

However, they are also associated with a unique set of

challenges, including accurate source location and inadequate or irregular raypath density. Mining-induced microseismic events are well suited for utilization as passive

sources in velocity tomography. The events are usually

located in areas of active mining that are the target areas

for velocity tomography. Microseismic events in active

mining areas are frequent enough to allow for adequate

raypath density. Numerous studies have shown that

analyses of microseismic activity provides insight into

ground failure processes [9–11]. Microseismic sources allow

for noninvasive, remote time-lapse monitoring over a

period of days, weeks, or even months.

The site chosen for this study was an underground

longwall coal mine. A retreating longwall panel was

monitored for 18 days. The site has considerable microseismic activity, making it ideal for passive source velocity

tomography.

2. Tomography

Tomography has become an essential diagnostic tool in

the medical industry; a CAT-scan, computer-assisted

tomography, is one example [12]. Tomography also has

many geotechnical applications including study of faults

and ore body delineation [13,14]. Tomography has been

applied as a tool for imaging stress in laboratory rock

specimens [15–17] and in underground mines with moderate success.

Stress distribution in numerous underground structures

has been imaged, including pillars, tunnels, and longwall

panels. Pillars have been studied extensively due to their

relatively small scale and predictable stress concentrations.

Friedel et al. conducted active source imaging of the

footprint left by two coal pillars on the mine floor,

determining that velocity increased as the face approached

the pillar and that velocity decreases around the pillar edge

corresponded with failure due to spalling [18]. Active

source imaging has been implemented for pillar tomography at Homestake Mine [19], and at Edgar Experimental

Mine [20]. Watanabe and Sassa also used active sources to

image both a pillar and a triangular area between two drifts

[21], while Manthei used active source geometry to image

pillars in a potash mine [22].

Tunnels have also been studied extensively to determine

stress redistribution around openings. Many of these

studies have been conducted at the Underground Research

Laboratory (URL) in Canada; passive source [23,24] and

active source studies [17] of tunnels at the URL can be

found in the literature.

Tunnel and pillar studies are relatively simple since the

small-scale geometry allows for optimum source and

receiver placement. Larger scale studies are more difficult

to design, but have been conducted successfully. Ko ̈rmendi

et al. used in-seam receivers with active source geometry

for a longwall panel in an underground coal mine, and

found that high-velocity areas advanced with the face and

were typical of stress redistribution encountered on a

longwall [25]. Active source tomograms have been compared to ‘‘simulated passive source’’ tomograms [26].

Active sources have been used in metal mines, and highvelocity areas were imaged ahead of working faces [24,27].

A longwall shearer provided an active source to produce

tomograms of a longwall panel showing high-stress areas

from mid-face towards the tailgate [28]. No long-term timelapse studies utilizing passive sources are found in the

literature.

Velocity tomography relies on a simple relationship, that

the velocity along a seismic ray is the raypath distance

divided by the time to travel between the source and

receiver. From this relationship, it is understood that the

time is the integral of the inverse velocity, 1/v, or slowness,

p, from the source to the receiver as shown in Eq. (1) [29]:

 d 

v 1⁄4 ! vt 1⁄4 d, (1) t 

 Z Z R 1 R 

t 1⁄4 dl 1⁄4 p dl, (2)

S v S 

 X

M 

ti 1⁄4 pjdij ði 1⁄4 1; ... ; NÞ, (3)

j1⁄41

where v is the velocity (m/s), d is the distance (m), t is the

travel time (s), p is the slowness (s/m), N is the total number

of rays, and M is the number of voxels [1].

The microseismic event location and subsequent raypath

are calculated using an initial velocity model to represent

the rock mass. The velocity model is developed from

measured data and allows for calculation of the distance

and travel time along the raypath. However, the velocity,

distance, and time in an individual voxel or grid cell are not

known. Although the distance in each grid cell can be

readily solved, the time and velocity are still unknown.

Arranging the time, distance, and slowness for each voxel

into matrices, the velocity can be determined through

inverse theory as shown in Eq. (4) [29]:

T DP P D-1 1⁄4 ! 1⁄4 T, (4)

where T is the travel time per ray matrix (1 x N), ti is the

travel time of the ith ray, D is the distance per ray per voxel

matrix (N x M), dij is the distance of the ith ray in the jth

voxel, P is the slowness per grid cell matrix (1 x M), and pj 

is the slowness of the jth voxel.

Usually, the inverse problem is either underdetermined

(more voxels than rays), or overdetermined (more rays

than voxels) [22,30,31]. The most effective way to solve this

problem is by an iterative process.
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3. Case study

3.1. Site characteristics 

Data for this study were collected between July 7, 1997

and August 8, 1997, at an underground coal mine in the

western United States. The mine employs longwall mining,

and has produced an average of 7.5 million tons per year

between 1995 and 2004 [32]. The coal seam ranges in

thickness from 2.6 to 3.0 m (8.5–9.8 ft) with a depth of

approximately 350 m (1150 ft). The mine operates longwall

panels that are approximately 5490 m (17,980 ft) long and

250 m (815 ft) wide. Over the course of the study, the face

advanced 431 m (1415 ft), averaging about 24 m (79 ft) per

day. Sixteen geophones were assembled on the surface to

monitor and locate microseismic events. Fig. 1 displays a

plan view of the geophone locations over the portion of the

longwall panel of interest. The geophones provide adequate spatial coverage of the entire area of study.

Fig. 1. Plan view of the area under study. The gray area indicates total

area mined over 18 days of study.

3.2. Inversion parameters 

The data were analyzed using GeoTOM, a commercial

program that generates tomograms through the simultaneous iterative reconstructive technique (SIRT) [33]. SIRT

is an appropriate algorithm because the solution tends to

both converge and diverge slowly, so that the solution is

relatively stable [33,34]. A voxel size of 15 m per side

(approximately 50 ft per side) was input into the program.

This voxel size was determined to be sufficiently small to

ascertain the general stress trend, but sufficiently large that

artifacts would not disrupt interpretation of the tomogram.

Ideal voxel size has an edge length equal to the typical

wavelength of the rays [21], and at the smallest half of the

typical wavelength [18]. The average p-wave velocity for

this data set is 3600 m/s (12,000 ft/s) with a typical

frequency content of 30 Hz, indicating a wavelength of

120 m and, therefore, ideal voxel size of 120 m. This voxel

size would not adequately delineate expected velocity

features. Many of the 15 m voxels are traversed by over

1000 rays, so they are well constrained. However, by

decreasing the voxel size there is a risk of creating artifacts

in the model. Artifacts are broadly defined as an error in

the reconstructed image due to an inaccuracy of measurement [35] or velocity anomalies that have been displaced

relative to their proper locations [36]. In this case, artifacts

are velocity anomalies that do not represent a physical state

or structure in the model, and they may occur in areas of

the model where ray coverage is poor. The inversion

algorithm assigns these abnormally high or low velocities

as it attempts to fit the model to the data. In order to

decrease the voxel size without creating artifacts, velocities

for voxels that were not traversed by any rays were

removed from the results. The remaining data were input

into a three-dimensional modeling program, and the

missing values were assigned based on the nearest voxels,

using an inverse distance algorithm. Straight raypaths for

day 18 of the study are displayed in Fig. 2.

Fig. 2. Straight raypaths for day 18 of the study. The side view (top)

shows the area of interest outlined in gray, with the geophones located on

the surface in gray and the location of the coal seam plotted in dark gray.

The plan view (bottom) shows the area of interest outlined in gray, with

the geophone locations in gray.

Additional input parameters, including an initial velocity

model, anisotropy, smoothing, and the number of curved

and straight ray iterations to be performed, were required.

An initial velocity model is a three-dimensional model of
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the p-wave velocity of the rock mass based on geophysical

data that has been previously collected. SIRT is an iterative

technique; the algorithm must have an initial velocity value

to perturb the first iteration. The initial velocity model

allows the inversion to be calculated more efficiently and

accurately. The initial velocity model was provided with

the raw data from National Institute for Occupational

Safety and Health (NIOSH), and a one-dimensional

interpretation of the model is displayed in Fig. 3.

 

 

 

 

 

 

Fig. 3. Initial velocity model. The coal seam is displayed in black at

approximately 1700 m. The model is layered normal to the given

anisotropy vector.

Anisotropy refers to the variation of a characteristic of a

material with the direction of measurement [37]. In this

situation, anisotropy refers to the variation in p-wave

velocity as measured parallel or perpendicular to the

bedding layers. Both the direction and magnitude of the

anisotropy were inputted. The anisotropy vector is taken to

be normal to the dipping layers of the initial velocity model

and is [-0.068, 0.057, 0.996], as provided by NIOSH. The

anisotropy magnitude refers to the ratio of the velocity

measured orthogonally to the anisotropy vector to the

velocity that has been measured parallel to the anisotropy

vector. The magnitude of anisotropy was determined

experimentally by inverting the data with anisotropy

magnitudes varying from 0.8 to 1.2, with the goal of

minimizing the travel time residuals resulting from the

inversion. An anisotropy magnitude of 1.1 minimized the

residuals, indicating that this value improves the model so

that it better fits the data. This value indicates that the

velocity along the seismic ray is 1.1 times faster when the

ray is oriented orthogonal to the anisotropy vector as

opposed to when the ray is parallel to the vector. An

anisotropy magnitude of 1.1 is reasonable as Cox states

that published values generally range from 1.0 to 1.45 [38].

Tomographic inversions were performed assuming both

straight and curved raypaths. The straight ray calculation is

simply the straight line distance between the source and the

receiver, while the curved ray calculation allows for ray

bending according to Snell’s Law. Snell’s Law implies that

for the layered initial velocity model the straight ray

assumption is not valid. However, the root-mean-square

travel time residuals were actually smaller for the straight ray

assumption than for the curved ray assumption, while the

sum of the residuals were significantly smaller for the curved

ray assumption. The sum of the residuals is simply the sum

of the travel time residuals for each ray in the iteration and is

not a measure of the magnitude of the residuals, but rather of

their distribution about zero. The higher sum of the residuals

for the straight ray assumption indicates that the straight ray

algorithm consistently underestimates the raypath length.

Clement and Knoll generated synthetic tomograms for cross

borehole data with straight and curved ray algorithms and

found similar results in their tests; the root-mean-square

error was smaller for the straight ray algorithm than for the

curved ray algorithm. They still concluded that the curved

ray algorithm was favorable because it more accurately

portrayed their model [39]. By the same logic, it was

determined that the curved ray assumption was appropriate

for this data, and each tomogram was generated with 10

curved ray iterations.

A smoothing constant was applied in all directions.

Smoothing replaces the velocity value at a node by a

weighted average of the velocity at that node and the

surrounding nodes. Smoothing can help to remove inconsistencies in the model, but if a model is oversmoothed

important anomalies can be removed. A fairly small

smoothing constant of 0.02 was applied to surrounding

nodes in order to avoid oversmoothing.

4. Results

4.1. Abutment stress 

Major stress features resulting from abutment stress

were expected to be imaged through velocity tomography.
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Abutment stress is a result of stress redistribution due to

the extraction of ore, and occurs along or near the

boundary where material has been removed [40]. An

undisturbed coal seam with competent roof and floor

strata will have a fairly uniform stress distribution. As coal

is removed this distribution is disrupted and the load shifts

to another intact area. In longwall mining, this stress is

transferred immediately in front of the face, and to the

sides of the panel (headgate and tailgate). Failure of the

roof strata behind the longwall shields is termed the ‘gob’

and allows for pressure relief.

Very competent strata above a longwall system, such as

massive sandstone, may not cave immediately, contributing

to extremely high abutment stress in front of the face which

can result in rockbursts at the face, and damage to shields

due to dynamic loading [41]. The exact distribution of the

abutment load is dependent upon the properties of the roof

strata and the mining geometry, but abutment stress is

usually the largest on the tailgate, if it is adjacent to a

previously mined out panel. Front abutment pressure is

detectable at a lateral distance ahead of the face

approximately equal to the overburden depth, and

typically reaches a maximum at a distance of one-tenth

the overburden depth. In weak roof, maximum abutment

stress along the faceline occurs at the headgate and tailgate

corners, but in more competent roof a peak may occur

mid-face, depending upon the face length [41]. In addition

to vertical stress redistribution, joints, faults, inhomogeneous layering, and horizontal stress orientation may

contribute to larger abutment stresses and more erratic

failure. Even in optimum conditions roof failure behind

longwall shields is rarely uniform [42].

4.2. Velocity tomograms and comparison to numerical 

modeling 

Tomograms were generated for each of the 18 days of

the study. Six of these images are presented in Fig. 4.

Three-dimensional tomograms were generated, and then

sliced laterally at seam level, at an elevation of approximately 1690 m. Plan views for days 2, 5, 7, 12, 15, 18 are

displayed with the mining geometry overlain onto the

tomogram. In these images, three distinct features can be

observed. First, a high-velocity region is identifiable

immediately in front of the face for each of the days of

the study. Second, a high-velocity region is visible to

varying degrees running from the active face down the

tailgate alongside the gob. Both of these regions are areas

where high abutment stress is expected. Finally, a lowvelocity feature moves in conjunction with the face in the

location of the gob, as expected.

In order to validate the behavior observed on the

tomograms, a simple numerical model of the panel was

generated to observe expected vertical stress. The LAMODEL (Laminate Model) program was utilized due to its

relative ease of use and specific application to tabular

deposits. LAMODEL is a boundary element, displacement–discontinuity routine that calculates stress for

tabular seams. It simulates the overburden as a stack of

homogenous isotropic layers with the same Poisson’s ratio,

Young’s modulus, and frictionless interfaces [43]. In Fig. 5,

the LAMODEL plot for day 18 of the study is displayed

alongside the tomogram for the same day. Many of the

same features are evident. Additionally, Fig. 6 shows the

LAMODEL stress distribution as a wireframe plot that

emphasizes the relatively higher stress predicted on the

tailgate.

5. Conclusions

The tomograms generated from the 18-day study

produced repeatable high-velocity features in areas that

typically exhibit high stress on longwall panels and in areas

that numerical modeling predicts will encounter high stress,

including a high-velocity region that is consistently present

immediately ahead of the active face and a high-velocity

region that is visible along the tailgate side of the panel.

Also, these regions are observed to redistribute with

longwall face retreat. The tomograms do not display the

same degree of resolution as the LAMODEL stress plots,

and velocity patterns corresponding with individual pillars

cannot be ascertained.

While the velocity distribution shown on the tomograms

is not as uniform as the stress distribution displayed in the

LAMODEL plots, true stress redistribution is rarely

perfectly uniform due to inhomogeneity in both geologic

properties and fracture and deformation. Additionally, the

LAMODEL plots display more specific stress details. Stress

on each of the headgate and tailgate pillars is identifiable,

while no such detail is visible on the velocity tomograms.

One reason for the lack of detail on the tomograms may be

insufficient ray coverage. While the mining-induced microseismic events are ideal for long-term sources they do not

provide the dense and uniform ray coverage provided by

active sources. Also, the nature of the velocity–stress

relationship causes some ambiguity in the image. In rocks

with high elastic moduli stress increase may not translate to

high p-wave velocity, so while differences in high-stress

regions are discernible on the LAMODEL plots, they are

not discernible on the velocity tomograms.

Several improvements can be made to this method to

provide better information about the state of stress in the

rock mass including implementation of attenuation tomography, double difference tomography, and adaptive mesh.

Attenuation tomography could provide additional information about the degree of fracture in the rock mass, while

double difference tomography and the application of an

adaptive mesh could assist with some of the challenges of

passive source implementation. Double difference tomography combines the inversion of the velocity data with the

location of the microseismic events, optimizing both [44].

Adaptive mesh tomography allows for variation in voxel

size to account for nonuniform ray coverage [45]. Additionally, quantification of uncertainty will be addressed in
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Fig. 4. Plan view velocity tomograms at seam level, z 1⁄4 1695 m. Days 2, 5, 7, 12, 15, and 18 of the study are shown. The face is retreating in the southwest

direction.
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Fig. 5. LAMODEL stress plot (left) and velocity tomogram (right), plan view at seam level, z 1⁄4 1695 m, for day 18. High-velocity areas corresponding to

the forward abutment and tailgate side abutment zones are circled.

Fig. 6. LAMODEL wireframe stress plot, illustrating the relatively higher stress predicted on the tailgate side of the panel, along with the front abutment

stress.

 

 

 

 

 

	 

 

	 	 

 

	 

 

	 

 

future studies. By applying these techniques in concert,

time-lapse tomographic images of velocity distributions in

underground mines can be improved and utilized for

noninvasive examination of stress redistribution in a rock

mass, thereby increasing the safety and efficiency of the

mining process.

Acknowledgments

The authors are grateful to the National Institute

for Occupational Safety and Health for providing

the raw data for this study. This research was funded

by a National Science Foundation CAREER Grant

(CMS-0134034).	 

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