An Overview of Data Collection

and Analysis Methods for Calculating

the Volume of Mine Materials

Technical Note 448

June 2016
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Publishing Services Section in Denver, Colorado.

Suggested citation:

Frels, J. 2016. An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine 

Materials. Tech Note 448. U.S. Department of the Interior, Bureau of Land Management, National Operations 

Center, Denver, CO.

BLM/OC/ST-16/001+3720
Technical Note 448

An Overview of Data Collection

and Analysis Methods for Calculating

the Volume of Mine Materials

Author:

Jason Frels

Physical Scientist

Bureau of Land Management

National Operations Center

Denver, Colorado

June 2016
ii | Technical Note 448 | June 2016 |

An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

Table of Contents |

Abstract_____________________________________ 1

1. Introduction _______________________________ 2

1.1 Why Are Volume Calculations Necessary? ____ 2

1.2 Volume Calculations: An Overview__________ 2

2. Data Collection Phase________________________ 3

2.1 Geometric Object Concept ________________ 3

2.2 Data Collection Methods __________________ 4

3. Data Collection Methods for Deposits ___________ 5

3.1 Surface Plane Measurements _______________ 5

 3.1.1 Global Positioning System ____________ 5

 3.1.1.1 Standalone GPS ______________ 5

 3.1.1.2 Differential GPS ______________ 6

 3.1.2 Laser Scanning _____________________ 7

 3.1.2.1 Terrestrial Laser Scanning ______ 7

 3.1.2.2 Airborne Laser Scanning _______ 8

 3.1.3 Photogrammetry____________________ 8

 3.1.3.1 Ground-Based Photogrammetry _ 9

 3.1.3.2 Airborne Photogrammetry _____ 9

 3.1.4 Analog Measurements ______________ 10

3.2 Subsurface Plane Measurements ___________ 11

 3.2.1 Intrusive Methods__________________ 11

 3.2.1.1 Drilling____________________ 11

 3.2.1.2 Trenching __________________ 12

 3.2.2 Non-Intrusive Methods _____________ 13

 3.2.2.1 Geophysics _________________ 13

 3.2.2.2 Landscape Interpolation ______ 13

 3.2.2.3 Aerial Photography __________ 14

4. Data Collection Methods for Pits ______________ 16

4.1 Subsurface Plane Measurements ___________ 16

 4.1.1 Global Positioning System ___________ 16

 4.1.1.1 Standalone GPS _____________ 16

 4.1.1.2 Differential GPS _____________ 17

 4.1.2 Laser Scanning ____________________ 18

 4.1.2.1 Terrestrial Laser Scanning _____ 18

 4.1.2.2 Airborne Laser Scanning ______ 19

 4.1.3 Photogrammetry___________________ 20

 4.1.3.1 Ground-Based Photogrammetry 20

 4.1.3.2 Airborne Photogrammetry ____ 21

 4.1.4 Analog Measurements _______________ 21

4.2 Surface Plane Measurements ______________ 22

 4.2.1 Preexisting Data ___________________ 22

 4.2.2 Aerial Photography_________________ 22

 4.2.3 “Flat Cap” ________________________ 23

 4.2.4 Landscape Interpolation _____________ 23

5. Data Collection Method Comparisons__________ 24

6. Data Analysis Phase ________________________ 26

6.1 Data Preparation _______________________ 26

6.2 Data Analysis Methods __________________ 26

 6.2.1 Digital Terrain Model Software________ 26

 6.2.2 Average End Area __________________ 26

 6.2.3 Geometric Calculations (Paper/Pencil) _ 26

7. Active Mine Monitoring Application ___________ 27

8. Glossary _________________________________ 28

9. References________________________________ 30
An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

 | Technical Note 448 | June 2016 | 1

Abstract |

The purpose of this technical note is to assist 

Bureau of Land Management employees in 

determining which data collection methods 

are most appropriate to calculate the 

volumes of remaining or removed mining 

material at a site. This tech note primarily 

provides an overview of data collection 

methods for calculating the volumes of 

surface mineral material remaining at 

abandoned mine land sites or the volumes of 

material removed from gravel or sand sites. 

Data analysis methods are also provided. 

The goal of this tech note is to assist BLM 

field staff in (1) understanding the available 

data collection methods and (2) determining 

the most appropriate data collection method 

for their project. The data collection 

methods highlighted for deposits include 

Global Positioning System (GPS), laser 

scanning, photogrammetry, analog 

measurements, drilling, trenching, 

geophysics, landscape interpolation by GPS, 

and aerial photography. The data collection 

methods highlighted for pits include GPS, 

laser scanning, photogrammetry, analog 

measurements, preexisting data, aerial 

photography, “flat cap,” and landscape 

interpolation. Each data collection method 

is rated qualitatively based on the following 

criteria: applicability, level of effort, 

reliability, and others. The data analysis 

methods highlighted in this tech note 

include digital terrain model software, 

average end area, and geometric 

calculations.
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An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

1. Introduction |

The primary audience of this technical 

note is the Bureau of Land Management’s 

(BLM’s) Abandoned Mine Lands and 

Mineral Materials Programs. This tech note 

primarily provides an overview of the data 

collection methods for calculating volumes 

of remaining or removed material at mine or 

mineral sites. Data analysis methods are also 

discussed.

As this is an overview of commonly used 

data collection methods, this tech note 

does not provide a quantitative comparison 

of the different methods. However, 

the tech note includes summaries of 

qualitative descriptions regarding accuracy, 

applicability, level of effort, reliability, cost, 

and other metrics of each method. This 

tech note will assist staff in determining the 

appropriate data collection method for 

their project.

1.1 Why Are Volume 

Calculations Necessary?

The BLM’s Abandoned Mine Lands 

Program addresses the physical safety and 

environmental hazards at abandoned mine 

sites. While planning remediation options 

for a site, an accurate calculation of the 

volume of waste rock or tailings piles can 

refine the remedy alternatives and provide 

more precise cost estimates for the remedy 

alternatives. 

In the Mineral Materials Program, the 

BLM inspects and monitors the activity of 

active mineral operations (e.g., sand, gravel, 

stone) to verify that the amount of mined 

material is properly reported. Accurate 

volume calculations assist the solid minerals 

staff in reliably and correctly validating the 

production reports and ensuring proper 

royalty payments. 

Whether a site contains several tailings 

deposits or is a large gravel pit, the data 

collection methods presented in this tech 

note are appropriate at either type of site 

to calculate volumes for the material that 

remains or for the material that has been 

removed. 

1.2 Volume Calculations: 

An Overview

Volume calculations consist of two phases: 

data collection and data analysis. The 

data collection phase involves taking 

measurements of the target object (e.g., 

tailings pile, gravel pit). This phase may 

include researching historical sources of 

data, such as aerial photography. In the 

data analysis phase, the information from 

the data collection phase is processed to 

calculate volumes. Most analytical methods 

rely upon the assistance of computers 

to calculate volumes, though there are 

exceptions in which hand-based calculations 

are sufficient.
An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

 | Technical Note 448 | June 2016 | 3

The data collection phase, the first phase 

for calculating the volume, involves taking 

measurements of the target object (e.g., 

talings pile, waste rock dump, gravel pit, fill 

material). For deposits, volume calculations 

help determine the remaining amount of 

earth material or mine waste (see Figure 

1). For pits, volume calculations help 

determine the “void space,” which represents 

the amount of material that has been 

removed (see Figure 2). For these volume 

calculations, staff collect and compare two 

“planes” of information using the geometric 

object concept. 

2.1 Geometric Object 

Concept

Two planes of analysis are required for 

calculating volumes of deposits and pits. 

One plane can be accurately measured, while 

the other can only be estimated. Calculating 

volumes for deposits and pits differ between 

which plane is measured and which plane is 

estimated. Table 1 presents the target objects 

and the measured and estimated planes.

Deposit

(mine waste)

Pit

(void

space)

2. Data Collection Phase |

Figure 1. Representation of the volume of 

remaining mine waste

Figure 2. Representation of the volume of 

removed material

Table 1. The exposed face, measured plane, and estimated plane of deposits and pits

Target Object Exposed Face Measured Plane Estimated Plane

Deposit surface of deposit surface plane subsurface plane

Pit bottom of pit subsurface plane surface plane

For deposits, the goal is to calculate the 

volume of the remaining amount of 

earth material or mine waste. The area 

and location of the surface plane can 

be accurately measured. However, the 

subsurface plane, or the contact area 

between the deposited material and a 

reference material (e.g., undisturbed earth), 

is frequently estimated (see Figure 3). 

For pits, the goal is to calculate the volume 

of the void space representing the material 

(e.g., sand, gravel, stone) removed from the 

pit. The subsurface plane of the void space 

is the exposed earth of the pit and can be 

accurately measured. The surface plane of 

the void space is the earth’s surface prior 

to disturbance/excavation and is typically 

estimated (see Figure 4). In some cases, 

preexisting data are available.

A note on location: Spatial information 

(e.g., latitude/longitude) is not necessary 

to calculate volumes. However, spatial 

information is necessary to determine the

object’s exact location in a GIS environment. 

Typically, this is achieved through the use 

of a Global Positioning System (GPS). Local 

coordinate systems, such as distance from a 

known marker, can also be used.

A note on resolution: Appropriate 

resolution should be determined prior to the 

Subsurface Plane

(estimated plane)

Surface

Plane

(measured

plane)

Mine Waste

Figure 3.

Surface and 

subsurface

planes 

of deposits

Figure 4.

Surface and

subsurface

planes

of pits

Subsurface Plane

(measured plane)

Surface Plane

(estimated plane)

Void Space (open pit area)
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An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

start of any project. Several factors, such as 

target object size, data collection method, 

and intended use of the resultant volume 

calculations, will determine the appropriate 

resolution.

2.2 Data Collection 

Methods

This tech note presents the data collection 

methods in two sections: data collection 

methods for deposits and data collection 

methods for pits. While many of the same 

methods are applicable for both deposits 

and pits, certain methods perform better for 

deposits and others for pits.

Each data collection method is qualitatively 

described using the following criteria: 

accuracy, applicability, level of effort, 

reliability, specialized knowledge, cost, 

and overall ranking for both deposits and 

pits. The criteria are applicable to the data 

collection methods as follows:

a. Accuracy - The potential of the data 

collection method in measuring the 

target object’s true volume.

b. Applicability - The performance ability 

of the data collection method for 

measuring a particular pit or deposit. 

This criterion takes into account the 

physical location (setting), size, and 

shape of a target object and assesses 

how well the method can be used for 

a site.

c. Level of Effort - The amount of 

labor, time, and resources required to 

perform the data collection method. 

Intrusiveness, or the amount of 

destructiveness or disruptiveness of the 

method, is also considered.

d. Reliability - The likelihood that the 

collected data will successfully calculate 

volumes in the analysis phase.

e. Specialized Knowledge - The technical 

or professional knowledge required to 

collect or interpret the data.

f. Cost - The monetary resources 

required to perform data collection. 

BLM travel ceiling dollars are noted if 

applicable. All cost estimates are based 

on incurred costs at representative 

and/or existing sites throughout 

BLM-managed lands.

g. Overall - An overall ranking that 

factors in all of the other variables.

h. Defensibility (pits only) - The 

likelihood that the resultant data and 

models are commonly accepted for 

production verification in salable 

mineral operations.
An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

 | Technical Note 448 | June 2016 | 5

3. Data Collection Methods for Deposits |

Typical abandoned mine features requiring 

volume calculation include tailings piles 

or waste rock piles. The surface planes of 

these deposits can be accurately measured 

through several methods. The subsurface 

planes of these deposits are generally more 

difficult to accurately measure and result in 

the source of greatest error in final volume 

calculations. 

3.1 Surface Plane 

Measurements

The surface planes of deposits can be 

accurately measured, often to millimeter 

precision. In this tech note, the data 

collection methods for measuring the 

surfaces of deposits include GPS, laser 

scanning, photogrammetry, and analog 

measurements. This section presents these 

data collection methods and provides 

qualitative ratings, from very low to high, 

regarding their performance at measuring 

the surface planes of deposits. Overall 

ratings of data collection methods include 

poor, average, good, or very good.

3.1.1 Global Positioning System

GPS provides location information based on 

transmissions from a network of satellites 

orbiting the earth. GPS measures the surface 

of a deposit in two ways. First, a grid of 

user-defined resolution delineates point 

locations on the surface of the deposit. 

This information is then interpolated into 

a smooth surface containing the horizontal 

(X, Y) attribute information with the vertical 

(Z) elevation values. The second way is to 

collect continuous linear transects over the 

surface of the pile. The X, Y, and Z values 

for the surface of the pile are interpolated 

from the lines. The two types of GPS include 

standalone and differential.

3.1.1.1 Standalone GPS

A standalone system involves the use of a 

handheld unit that processes signals from 

at least four satellites to calculate location 

information.

a. Accuracy - Low

The accuracy of the resultant model 

relies on the accuracy and resolution of 

the collected data. Standalone systems 

provide accuracy within a range of 

±2 to 5 meters. The use of an external 

antenna can improve the accuracy by 

±1 to 2 meters. Generally, this amount 

of accuracy is not sufficient to calculate 

volumes for small to medium deposits.1

b. Applicability - Low

The main constraint with using GPS is 

those collecting the data must traverse 

the surface of the deposit. Safety 

concerns regarding slips, trips, and falls 

or the large dimensions of deposits 

often outweigh the benefit of using 

GPS to collect surface information. 

Additionally, the applicability of 

standalone GPS is limited to very large 

deposits in which the level of accuracy 

is insignificant compared to the size of 

the deposit. 

c. Level of Effort - Medium

The required level of effort for 

collecting GPS data depends on the 

size of the deposit and the desired 

resolution of the surface plane model. 

As the deposit size and desired 

resolution increases, the amount of 

time and effort increases.

d. Reliability - Very Low to Medium

Depending on the size of the deposit, 

the reliability of standalone GPS is very 

low (for small deposits) to medium 

(for large to very large deposits) for 

successfully calculating a surface plane. 

Standalone GPS reliability increases 

to medium when the deposit is so 

1

 See glossary for definitions of deposit and pit 

sizes.

 | 3. Data Collection Methods for Deposits | 3.1 Surface Plane Measurements | 3.1.1 Global Positioning System |
6 | Technical Note 448 | June 2016 |

An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

large that an accuracy range of ±2 to 

5 meters is insignificant compared to 

the overall size of the target object. 

The reliability is very low for smaller 

deposits because an accuracy range 

of ±2 to 5 meters significantly affects 

the confidence and accuracy of the 

resultant surface and volume.

e. Specialized Knowledge - Low

Many individuals are familiar with the 

operation of standalone GPS units for 

data collection. Individuals should be 

properly trained in configuring GPS 

devices prior to collecting data.

f. Cost - Low

Generally, standalone GPS units are 

inexpensive, often between $400 and 

$3,000. However, accuracy and desired 

model resolution should factor into 

which GPS device to use.

g. Overall - Average

A standalone system is a relatively 

simple method for BLM staff to collect 

surface data with minimal costs.

3.1.1.2 Differential GPS

A differential GPS system involves the 

use of a stationary base station and rover 

combination, which provides much higher 

positional accuracy than standalone GPS. 

Data collected in the field are processed 

and corrected afterward using information 

published by the Online Positioning User 

Service to improve the accuracy. Differential 

GPS can be performed in the field and 

corrected nearly instantaneously using radios 

known as “real time kinematic” (RTK). 

a. Accuracy - High

The accuracy of the resultant surface 

model relies on the accuracy and 

resolution of the collected data. 

Differential GPS systems can achieve 

subcentimeter accuracy. This can result 

in a very accurate surface measurement 

and is often more than enough 

information to calculate a reliable 

surface model for deposits. Higher 

density grids (increased number of 

total points on the surface) or shorter 

distances between linear transects 

result in a higher resolution surface 

model with greater accuracy.

b. Applicability - Medium

The main constraint with using GPS 

to collect data is that those collecting 

the data must traverse the surface of 

the deposit. Safety concerns regarding 

slips, trips, and falls or the large 

dimensions of deposits often outweigh 

the benefit of using GPS to collect 

surface information. Differential GPS 

is applicable for all sizes of deposits 

that do not pose safety hazards and 

in which deposit dimensions do not 

interfere with data collection.

c. Level of Effort - Medium

The required level of effort for 

collecting GPS data depends on the 

size of the deposit and the desired 

resolution. Since GPS data is collected 

from the location of the rover, the 

deposit must be traversed. The larger 

the deposit, the more time and effort 

required to collect information. Also, 

the higher the desired resolution, the 

more time required for collecting data. 

It is necessary to consider scale when 

deciding the resolution of any deposit.2

Differential GPS systems also have an 

additional time requirement associated 

with setting up and taking down a base 

station.

d. Reliability - Medium to High

The resolution of collected data points 

determines whether the reliability 

is medium or high. The higher the 

resolution, the higher the reliability.2 

2

 When determining the appropriate resolution 

for any project (e.g., whether to use a method 

that provides subcentimeter resolution or a 

method that provides meter resolution), take 

into account the size of the object and goal of 

the project. For example, subcentimeter resolution and a distance of 2 centimeters between 

GPS data collection points is likely overkill for 

calculating a volume of a tailings deposit that 

measures 100 meters long in two directions and 

50 meters tall and will ultimately be evaluated by 

engineers in cubic yards and transported by the 

 | 3. Data Collection Methods for Deposits | 3.1 Surface Plane Measurements | 3.1.1 Global Positioning System |truckload. 
An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

 | Technical Note 448 | June 2016 | 7

e. Specialized Knowledge - Medium

Setup, operation, and data transfer 

for differential GPS requires some 

training. Individuals require the ability 

to troubleshoot communication issues 

between the base and the rover in the 

field and knowledge of vendor-specific 

software protocols. 

f. Cost - Medium

RTK differential GPS systems cost 

between approximately $10,000 

and $30,000. Instead of purchasing 

an RTK system, users can also rent 

one. Startup costs for non-RTK 

differential GPS systems are lower but 

typically require yearly software fees 

for incorporating data processed by 

the Online Positioning User Service. 

There is a very low annual equipment 

maintenance cost, often $0, associated 

with RTK differential GPS systems. For 

BLM staff, the National Operations 

Center (NOC) in Denver, Colorado, 

maintains two RTK differential GPS 

systems. The NOC can train individuals 

on the operation of the units or 

perform the data collection if necessary. 

Travel ceiling implications apply when 

considering hands-on training or NOC 

data collection. However, shipping 

costs for the equipment are minimal. 

The largest cost associated with data 

collection via RTK differential GPS is 

typically travel costs (transportation, 

per diem).

g. Overall - Good

Although this method produces highly 

accurate and reliable results, it should 

only be used if the proper expertise is 

available.

3.1.2 Laser Scanning

Laser scanning, also referred to as light 

detection and ranging (LiDAR), operates on 

the principle of measuring the amount of 

time it takes a pulse of light to reflect off an 

object and back to the scanner. This provides 

a measurement of the distance between 

the scanner and object, which can create 

scaled 3D models of any object off of which 

the light reflects. The datasets are generally 

referred to as point clouds, with each 

measurement representing a point in space. 

LiDAR captures datasets from the ground 

(terrestrial laser scanning) or from the air 

(airborne laser scanning).

3.1.2.1 Terrestrial Laser Scanning

In terrestrial laser scanning, a laser scanner 

collects data from a stationary location on 

the ground. Sometimes, to capture an entire 

deposit with terrestrial laser scanning, 

multiple data collection locations are 

necessary.

a. Accuracy - High

Laser scanners can accurately measure 

the shape and size of deposits to 

decimeter resolution. External 

reference control (e.g., GPS) is 

required to georeference the location 

of the resultant model. However, laser 

scanners can create accurately scaled 

models without external reference. 

b. Applicability - Medium to High

A laser scanner in a stationary location 

can only collect data for the portion 

of the deposit in its line of sight. The 

scanner must be moved to different 

locations around the deposit to 

create a complete model. For simple, 

smooth deposits, the applicability of 

laser scanning is high. For complex 

deposits with topographic features (e.g., 

undulations) that hide portions of the 

surface from the scanner’s viewshed, 

the applicability drops to medium.

c. Level of Effort - Low to Medium

The level of effort is low for simple 

deposits. Generally, a laser scanner 

is placed in more than one location 

to capture the entire exposed surface 

of the deposit. The level of effort 

rises to medium with greater deposit 

complexity and size. 

d. Reliability - High

The surface plane created using 

laser scanning is highly reliable. The 

data collected by the laser scanner 

typically has a low amount of error 

 | 3. Data Collection Methods for Deposits | 3.1 Surface Plane Measurements | 3.1.2 Laser Scanning |
8 | Technical Note 448 | June 2016 |

An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

and is accurate and precise. Reliability 

increases when the resolution and 

number of data collection locations 

increase. 

e. Specialized Knowledge - Medium

Most individuals require training in 

the operation of LiDAR equipment and 

data processing. However, advances in 

the LiDAR field have resulted in “user 

friendly” LiDAR instrumentation and 

data processing software packages. 

Once trained, data collection and 

processing require little additional 

specialized knowledge.

f. Cost - Medium to High

Laser scanner costs range from 

approximately $40,000 to $60,000 

depending on the model. This does 

not include training costs. Annual 

maintenance costs are very low, often 

$0. 

g. Overall - Good

Although this method requires several 

data collection locations, which 

increase the amount of time in the field, 

the data are reliable.

3.1.2.2 Airborne Laser Scanning

Airborne laser scanning uses laser scanners 

that are mounted on manned or unmanned 

aircraft. The laser scanners collect data 

when the aircraft flies over individual site 

locations. Unlike terrestrial laser scanning, 

the sensor is constantly in motion, which 

prevents the user from having to physically 

move the laser scanner to multiple locations 

around the deposit. 

a. Accuracy - High

Laser scanners can accurately measure 

the shape and size of deposits to 

decimeter resolution. External 

reference control (e.g., GPS) is 

required to georeference the location 

of the resultant model. However, laser 

scanners can create accurately scaled 

models without external reference. 

b. Applicability - High

Airborne laser scanners can capture 

nearly every deposit that is visible from 

the air.

c. Level of Effort - Medium

Airborne laser scanning is rated 

medium due to the contracting 

or coordination requirements for 

obtaining flight clearances and aircraft. 

The NOC currently does not maintain 

an unmanned aerial system (UAS)-

ready laser scanner, so contracting is 

necessary. 

d. Reliability - High

The surface plane created using 

airborne laser scanning is highly 

reliable. The data collected by the laser 

scanner typically has a low amount of 

error and is accurate and precise. 

e. Specialized Knowledge - High

Airborne data collection via aircraft 

requires a licensed and certified pilot, 

a plane, and special equipment. UAS 

data collection requires a pilot certified 

by the Department of the Interior to 

operate the UAS.

f. Cost - Medium

An airborne data collection event can 

cost between $30,000 and $35,000. 

This amount is cost prohibitive if only 

one deposit is captured. However, if 

multiple deposits lie within a defined 

geographic radius, the cost per site 

decreases. 

g. Overall - Average to Good

Terrestrial laser scanning is not as 

efficient at capturing the surface of 

deposits because it requires data to be 

collected from stationary points around 

the surface, potentially increasing field 

time. For airborne laser scanning, 

this time or logistical impediment is 

removed, but the overall cost of data 

collection is greater. Ultimately, laser 

scanning is a reliable data collection 

method for deposits.

3.1.3 Photogrammetry

Photogrammetry calculates a 3D model 

of surfaces using adjacent, overlapping 

 | 3. Data Collection Methods for Deposits | 3.1 Surface Plane Measurements | 3.1.3 Photogrammetry |
An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

 | Technical Note 448 | June 2016 | 9

photographs. This data collection method 

results in very accurate 3D models by 

using effectively captured photographs of 

an object. The two methods of collecting 

photogrammetric images include ground 

based and airborne.

3.1.3.1 Ground-Based 

Photogrammetry

Ground-based photogrammetry involves 

capturing photographs from either the 

photographer’s eye level or from an object 

extended up from ground level (e.g., 

monopod, cherry picker).

a. Accuracy - High

Photogrammetry can produce surface 

models that accurately represent 

the shape and size of deposits. With 

current photographic technology, this 

can equate to subcentimeter resolution. 

External reference control (e.g., GPS) 

is required to georeference the location 

of the resultant model. However, 

photogrammetry can create accurately 

scaled models without an external 

reference.

b. Applicability - Medium

In order to create an accurate surface 

model, the photographer must capture 

the entire deposit in overlapping 

photographs. This requires the 

photographer to move the camera 

around the deposit and adequately 

capture the surface. The greater the 

complexity of the topographic features 

or the greater the size of the deposit, 

the more difficult and less applicable 

this method becomes. This is due to 

the limitations of the photographer in 

reaching the necessary vantage points 

to adequately capture the deposit 

stereoscopically, or in stereo.

c. Level of Effort - Low to High

Photographers can capture small or 

simple deposits stereoscopically in 

less than an hour. Larger deposits 

or complex topographic features on 

the surface of deposits can prove 

challenging and time consuming, often 

requiring multiple days to capture 

stereoscopically. 

d. Reliability - High

Assuming the photographer collected 

effective photographs, surface 

models derived from ground-based 

photogrammetry are very reliable. The 

models fail when effective photographs 

of the deposit have not been captured, 

which occasionally occurs when 

collected from the ground.

e. Specialized Knowledge - Medium

If not already known, initial training 

of how to capture objects in stereo 

is required. For complex deposits, 

a higher level of understanding 

of photogrammetric principles 

is recommended, but not always 

necessary, for successful 3D models. 

f. Cost - Low

A fixed-aperture digital single-lens 

reflex (DSLR) camera, approximately 

$300, is the minimum recommended 

technology for capturing effective 

photographs. Higher megapixel, fully 

programmable DSLR cameras (which 

range from $800 to $6,000) are more 

reliable. Camera and travel costs are the 

only required costs, besides labor hours 

for photogrammetric data collection.

g. Overall - Poor to Good

Ground-based photogrammetry is 

a good method for collecting data 

for simple, small- to medium-sized 

deposits. It can adequately capture 

accurate information about large or 

complex deposits but requires a greater 

level of effort. This data collection 

method can also fail for larger or 

complex deposits.

3.1.3.2 Airborne Photogrammetry

Airborne photogrammetric data collection 

involves fixing a camera to an aircraft and 

collecting stereoscopic photographs from 

the air. These aircraft can include a fixedwing or rotary-wing passenger aircraft or 

a UAS. The airborne aspect of this method 

eliminates vantage point issues associated 

with ground-based photogrammetry.

a. Accuracy - High

Photogrammetry can produce surface 

 | 3. Data Collection Methods for Deposits | 3.1 Surface Plane Measurements | 3.1.3 Photogrammetry |
10 | Technical Note 448 | June 2016 |

An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

models that accurately represent 

the shape and size of deposits. With 

current photographic technology, this 

can equate to subcentimeter resolution. 

External reference control (e.g., GPS) 

is required to georeference the location 

of the resultant model. However, 

photogrammetry can create accurately 

scaled models without an external 

reference. Occasionally, onboard 

external reference control is included 

with airborne photogrammetry data.

b. Applicability - High

Airborne photogrammetry can capture 

nearly every deposit that is visible from 

the air. 

c. Level of Effort - Medium

Generally, a pilot is necessary to collect 

airborne photogrammetric data. Either 

contracted pilots or the NOC’s UAS 

services can collect the imagery. UAS 

data collection may require several 

days of field work, depending on the 

size of the deposit(s). A minimum of 

2 to 4 weeks of mission planning is 

also required to use a UAS. Contracted 

data collection missions can be flown 

in a matter of days if the effort meets 

certain contracting criteria. It is 

possible to successfully use kites and 

balloons at smaller sites.

d. Reliability - High

The surface models derived from 

airborne data collection methods are 

highly reliable. 

e. Specialized Knowledge - High

Airborne data collection via fixed-wing 

aircraft requires a licensed and certified 

pilot, a plane, and special cameras 

and accessories. UAS data collection 

requires a pilot certified by the 

Department of the Interior to operate 

the UAS.

f. Cost - Low to Medium

The NOC maintains two UASs. The 

cost to use these services in 2016 is 

about $4,000, most of which is travel 

costs for the aircraft and certified UAS 

pilot. As of 2016, the NOC covers the 

base salary of NOC UAS pilots. UAS 

services can occasionally be contracted 

for $3,500, depending on the size, 

location, and complexity of the project. 

A contracted fixed-wing data collection 

event generally costs about $20,000. 

However, the fixed-wing data collection 

event can capture multiple deposits 

within a geographic area for minimal 

price increases, reducing the cost 

per site.

g. Overall - Average to Good

Airborne photogrammetry provides 

highly accurate, high-resolution 

models of the surfaces of deposits. If 

resources are available, this method 

produces reliable results. Cost and time 

sensitivity are the most prohibitive 

factors with this method. 

3.1.4 Analog Measurements

Analog measurements involve the use of 

nondigital devices (e.g., tape measures, 

measuring wheels) to measure the 

dimensions of deposits.

a. Accuracy - Low

Errors in analog measurements 

can range from feet to meters. This 

inaccuracy can lead to severe overor underestimation of the volume 

calculation of the deposit. 

b. Applicability - High

Analog devices can measure virtually 

any deposit that is accessible.

c. Level of Effort - Low

Analog measurements do not require 

much time or resources, other than the 

potential need to traverse terrain in 

order to take the measurements.

d. Reliability - Low

Inaccurate measurements lead to 

over- or underestimates of volumes of 

deposit material. 

e. Specialized Knowledge - Low

Using analog methods to measure 

 | 3. Data Collection Methods for Deposits | 3.1 Surface Plane Measurements | 3.1.4 Analog Measurements |
An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

 | Technical Note 448 | June 2016 | 11

surfaces of deposits requires an 

understanding of geometry and how to 

collect proper measurements.

f. Cost - Low

Tape measures or measuring wheels 

cost less than $100. Hand sights range 

from $100 to $500. Certified surveyors 

can make the measurements, though 

these generally require contracting or 

larger amounts of money.

g. Overall - Poor

Analog measurements are appropriate 

when rough estimates are sufficient or 

when other methods are unavailable. 

However, this method is beneficial 

during early site visits to approximate 

the scale of future data collection 

events.

3.2 Subsurface Plane 

Measurements

The subsurface plane of a deposit is the 

contact between the deposited material (e.g., 

mine waste) and a reference material (often 

undisturbed earth) (see Figure 3). For the 

purpose of this tech note, the data collection 

methods discussed in this section exclude the 

possibility of relocating the entire deposit 

and measuring the subsurface plane itself. 

The data collected using the methods in this 

section do not represent the entire subsurface 

plane of the deposit. These methods measure 

information about either points or linear 

transects along the subsurface plane, which 

are then extrapolated to create a plane. The 

subsurface plane derived using these 

methods does not represent the “true” 

subsurface plane of the deposit but a “best 

fit” subsurface plane due to the assumptions 

made when extrapolating points or lines of a 

plane. In this section, the data collection 

methods include intrusive and non-intrusive 

techniques, including drilling, trenching, 

geophysics, landscape interpolation by GPS, 

and aerial photography. The data collection 

method ratings range from very low to high 

regarding their performance at measuring 

the subsurface plane of deposits. However, 

the accuracy section analyzes how well the 

data can be used to make the “best fit” 

subsurface plane. Methods also include 

overall ratings of poor, average, good, or 

very good.

3.2.1 Intrusive Methods

Intrusive data collection methods expose 

the contact between the deposit and the 

reference material (e.g., undisturbed 

earth). These methods are used to measure 

the distance of points and lines along the 

subsurface plane of the deposit. Intrusive 

methods typically involve the use of heavy 

machinery.

3.2.1.1 Drilling

Drilling, also referred to as boring, 

involves excavating deposit material at 

point locations until the contact between 

the deposit and the reference material 

is exposed. Measurements are typically 

recorded as depth distance, or “beneath 

ground surface.” Machine operators use 

heavy machinery to complete most of the 

drilling. On occasion, hand augers substitute 

heavy machinery. Those conducting the 

drilling do not see the contact between the 

deposit and the reference material “in situ” 

(or at its actual location); drillers identify 

the contact through the material brought up 

by the drilling process.

a. Accuracy - Varies

Drilling exposes the contact between 

the deposit and the reference material, 

accurate to inches. The resulting 

accuracy of the subsurface plane 

depends on the density of drilled 

points.

b. Applicability - Medium to High

Drilling equipment bores a hole 

vertically through the deposit, 

therefore requiring the equipment to 

be on top of the deposit. The 

applicability of drilling decreases 

as the size and complexity of the 

deposit increases. However, drilling 

is applicable for the largest deposits 

with graded and stable surface access. 

Hand augers are well suited for small 

deposits or deposits with a fine material 

 | 3. Data Collection Methods for Deposits | 3.2 Subsurface Plane Measurements | 3.2.1 Intrusive Methods |
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An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

consistency in which manual boring 

can be performed. The hand auger’s 

applicability decreases as the deposit or 

deposit particle size increases. 

c. Level of Effort - High

To perform drilling on BLM sites, 

requirements include contracting, staff 

oversight, and records management.

d. Reliability - Medium to High

The reliability of the subsurface plane 

created from drilling data ranges from 

medium to high, increasing with the 

density of point data. Though rare, the 

contact boundary can be incorrectly 

identified since the boundary is not 

visible from the surface.

e. Specialized Knowledge - High

Equipment operators and geologic 

technicians operate equipment and 

recognize when drilling operations 

reach the boundary between the 

deposit and reference material. 

f. Cost - Medium

Due to the specialized knowledge 

and required equipment, contractors 

perform drilling work. Contract 

costs typically range from $10,000 to 

$30,000 but can be higher depending 

on site location and number of drilling 

locations.

g. Overall - Good

Though somewhat expensive, this 

method reliably creates a subsurface 

plane for calculating volumes. 

3.2.1.2 Trenching

Trenching involves excavating material in a 

linear orientation across deposits, exposing 

the contact between the deposit and the 

reference material along a transect. Those 

conducting trenching identify the contact 

“in situ” and conduct measurements along 

the transect. Equipment operators perform 

trenching with heavy machinery.

a. Accuracy - High

Linear information about the contact 

between the deposit and the reference 

material allows for highly accurate 

measurements of the subsurface plane. 

Increasing the number of transects 

across the pile increases the accuracy of 

the subsurface plane.

b. Applicability - High

Trenching is highly viable for small to 

medium deposits, as long as the deposit 

is accessible to equipment and as long 

as space is available to store excavated 

material. As the sizes of deposits 

increase, the applicability of trenching 

decreases, since operators must remove 

a greater volume of material to expose a 

linear transect along the subsurface 

plane. 

c. Level of Effort - High

Trenching on BLM sites usually requires 

contracting, staff oversight, and records 

management. Mobilization and 

operation of equipment also requires a 

substantial amount of time. Additionally, 

the larger the pile, the greater the level of 

effort in order to expose a complete 

transect across the pile.

d. Reliability - High

Trenching produces reliable 

information about linear transects of 

the subsurface plane. This information 

can be used to easily and reliably 

calculate a subsurface plane for volume 

calculation.

e. Specialized Knowledge - Medium

Trained equipment operators 

and geologic technicians operate 

equipment, recognize when trenching 

operations reach the boundary between 

the deposit and reference material, 

and are aware of the safety hazards 

associated with trenching.

f. Cost - Medium to High

Due to the high level of effort, 

operation time, and mobilization, 

trenching costs range from $20,000 

to $50,000 or higher, depending on 

the size of the deposit and number of 

transects.

 | 3. Data Collection Methods for Deposits | 3.2 Subsurface Plane Measurements | 3.2.1 Intrusive Methods |
An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

 | Technical Note 448 | June 2016 | 13

g. Overall - Good

Trenching produces the largest 

amount of reliable information of the 

subsurface plane without relocating 

the entire deposit and measuring the 

plane itself. Costs increase as deposit 

size increases. Only the largest deposits 

render this method ineffective.

3.2.2 Non-Intrusive Methods

Non-intrusive data collection methods do 

not disturb earth or expose the contact 

between the deposit and the reference 

material. Rather, these methods use 

information gathered about the surface or 

measurements of the subsurface to estimate 

where the subsurface plane exists.

3.2.2.1 Geophysics

Geophysical methods (e.g., direct current 

resistivity, ground-penetrating radar) 

measure the physical properties of the 

subsurface. Measurements of both the 

deposit and reference material are usually 

collected in linear or 3D orientations from 

the surface at varying but defined depths. 

A geologist or geophysicist interprets 

the collected data to identify the contact 

between the deposit and reference material. 

a. Accuracy - Medium

Depending on the geophysical method 

and the amount of spacing between 

data collection lines or electrodes, 

accuracy ranges from inches to several 

feet. The subsurface plane calculated 

from these data is fairly accurate within 

this range since it is based on linear 

survey lines and not points.

b. Applicability - Medium

Some site-specific conditions (e.g., 

electrically conductive sites, sites in 

which the physicochemical differences 

between the deposit and the reference 

material are minimal) interfere with 

or inhibit certain geophysical methods 

and decrease applicability. Otherwise, 

geophysical methods can be performed 

at any site where access is permitted.

c. Level of Effort - Medium

Most data collection events take no 

more than 2 days. For larger sites, 

data collection takes days to weeks. In 

addition, a geophysical survey requires 

time for contracting procedures. 

d. Reliability - Medium

A trained individual measures 

the geophysical properties of the 

subsurface and interprets the data. 

When correctly interpreted, the 

subsurface plane allows for reliable 

volume calculation.

e. Specialized Knowledge - High

Using geophysical methods to measure 

the subsurface plane of deposits 

requires specialized knowledge about 

which geophysical method to use, how 

to operate the equipment, and how to 

correctly interpret the data.

f. Cost - Low to Medium

The initial purchase cost of geophysical 

equipment is high (between $50,000 

and $100,000). However, the NOC 

maintains some equipment. If the 

NOC’s services are used, travel and 

labor hours are the only associated cost 

(estimate of $3,500) with geophysical 

data collection. Costs for geophysical 

data collection are higher when 

contracted ($20,000-$30,000 per site).

g. Overall - Average

Based on the specialized knowledge 

requirement and the uncertainty 

involved with interpretation, 

geophysics is an adequate solution 

for calculating the area of a 

subsurface plane. 

3.2.2.2 Landscape Interpolation

GPS can be used to measure information 

about an area surrounding a deposit. 

These data points are then uploaded into a 

geographic information system and used to 

interpolate the subsurface plane of the area 

underneath the deposit. GPS measurements 

generally start at the outermost extent of 

the deposit and radiate outward. Landscape 

interpolation should always be performed 

with the best available GPS data collection 

 | 3. Data Collection Methods for Deposits | 3.2 Subsurface Plane Measurements | 3.2.2 Non-Intrusive Methods |
14 | Technical Note 448 | June 2016 |

An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

technique (i.e., differentially corrected 

GPS data).

a. Accuracy - Low

Although GPS is capable of achieving 

subcentimeter accuracy, the 

information about the subsurface plane 

is low due to interpolation. Additional 

information, such as drilling or handaugured data, to validate the plane 

increases the accuracy. The accuracy of 

this method is better for less complex 

or flatter landscapes.

b. Applicability - High

This method can be performed at any 

site in which access to the deposit is 

permitted.

c. Level of Effort - Low

This method only requires the 

collection of points at and surrounding 

the edge of the deposit. The level of 

effort increases with difficult terrain, 

larger deposit sizes, and higher point 

density.

d. Reliability - Low

The elevation of the subsurface of the 

interpolated plane can vary widely. In 

some cases, areas of the interpolated 

plane, based on the interpolation 

technique, can be calculated to exist 

above the surface (measured) plane; 

thus, the volume of the area where 

the subsurface plane was calculated to 

exist above the measured plane would 

be negative, essentially invalidating 

this method. Less complex or flatter 

landscapes produce a more reliable 

subsurface plane, as do interpolated 

surfaces informed with drilling or 

hand-augered data.

e. Specialized Knowledge - Medium

Setup, operation, and data transfer 

for differential GPS requires some 

training. Individuals require the ability 

to troubleshoot communication issues 

between the base and the rover in the 

field and knowledge of vendor-specific 

software protocols. Individuals also 

require training in spatial analysis 

and interpolation techniques in order 

to successfully perform landscape 

interpolation.

f. Cost - Low to Medium

Most of the costs associated with 

landscape interpolation are related to 

data collection (estimate of $3,500). 

If differential GPS is used, costs are 

incurred from acquiring equipment 

or services and performing the 

interpolation (estimate of $10,000). 

Most interpolation can be performed 

using GIS software (e.g., ArcGIS), 

which can be obtained through 

an annual software license for 

approximately $1,000.

g. Overall - Poor

The quality of the subsurface plane 

based on GPS data is highly variable. 

This technique should only be used 

when the landscape surrounding the 

deposit is very simple or flat.

3.2.2.3 Aerial Photography

If aerial photography was captured prior 

to mining disturbance and is available 

in stereo, very accurate models of the 

subsurface plane can be calculated using 

photogrammetry. This method is very 

accurate, assuming undisturbed earth is the 

reference medium upon which the deposit 

sits. This method requires georeferencing 

the surface plane so it correlates to the aerial 

photography. Overburden (e.g., soil) can 

be factored into volume calculations if the 

surface is undisturbed.

a. Accuracy - Medium to High

The accuracy of the subsurface plane 

ranges from inches up to a foot and is 

based on the scale of the photography. 

b. Applicability - Low

Many sites predate aerial photography 

or do not indicate premine site 

conditions. Additionally, the scale of 

the photography and its subsequent 

effects on the resolution of the model 

should be evaluated against project 

objectives. Based on the lack of 

availability, the applicability of this 

method is low.

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An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

 | Technical Note 448 | June 2016 | 15

c. Level of Effort - Low

Efforts include staff time to research 

the availability of the photography and, 

if available, to calculate the subsurface 

plane.

d. Reliability - High

If available, aerial photographs are very 

reliable for calculating the area of a 

subsurface plane.

e. Specialized Knowledge - Medium

Individuals require knowledge about 

photogrammetry and digitization and 

the ability to calculate a subsurface 

plane based on aerial photography.

f. Cost - Low

Staff time is the main cost associated 

with this data collection method. 

Also, sometimes aerial photography is 

available from private companies at a 

minimal cost. This cost ranges from 

$0 if available within the BLM to $1,000 

if purchased.

g. Overall - Very Good

This method is a very inexpensive 

yet reliable method of calculating a 

subsurface plane if the imagery is 

available.

 | 3. Data Collection Methods for Deposits | 3.2 Subsurface Plane Measurements | 3.2.2 Non-Intrusive Methods |
16 | Technical Note 448 | June 2016 |

An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

4. Data Collection Methods for Pits |

For active mining monitoring compliance, 

the volume of material (e.g., sand, gravel, 

stone) is calculated. The exposed faces of 

pits (the subsurface planes) can be 

accurately measured through several 

methods. The surface planes of pits are 

typically estimated unless other data 

are available (e.g., aerial photography, 

preexisting data). Further, pit volume 

calculations can be used for Abandoned 

Mine Lands Program operations. For 

example, pit volume calculations can 

facilitate high well reduction for physical 

safety hazard mitigation.

4.1 Subsurface Plane 

Measurements

The exposed faces, or subsurface planes, 

of pits can be accurately measured. In this 

tech note, the data collection methods for 

measuring the subsurface planes of pits and 

the surface planes of deposits are identical; 

however, some methods are better suited for 

measuring the subsurface planes of pits than 

the surface planes of deposits. This section 

presents these data collection methods 

and provides qualitative ratings from very 

low to high regarding their performance at 

measuring the subsurface planes of pits. In 

addition to the criteria used to rate the data 

collection methods for the surface planes of 

deposits, defensibility is added due to the 

legal implications of production verification 

at active mining operations. Overall ratings 

of data collection methods for pits include 

poor, average, good, or very good.

4.1.1 Global Positioning System

GPS provides location information based on 

transmissions from a network of satellites 

orbiting the earth. GPS measures the surface 

of a deposit in two ways. First, a grid of userdefined resolution delineates point locations 

on the surface of the pit. This information 

is then interpolated into a smooth surface 

containing the horizontal (X, Y) attribute 

information with the vertical (Z) elevation 

values. The second way is to collect 

continuous linear transects over the pit. The 

X, Y, and Z values of the exposed surface are 

interpolated from the lines. The two types of 

GPS include standalone and differential.

4.1.1.1 Standalone GPS

A standalone system involves the use of a 

handheld unit that processes signals from 

at least four satellites to calculate location 

information.

a. Accuracy - Low to High

The accuracy of the resultant model 

relies on the accuracy and resolution of 

the collected data. Standalone systems 

provide accuracy within a range of 

±2 to 5 meters. The use of an external 

antenna can improve the accuracy by 

±1 to 2 meters. Generally, this amount 

of accuracy is not sufficient to calculate 

volumes for small to medium deposits. 

b. Applicability - Medium

The main constraint with using GPS is 

those collecting the data must traverse 

the exposed surface of the pit. Safety 

concerns regarding slips, trips, and falls 

or the large dimensions of pits often 

outweigh the benefit of using GPS 

to collect information. Additionally, 

the applicability of standalone GPS 

is limited to very large pits in which 

the level of accuracy is insignificant 

compared to the size of the pit.

c. Level of Effort - Medium

The required level of effort for 

collecting GPS data depends on the size 

of the pit and the desired resolution of 

the surface plane model. As the pit size 

and desired resolution increases, the 

amount of time and effort increases.

d. Reliability - Very Low to Medium

The reliability of standalone GPS 

is very low to medium, depending 

on the size of the pit. Standalone GPS 

reliability increases when the pit is 

 | 4. Data Collection Methods for Pits | 4.1 Subsurface Plane Measurements | 4.1.1 Global Positioning System |
An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

 | Technical Note 448 | June 2016 | 17

so large that an accuracy range of 

±2 to 5 meters is insignificant 

compared to the overall size of the 

target object. The reliability is very low 

for smaller pits because an accuracy 

range of ±2 to 5 meters significantly 

affects the confidence and accuracy 

of the resultant model and volume 

estimate.

e. Specialized Knowledge - Low

Many individuals are familiar with the 

operation of standalone GPS units for 

data collection. Individuals should be 

properly trained in configuring GPS 

devices prior to collecting data.

f. Cost - Low

Generally, standalone GPS units are 

inexpensive, often between $400 and 

$3,000. However, accuracy and desired 

model resolution should factor into 

which GPS device to use.

g. Overall - Average

GPS can serve as a data collection 

method for measuring points along the 

exposed face of pits. However, based 

on the size and complexity of most pits, 

GPS can be a very time-consuming 

method. If time is available, GPS can 

produce a very accurate plane for 

volume calculations.

h. Defensible - No

Typically, GPS points alone are 

insufficient to serve as defensible data. 

4.1.1.2 Differential GPS

A differential GPS system involves the 

use of a stationary base station and rover 

combination, which provides much higher 

positional accuracy than standalone GPS. 

Data collected in the field are processed 

and corrected afterward using information 

published by the Online Positioning User 

Service to improve the accuracy. Differential 

GPS can be performed in the field and 

corrected nearly instantaneously using 

radios known as “real time kinematic” 

(RTK).

a. Accuracy - High

The accuracy of the resultant 

subsurface plane relies on the accuracy 

and resolution of the collected data. 

Differential GPS systems can achieve 

subcentimeter accuracy. This can 

result in a very accurate subsurface 

measurement and is often more than 

enough information to calculate a 

reliable model for pits. Higher density 

grids (increased number of total 

points on the exposed face) or shorter 

distances between linear transects 

result in a higher resolution model with 

greater accuracy.

b. Applicability - Medium

The main constraint with using GPS 

to collect data is that those collecting 

the data must traverse the exposed face 

of the pit. Safety concerns regarding 

slips, trips, and falls or the large 

dimensions of pits often outweigh the 

benefit of using GPS. Differential GPS 

is applicable for all sizes of pits that do 

not pose safety hazards and in which 

pit dimensions do not interfere with 

data collection.

c. Level of Effort - Medium

The required level of effort for 

collecting GPS data depends on the size 

of the pit and the desired resolution. 

Since GPS data is collected from the 

location of the rover, the pit must 

be traversed. The larger the pit, the 

more time and exertion required to 

collect information. Also, the higher 

the desired resolution, the more time 

required for collecting data. Differential 

GPS systems also have an additional 

time requirement associated with 

setting up and taking down a base 

station.

d. Reliability - Medium to High

The resolution of collected data points 

determines whether the reliability 

is medium or high. The higher the 

resolution, the higher the reliability.

e. Specialized Knowledge - Medium

Setup, operation, and data transfer 

 | 4. Data Collection Methods for Pits | 4.1 Subsurface Plane Measurements | 4.1.1 Global Positioning System |
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An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

for differential GPS requires some 

training. Individuals require the ability 

to troubleshoot communication issues 

between the base and the rover in the 

field and knowledge of vendor-specific 

software protocols.

f. Cost - Low to Medium

RTK differential GPS systems cost 

between approximately $10,000 

and $30,000. Instead of purchasing 

an RTK system, users can also rent 

one. Startup costs for non-RTK 

differential GPS systems are lower but 

typically require yearly software fees 

for incorporating data processed by 

the Online Positioning User Service. 

There is a very low annual equipment 

maintenance cost, often $0, associated 

with RTK differential GPS systems. 

For BLM staff, the NOC maintains 

two RTK differential GPS systems. 

The NOC can train individuals on 

the operation of the units or perform 

the data collection if necessary. Travel 

ceiling implications apply when 

considering hands-on training or NOC 

data collection. However, shipping 

costs for the equipment are minimal. 

The largest cost associated with data 

collection via RTK differential GPS is 

typically travel costs (transportation, 

per diem).

g. Overall - Good

Although this method produces highly 

accurate and reliable results, it should 

only be used if the proper expertise is 

available and defensible data are not 

needed.

h. Defensible - No

Typically, GPS points alone are 

insufficient to serve as defensible data.

4.1.2 Laser Scanning

Laser scanning, also referred to as light 

detection and ranging (LiDAR), operates on 

the principle of measuring the amount of 

time it takes a pulse of light to reflect off an 

object and back to the scanner. This provides 

a measurement of the distance between 

the scanner and object, which can create 

scaled 3D models of any object off of which 

the light reflects. The datasets are generally 

referred to as point clouds, with each 

measurement representing a point in space. 

LiDAR captures datasets from the ground 

(terrestrial laser scanning) or from the air 

(airborne laser scanning).

4.1.2.1 Terrestrial Laser Scanning

In terrestrial laser scanning, a laser scanner 

collects data from a stationary location on 

the ground. Sometimes, to capture an entire 

pit with terrestrial laser scanning, multiple 

data locations are necessary.

a. Accuracy - High

Laser scanners can accurately measure 

the shape and size of pits to decimeter 

resolution. External reference control 

(e.g., GPS) is required to georeference 

the location of the resultant model. 

However, laser scanners can create 

accurately scaled models without 

external reference. 

b. Applicability - High

Laser scanners collect information 

from a stationary location. An 

individual can scan most pits from as 

little as two locations. An individual 

can scan small pits from one location, 

assuming all edges of the pit can be 

seen from that location.

c. Level of Effort - Low

The level of effort is low for most pits, 

which require scanning from only one 

or two locations. Larger, more complex 

pits require additional data collection 

locations to adequately capture the 

surface.

d. Reliability - High

The subsurface plane created using 

laser scanning is highly reliable. The 

data collected by the laser scanner 

typically has a low amount of error 

and is accurate and precise. Reliability 

increases when the resolution and 

number of data collection locations 

increase. 

 | 4. Data Collection Methods for Pits | 4.1 Subsurface Plane Measurements | 4.1.2 Laser Scanning
An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

 | Technical Note 448 | June 2016 | 19

e. Specialized Knowledge - Medium

Most individuals require training in 

the operation of LiDAR equipment and 

data processing. However, advances in 

the LiDAR field have resulted in “user 

friendly” LiDAR instrumentation and 

data processing software packages. 

Once trained, data collection and 

processing require little additional 

specialized knowledge.

f. Cost - Medium to High

Laser scanner costs range from 

approximately $40,000 to $60,000, 

depending on the model. This does 

not include training costs. Annual 

maintenance costs are very low, 

often $0.

g. Overall - Good

Though startup costs for laser scanning 

are high, the low maintenance and 

ease of use make it one of the industry 

standard methods in measuring the 

exposed faces of pits. 

h. Defensible - Yes

The models created using laser 

scanning data can be reproduced, 

and when tied to locations with 

external references or ground control 

(e.g., GPS), the models have a high 

defensibility. 

4.1.2.2 Airborne Laser Scanning

Airborne laser scanning uses laser scanners 

that are mounted on manned or unmanned 

aircraft. The laser scanners collect data 

when the aircraft flies over individual site 

locations. Unlike terrestrial laser scanning, 

the sensor is constantly in motion, which 

prevents the user from having to physically 

move the laser scanner to multiple locations 

around the pit.

a. Accuracy - High

Laser scanners can accurately measure 

the shape and size of pits to decimeter 

resolution. External reference control 

(e.g., GPS) is required to georeference 

the location of the resultant model. 

However, laser scanners can create 

accurately scaled models without 

external reference. 

b. Applicability - High

Laser scanners affixed to an aircraft can 

capture nearly every pit that is visible 

from the air.

c. Level of Effort - Medium

Airborne laser scanning is rated 

medium due to the contracting 

or coordination requirements for 

obtaining flight clearances and 

aircraft. The NOC currently does not 

maintain a UAS-ready laser scanner, so 

contracting is necessary.

d. Reliability - High

The subsurface plane created using 

laser scanning is highly reliable. The 

data collected by the laser scanner 

typically has a low amount of error and 

is accurate and precise. 

e. Specialized Knowledge - High

Airborne data collection via aircraft 

requires a licensed and certified pilot, 

a plane, and special equipment. UAS 

data collection requires a pilot certified 

by the Department of the Interior to 

operate the UAS.

f. Cost - Medium

An airborne data collection event can 

cost between $30,000 and $35,000. This 

amount is cost prohibitive if only one 

pit is captured. However, if multiple 

sites lie within a defined geographic 

radius, the cost per site decreases.

g. Overall - Good

Though the cost of the data collection 

mission can be relatively high, 

incorporating multiple sites into a 

single mission can reduce the cost per 

site. LiDAR datasets are defensible, 

accurate, and highly reliable.

h. Defensible - Yes

The models created using laser 

scanning data can be reproduced, 

and when tied to locations with 

external references or ground control 

(e.g., GPS), the models have a high 

defensibility. 

 | 4. Data Collection Methods for Pits | 4.1 Subsurface Plane Measurements | 4.1.2 Laser Scanning |
20 | Technical Note 448 | June 2016 |

An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

4.1.3 Photogrammetry

Photogrammetry calculates a 3D model 

of surfaces using adjacent, overlapping 

photographs. This data collection method 

results in very accurate 3D models by 

using effectively captured photographs of 

an object. The two methods of collecting 

photogrammetric images include ground 

based and airborne.

4.1.3.1 Ground-Based 

Photogrammetry

Ground-based photogrammetry involves 

capturing photographs from either the 

photographer’s eye level or from an object 

extended up from ground level (e.g., 

monopod, cherry picker).

a. Accuracy - High

Photogrammetry can produce 

models that accurately represent the 

shape and size of pits. With current 

photographic technology, this can 

equate to subcentimeter resolution. 

External reference control (e.g., GPS) 

is required to georeference the location 

of the resultant model. However, 

photogrammetry can create accurately 

scaled models without an external 

reference. 

b. Applicability - Medium

In order to create an accurate model, 

the photographer must capture the 

entire exposed face, including the pit 

floor, in overlapping photographs. 

This requires the photographer to 

move the camera around the pit to 

adequately capture the exposed face. 

The greater the complexity of the 

topographic features or the greater the 

size of the pit, the more difficult and 

less applicable this method becomes. 

This is due to the limitations of the 

photographer in reaching the necessary 

vantage points to adequately capture 

the pit stereoscopically, or in stereo. 

c. Level of Effort - Low to High

Photographers can capture small or 

simple pits stereoscopically in less 

than an hour. Larger pits or more 

complex topographic features on the 

exposed surface of pits can prove 

challenging and time consuming, often 

requiring multiple days to capture 

stereoscopically.

d. Reliability - Medium

Assuming the photographer collected 

effective photographs, models derived 

from ground-based photogrammetry 

are reliable. The models fail when 

effective photographs of the pit have 

not been captured, which occasionally 

occurs when collected from the 

ground.

e. Specialized Knowledge - Medium

If not already known, initial training 

of how to capture objects in stereo 

is required. For complex pits, a 

higher level of understanding of 

photogrammetric principles is 

recommended, but not always 

necessary, for successful 3D models.

f. Cost - Low

A fixed-aperture DSLR camera, 

approximately $300, is the minimum 

recommended technology for 

capturing effective photographs. 

Higher megapixel, fully programmable 

DSLR cameras (which range from 

$800 to $6,000) are more reliable. 

Camera and travel costs are the only 

required costs, besides labor hours for 

photogrammetric data collection.

g. Overall - Average

Ground-based photogrammetry is a 

good method for collecting data about 

small pits. Its overall rating decreases 

substantially for larger or more 

complex pits due to the increased level 

of effort and higher chance that the 

models will fail.

h. Defensible - Yes

Successful models created using 

ground-based photogrammetry data 

can be reproduced, and when tied to 

locations with external references or 

ground control (e.g., GPS), the models 

have a high defensibility.

 | 4. Data Collection Methods for Pits | 4.1 Subsurface Plane Measurements | 4.1.3 Photogrammetry |
An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

 | Technical Note 448 | June 2016 | 21

4.1.3.2 Airborne Photogrammetry

Airborne photogrammetric data collection 

involves fixing a camera to an aircraft and 

collecting stereoscopic photographs from 

the air. These aircraft can include a fixedwing or rotary-wing passenger aircraft or 

a UAS. The airborne aspect of this method 

eliminates vantage point issues associated 

with ground-based photogrammetry.

a. Accuracy - High

Photogrammetry can produce 

models that accurately represent the 

shape and size of pits. With current 

photographic technology, this can 

equate to subcentimeter resolution. 

External reference control (e.g., GPS) 

is required to georeference the location 

of the resultant model. However, 

photogrammetry can create accurately 

scaled models without an external 

reference. Occasionally, onboard 

external reference control is included 

with airborne photogrammetry data.

b. Applicability - High

Airborne photogrammetry can capture 

nearly every pit that is visible from the 

air.

c. Level of Effort - Low to Medium

Generally, a pilot is necessary to collect 

airborne photogrammetric data. Either 

contracted pilots or the NOC’s UAS 

services can collect the imagery. UAS 

data collection may require several days 

of field work, depending on the size of 

the pit(s). A minimum of 2 to 4 weeks 

of mission planning is also required to 

use a UAS. Contracted data collection 

missions can be flown in a matter 

of days if the effort meets certain 

contracting criteria. It is possible to 

successfully use kites and balloons at 

smaller sites.

d. Reliability - High

The models derived from airborne data 

collection methods are highly reliable.

e. Specialized Knowledge - High

Airborne data collection via fixed-wing 

aircraft requires a licensed and certified 

pilot, a plane, and special cameras 

and accessories. UAS data collection 

requires a pilot certified by the 

Department of the Interior to operate 

the UAS.

f. Cost - Low to Medium

The NOC maintains two UASs. The 

cost to use these services in 2016 is 

about $4,000, most of which is travel 

costs for the aircraft and certified UAS 

pilot. As of 2016, the NOC covers the 

base salary of NOC UAS pilots. UAS 

services can occasionally be contracted 

for $3,500, depending on the size, 

location, and complexity of the project. 

A contracted fixed-wing data collection 

event generally costs about $20,000. 

However, the fixed-wing data collection 

event can capture multiple pits within 

a geographic area for minimal price 

increases, reducing the cost per site.

g. Overall - Very Good

Airborne photogrammetry provides 

highly accurate, high-resolution 

models of the exposed faces of pits. If 

resources are available, this method 

produces reliable results. Cost and time 

sensitivity are the most prohibitive 

factors with this method.

h. Defensible - Yes

The models created using airborne 

photogrammetry data can be 

reproduced, and when tied to locations 

with external references or ground 

control (e.g., GPS), the models have a 

high defensibility

4.1.4 Analog Measurements

Analog measurements involve the use of 

nondigital devices (e.g., tape measures, 

measuring wheels) to measure the 

dimensions of pits.

a. Accuracy - Low

Errors in analog measurements 

can range from feet to meters. This 

inaccuracy can lead to severe overor underestimation of the volume 

calculation of the pit. 

 | 4. Data Collection Methods for Pits | 4.1 Subsurface Plane Measurements | 4.1.4 Analog Measurements |
22 | Technical Note 448 | June 2016 |

An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

b. Applicability - High

Analog devices can measure virtually 

any pit face that is accessible.

c. Level of Effort - Low

Analog measurements do not require 

much time or resources, other than 

the potential need to traverse terrain 

in order to take the measurements. 

Analog measurements of very large pits 

can take days depending on the tool 

used.

d. Reliability - Low

Inaccurate measurements lead to 

over- or underestimates of volumes of 

material removed from pits. 

e. Specialized Knowledge - Low

Using analog methods to measure the 

faces of pits requires an understanding 

of geometry and how to collect proper 

measurements.

f. Cost - Low

Tape measures or measuring wheels 

cost less than $100. Hand sights range 

from $100 to $500. Certified surveyors 

can make the measurements, though 

these generally require contracting or 

larger amounts of money.

g. Overall - Poor

Analog measurements are appropriate 

when rough estimates are sufficient or 

when other methods are unavailable. 

However, this method is beneficial 

during early site visits to approximate 

the scale of future data collection 

events. 

h. Defensible - No

Unless certified surveyors perform the 

measurements, the plane calculated 

from field measurements is generally 

not defensible.

4.2 Surface Plane 

Measurements 

The surface plane of a pit is usually the 

undisturbed surface prior to mining 

activity and may or may not include soil 

(overburden). Limited methods are available 

to re-create the initial (undisturbed) 

surface plane model. However, in most 

compliance monitoring cases where several 

data collection events occur for the same 

pit, the measurements of the subsurface 

plane from one mission may be used as 

the measurements of the surface plane in 

the next mission. In this section, the data 

collection methods for the surface planes 

of pits include preexisting data, aerial 

photography, “flat cap,” and landscape 

interpolation. If possible, an original 

ground survey should be conducted prior 

to permitting a new pit area in order to 

provide this information for later volume 

calculations.

4.2.1 Preexisting Data

Data used to create the subsurface plane 

of a pit in one data collection effort may 

be used to represent the surface plane in a 

future data collection effort. Preexisting data 

is typically the most reliable source of data 

for calculating changes in material removed 

from pits between points in time. This is 

discussed further in section 7, “Active Mine 

Monitoring Application.”

4.2.2 Aerial Photography

If aerial photography predates mining 

operations and is available in stereo, a 

reliable surface plane can be calculated 

using photogrammetry. However, the 

resulting volume calculation has the 

potential to include overburden material 

(i.e., the material—usually natural rock and 

soil—that overlays the material that will be 

mined). If the photography was captured at 

a point in time when the overburden had 

been removed, then overburden will not 

be included in the volume calculation. If 

the target mine material had not yet been 

mined, then overburden may be included 

in the volume calculation; this is acceptable 

for scenarios in which the total undisturbed 

volume is desired. Otherwise, an estimate 

of the volume of the overburden must be 

subtracted from the volume of the final 

mined material.

 | 4. Data Collection Methods for Pits | 4.2 Surface Plane Measurements | 4.2.1 Preexisting Data |
An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

 | Technical Note 448 | June 2016 | 23

4.2.3 “Flat Cap”

This method is used to create the initial 

surface when preexisting surface data is 

unavailable. The flat cap method assumes 

that the most elevated points of the pits 

represent the widest extent of the surface 

plane. A minimum bounding surface is 

created between these points. The surface 

developed from this approach results in a 

conservative minimum volume estimate.

4.2.4 Landscape Interpolation

Landscape interpolation uses topographic 

information surrounding pits to develop 

a best fit model that represents the natural 

shape of the surface prior to excavation. This 

method generally is very time consuming 

and often results in an unrealistic surface 

plane. 

 | 4. Data Collection Methods for Pits | 4.2 Surface Plane Measurements | 4.2.3 “Flat Cap” |
24 | Technical Note 448 | June 2016 |

An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

5. Data Collection Method Comparisons |

The previous sections present the 

data collection methods as individual 

components. Tables 2 and 3 provide a 

comparative overview of the data collection 

methods for the surface and subsurface 

planes of deposits and pits. 

Table 2. Comparative overview of the surface and subsurface plane data collection methods 

for deposits

 

Surface Plane 

Data Collection 

Methods

Accuracy Applicability Level of 

Effort Reliability Specialized Knowledge

Cost 

(Rating) Cost ($) Overall

Standalone GPS Low Low Medium Very Low 

to Medium Low Low $400 - $3,000 Average

Differential GPS High Medium Medium Medium to 

High Medium Medium $10,000 - $30,000 Good

Terrestrial Laser 

Scanning High Medium to High

Low to 

Medium High Medium Medium to High

$40,000 - 

$60,000 Good

Airborne Laser 

Scanning High High Medium High High Medium $30,000 - $35,000

Average 

to Good

Ground-Based 

Photogrammetry High Medium Low to High High Medium Low $300 - $6,000

Poor to 

Good

Airborne 

Photogrammetry High High Medium High High Low to Medium

$3,500 - 

$20,000

Average 

to Good

Analog 

Measurements Low High Low Low Low Low $100 - $500 Poor

Subsurface Plane 

Data Collection 

Methods

Accuracy Applicability Level of 

Effort Reliability Specialized Knowledge

Cost 

(Rating) Cost ($) Overall

Drilling Varies Medium to 

High High Medium to High High Medium $10,000 - $30,000 Good

Trenching High High High High Medium Medium 

to High

$20,000 - 

$50,000 Good

Geophysics Medium Medium Medium Medium High Low to 

Medium

$3,500 - 

$30,000 Average

Landscape 

Interpolation Low High Low Low Medium Low to Medium $3,500 Poor

Aerial 

Photography

Medium 

to High Low Low High Medium Low $0 - $1,000 Very Good
An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

 | Technical Note 448 | June 2016 | 25

Table 3. Comparative overview of the subsurface and surface plane data collection methods for pits 

Subsurface 

Plane Data

Collection 

Methods

Accuracy Applicability Level of 

Effort Reliability Specialized Knowledge

Cost

(Rating) Cost ($) Overall Defensible

Standalone GPS Low to 

High Medium Medium Very Low to Medium Low Low $400 - $3,000 Average No

Differential GPS High Medium Medium Medium to 

High Medium Low to Medium

$10,000 - 

$30,000 Good No

Terrestrial Laser 

Scanning High High Low High Medium Medium to High

$40,000 - 

$60,000 Good Yes

Airborne Laser 

Scanning High High Medium High High Medium $30,000 - $35,000 Good Yes

Ground-Based

Photogrammetry High Medium Low to High Medium Medium Low $300 - $6,000 Average Yes

Airborne

Photogrammetry High High Low to Medium High High Low to Medium

$3,500 - 

$20,000

Very 

Good Yes

Analog

Measurements Low High Low Low Low Low $100 - $500 Poor No

Surface Plane 

Data Collection 

Methods

Overall

Preexisting 

Data*

Very 

Good

Aerial

Photography Good

Flat Cap Average

Landscape

Interpolation Poor

*This method is only an option where data collection has occurred for the same pit in the past. For the first or a one-time data collection 

event, one of the other methods must be used.
26 | Technical Note 448 | June 2016 |

An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

6. Data Analysis Phase |

After information on both the surface and 

subsurface planes have been collected, 

the data are processed into planes during 

the data analysis phase, the second phase 

for calculating volumes. These planes are 

compared against each other to calculate 

volumes. This section discusses, in general, 

how data are prepared for analysis and the 

methods used to calculate volumes. 

6.1 Data Preparation

After collecting the data regarding target 

objects, some processing is required to 

generate the planes for volume calculation. 

For most analytical methods, both surface 

and subsurface planes are required to 

calculate volumes. The data collection 

methods presented in this document 

typically record the location of data points 

from a surface or the locations of lines of 

data along a surface. Through interpolation, 

planes can be created from these datasets. 

This step is often accomplished through 

contouring and surface modeling software 

packages including Golden’s Surfer or Esri’s 

ArcMap.

Prior to analysis, the surface and subsurface 

planes are aligned where X and Y directions 

correspond to locations in a coordinate 

system. Global (latitude/longitude) or local 

(user-defined) coordinate systems can be 

used. Z values of the planes must represent 

height above a global or local (user-defined) 

datum. After aligning the two planes, 

volumes can be calculated.

6.2 Data Analysis 

Methods

After the surface and subsurface planes 

have been created, volume calculations can 

be derived. The three general methods of 

calculating volumes3 include: 

3

 These methods calculate bank volumes. Factors 

for bulking or compaction need to be discussed 

with engineers and incorporated into the final 

volume calculation.

6.2.1 Digital Terrain Model 

Software

Software suites, such as ArcMap or 

AutoCAD Civil 3D, calculate volumes by 

comparing the differences between two 

surfaces. “Cut and fill” or surface subtraction 

types of analysis calculate distance 

differentials between the two surfaces at all 

regular, defined locations known as subareas 

or cells. Each differential is multiplied by 

the cell’s area to identify a partial volume. 

The partial volumes are added to calculate 

total volume (or total volume of material 

removed). 

6.2.2 Average End Area 

The “average end area” method requires a 

topographic drawing, either surveyed or 

calculated from the surface of a deposit 

or the subsurface of a pit, and a way to 

compute areas, such as an engineer scale or 

software, to determine the area of the target 

object at each contour. The area of each 

contour is determined and multiplied by the 

elevation difference between each contour. 

After each contour level area is multiplied 

by the heights, all calculations are added to 

determine the volume. 

6.2.3 Geometric Calculations 

(Paper/Pencil)

This method relies upon analog 

measurements when no other method is 

available. The shape of the target object is 

approximated or separated in a piecewise 

fashion to known geometries (e.g., cones, 

hemispheres) for which volumes are 

calculated using standard formulas. If 

precise measurements are known, they can 

be used in GIS or CAD software to create 

a 3D polygon for which volumes can be 

calculated. 
An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

 | Technical Note 448 | June 2016 | 27

7. Active Mine Monitoring Application |

Active mines require regular monitoring for 

compliance, which often results in multiple 

data collection events. Two approaches are 

used regularly to calculate the volume of 

mined material. In one approach (Figure 

5), a standard baseline surface plane (e.g., 

undisturbed earth) is used to calculate the 

amount of material removed for each data 

collection event. The subsurface plane is 

measured after each data collection event. 

After each data collection event, the volume 

of mined material is calculated using the 

standard baseline surface plane and the 

newly measured subsurface plane. The 

volume from one data collection event is 

subtracted from the volume of the previous 

data collection event to calculate the amount 

of mined material for each quarter.

For the second approach (Figure 6), instead 

of using a baseline surface plane, the volume 

of mined material is calculated by using the 

subsurface plane from data collection event 

1 as the surface plane for data collection 

event 2; the subsurface plane from data 

collection event 2 as the surface plane for 

data collection event 3; and so on. In either 

approach, data must be maintained from 

one data collection event to the next. If a 

baseline surface plane is not available, it is 

not possible to calculate the running total 

volume with this approach.

Figure 5. In this 

approach, the same 

baseline surface plane 

is used in each data 

collection event, and the 

new subsurface plane is 

measured each time.

Figure 6. In this 

approach, the subsurface 

plane for the previous 

data collection event 

becomes the surface 

plane for the next data 

collection event. The 

new subsurface plane 

is also measured each 

time.

Total volume of

mined material

= 100 yd3

Data collection events

1. January 2. April 3. July

Total volume of

mined material

= 120 yd3

Quarterly volume

= 20 yd3

Total volume of

mined material

= 150 yd3

Quarterly volume

= 30 yd3

100 yd3

120 yd3

150 yd3

baseline surface plane

baseline surface plane

baseline surface plane

subsurface plane 1

subsurface plane 2

subsurface plane 3

Data collection events

1. January 2. April 3. July

Total volume of

mined material

= 120 yd3

Quarterly volume

= 20 yd3

Total volume of

mined material

= 150 yd3

Quarterly volume

= 30 yd3

surface plane 1

surface plane 2

(subsurface

plane 1)

surface plane 3

(subsurface

plane 2)

subsurface plane 1

subsurface plane 2

subsurface plane 3

100 yd3

20 yd3

30 yd3
28 | Technical Note 448 | June 2016 |

An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

8. Glossary |

geometric object concept: the indirect 

calculation of a real world object’s volume 

through construction and analysis of 

a three-dimensional geometric object 

representing that real world object (e.g., 

tailings deposit). The geometric object 

is created through planes of analysis or 

surfaces that are measured (or estimated) of 

the real world object. 

surface plane: one of the measurements 

required to calculate the volume of material 

remaining at a deposit or material removed 

from a pit. The surface plane data source 

varies depending on which target object is 

being analyzed. For deposits, the surface 

plane is the exposed face or measured face. 

For pits, the surface plane is the estimated 

plane or exposed face prior to excavation or 

disturbance. 

subsurface plane: one of the measurements 

required to calculate the volume of material 

remaining at a deposit or material removed 

from a pit. The subsurface plane data source 

varies depending on which target object is 

being analyzed. For deposits, the subsurface 

plane is the estimated plane or the contact 

between the deposit and a reference medium 

(e.g., ground level or undisturbed earth). For 

pits, the subsurface plane is the bottom or 

exposed face of the pit that can be accurately 

measured.

measured plane: the exposed surface of a 

deposit or the bottom of a pit that can be 

directly measured.

estimated plane: either (a) the buried 

contact between a deposit and the earth or 

(b) the preexisting surface that was removed 

in open pit mining. Since these planes, or 

contacts, cannot be directly measured due 

to access or disturbances associated with 

mining, they are estimated.

pit: opening of the earth’s surface used 

for the purpose of extracting rock, ore, or 

minerals. 

deposit: processed or unprocessed earth 

material, including overburden (soil), 

waste rock, fill materials, and tailings, that 

has been removed from the subsurface 

and placed on the ground at a mine. In 

this publication, deposit does not refer to 

geologically emplaced deposits.

tailings: processed or unprocessed rock or 

ore deposits that are economically viable 

based on the precious minerals or other 

resources they contain.

waste rock dump: deposit of earth material 

that is removed during mining to reach ore 

or mineral bodies. Waste rock dumps are 

typically unprocessed. Also referred to as 

overburden.

Global Positioning System: a network of 

satellites that are used to determine the 

location (e.g., latitude, longitude) of an 

object on the earth’s surface by transmitting 

radio waves between the satellites in 

orbit and a receiver on the earth’s surface. 

Common receivers and manufacturers 

include Trimble (Juno, GeoXT) and Leica. 

Most smartphones are embedded with a 

GPS receiver. 

differential GPS: a GPS data collection 

method used to improve the accuracy and 

precision of GPS units. In some cases, 

differential GPS can achieve subcentimeter 

accuracy. The collection of data is achieved 

by the processing of certain phases of GPS 

signals by both a base station (at a fixed 

location) and a rover. In real time kinematic 

differential GPS, a radio attaches to the 

base station that broadcasts the location 

information of the base to the rover, which 

can process the information instantaneously 

and improve location quality.

georeferencing: the process by which an 

image or digital map is assigned location 

parameters in space, usually in a computerbased system, such as a geographic 

information system. For example, a scanned 

topographic map, after georeferencing, 
An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

 | Technical Note 448 | June 2016 | 29

aligns properly in a coordinate system (e.g., 

Universal Transverse Mercator, or UTM) so 

that elevation information for a particular 

point on that map can be extracted.

Deposit Sizes

small: between 1,000 and 20,000 cubic 

yards. Small deposits are typically 

reasonably navigable in at least two 

dimensions (e.g., width, length, or 

height) and can be traversed. Deposits 

at a typical low-production abandoned 

mine are generally on the higher end of 

small deposits.

medium: between 20,000 and 200,000 

cubic yards. For this tech note, mediumsized deposits can be qualitatively 

described as those deposits that are 

larger than the small deposits but 

smaller than the large deposits (i.e., 

deposits unable to be traversed by foot). 

Usually, deposits of a medium size 

can only be easily measured from the 

ground in two dimensions.

large: greater than 200,000 cubic yards. 

These deposits can be larger than office 

buildings. Large (or very large) deposits 

can be hundreds of yards long in a single 

direction and typically are measured 

using remote platforms.

Pit Sizes (Geometric objects representing 

pits are typically much larger than those 

representing deposits.) 

small: small pits have dimensions up 

to 800 meters across and no more than 

100 meters deep. Small pits can stand 

alone or be part of larger pit mining 

operations.

medium: medium pits have dimensions 

up to about 1.5 kilometers across and 

100-250 meters deep.

large: large pits are massive disturbances 

and can have dimensions of several 

kilometers across and up to a kilometer 

deep. 

photogrammetry: the science of making 

measurements from photographs. 

Photogrammetry can produce threedimensional surface models using 

overlapping, adjacent photographs. 

geophysics: the study and analysis of the 

physical properties of the earth’s subsurface 

in order to characterize and interpret 

natural or unnatural structures of the earth’s 

subsurface. Structures may include faults, 

geologic contacts, reservoirs, underground 

tanks, and voids.
30 | Technical Note 448 | June 2016 |

An Overview of Data Collection and Analysis Methods for Calculating the Volume of Mine Materials

9. References |

Atcheson, D.B. 1986. Estimating Earthwork 

Quantities. Lubbock, TX: Norseman 

Publishing Co.

Engineering ToolBox website. 2014. 

www.engineeringtoolbox.com.

Oglesby, C., and R. Hicks. 1982. Highway 

Engineering, 4th ed. New York: John 

Wiley and Sons.

Steinberg, J., and M. Stempel. 1973. 

Estimating for the Building Trades. 

Chicago: American Technical 

Society. 
The mention of company names, trade names, or commerical products does not constitute endorsement

or recommendation for use by the federal government.