Development of an Analytical Method for Ground-based Multi-spectral
Mapping: The Deepwater Deposits at Big Rock Quarry, Arkansas
MARIANA I. OLARIU*†, JOHN F. FERGUSON†, CARLOS L.V. AIKEN†,
and MOHAMED G. ABDEL-SALAM‡
†Geosciences Department, University of Texas at Dallas, P.O. Box 830688, FO
21, Richardson, TX 75083-0688
‡University of Missouri-Rolla, Rolla, MO 65409-0410
This study assesses how well and under what conditions sandstone may be
detected versus shale in a deepwater sedimentary succession using groundbased remote sensing techniques. Multi-spectral images of the outcrop at Big
Rock, Arkansas were co-registered and displayed in Red-Green-Blue colour
space to create false colour images that are useful for highlighting
lithologic variation. Remote sensing analysis for geologic mapping is
common, but here it is applied to digital acquisition from the ground at close
range, obliquely to demonstrate its use in detailed outcrop mapping.
Analyses of the spectral characteristics of sandstone and shale samples over
the visible, near infrared and thermal infrared part of the electromagnetic
spectrum identified spectral responses of these sedimentary rocks indicating
that these rocks can be discriminated using the information contained over
the thermal interval. Normal color images were acquired using a conventional
high-resolution digital camera and infrared images using a thermal infrared
camera. Recently available, handheld, infrared cameras have a spectral
range of 1 to 20 µm and can map rocks at wavelengths that usually can not
be used when remotely measuring spectra through the Earth’s atmosphere
due to the presence of absorption bands. However from the ground this is
possible and a suite of images from visible through thermal infrared of this
outcrop have been used to discriminate lithology.
Keywords: multi-spectral, ground-based infrared thermal image, deepwater,
lithologic mapping
*Corresponding author. Email: mjx011000@utdallas.edu
1. Introduction
In this study, multi-spectral imaging is used to identify lithological units on
outcrops. These methods normally applied in remote sensing from high altitude
airborne and space platforms are modified here for application to close range
imaging.
Imaging spectroscopy is a technique used to spectrally identify and spatially
map rocks based on their specific chemical/mineralogical composition. Today
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spectrometers are used in the laboratory, in the field, on aircrafts, and on
satellites. Absorption bands in the atmosphere (due to water vapour, carbon
dioxide) limit the use of spectral data in remote sensing (figure 1). Therefore
laboratory spectrometers will have a higher spectral resolution compared to
spectrometers that remotely measure spectra through the Earth’s atmosphere
(Floyd 1997). However, these spectral regions can be used at close range
outcrops, since the atmospheric path lengths are shorter.
Technological advances now provide automatic acquisition of satellite
(ASTER, LANDSAT) and airborne (SEBASS - Spatially Enhanced Broadband
Array Spectrograph System, TIMS - Thermal Infrared Multi-spectral Scanner)
photography, but the remotely sensed data are usually too coarsely sampled
(low resolution) for geological outcrop study purposes. Even when instruments are
flown at low to medium altitudes the acquired data is at a spatial resolution of tens
of meters/pixel (Hubbard 1998) or at the best meters/pixel (Smailbegovic 2000).
Detailed geological features exposed on near-vertical cliff faces are difficult to
image from overhead. Newly developed handheld thermal infrared cameras are
now available for the large public, but yet they have not been widely used for
geologic purposes. There are some studies that have successfully used infrared
thermal photography acquired from the ground to map high temperature features
such as lava lakes (Oppenheimer and Yirgu 2002) or for identifying hydraulically
active fractures (Rosenbom and Jacobsen 2005). To our knowledge this is the first
study to map sedimentary features using ground-based thermal infrared imagery.
2. Test Site: Big Rock Quarry, Arkansas
2.1. Geologic Setting
Big Rock Quarry is located in the south-eastern part of the Ouachita Mountains
along the north bank of the Arkansas River in North Little Rock, Arkansas. The cliff
faces of Big Rock Quarry expose a three-dimensional view of the lower part of the
upper Jackfork Group (Jordan et al. 1993). The exposure is oriented at different
angles and is up to 60 m high and almost 1 km long (figure 2).
The Jackfork Group is a succession (about 2000 meters thick) of deep-water
sedimentary rocks that were deposited in the Ouachita Basin during late
Carboniferous. Sediments were derived mainly from the northern and eastern
shelves (Coleman Jr. 2000).
The four facies that crop out at Big Rock Quarry are represented by massive to
parallel-laminated, fine-grained sandstone, shale intraclast breccia with a sandy
matrix, shale intraclast breccia with a shale matrix, and finely laminated shale (Link
and Stone 1986; Cook 1993).
Matrix-supported breccias are the product of cohesive debris flow. Clasts
consist of deepwater sediments eroded by the gravity flows during transport.
These beds commonly show erosional base.
Amalgamated, thick to very thick tabular to irregular-bedded, fine-grained, and
massive sandstones were deposited from high-concentration turbidity currents.
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Individual turbidite beds rarely exceed 30 cm in thickness, but they commonly
occur in amalgamated units that have an average thickness of 1-2 m and
frequently attain thickness of 6 to 8 m.
Thin bedded, massive to planar stratified, fine–grained sandstone deposited
from low-density turbidity currents are separated by discontinuous centimetre
scale siltstone and shale. Sandstone bed thickness ranges from centimetres to 1
meter.
3. Methodology
In order to accomplish this study a specific succession of steps had to be followed.
Rock samples were collected from the outcrop and their reflectance as well as
emittance spectra measured in the lab. Multi-spectral analysis is required to
identify spectral characteristics of the main types of rocks exposed at the outcrop.
Ground-based thermal infrared photography is integrated with conventional
photography to identify lithological units on outcrops. Finally digital image analysis
is performed using a principal component transformation.
3.1. Multi-spectral Analysis
Reflectance and emittance spectroscopy are sensitive to specific chemical bonds
in rocks. Every spectral feature is due to an interaction of photons of particular
energy with the electrons (atoms) in the rock. At different wavelengths, photon
interaction gives rise either to absorption, transmission, or scattering. The nature
of the absorption is unique to the specific chemical structure and therefore
diagnostic for a particular mineral. Absorption features usually are concentrated in
limited ranges of wavelength and between them are portions of the spectrum that
contain little information (Clark et al. 1990).
A reflectance and an emission spectrum of sandstone and shale samples
collected from Big Rock have been acquired in the laboratory using a Geophysical
and Environmental Research (GER) 3700 spectrometer (spectral range from 0.35
to 2.5 μm) and a GX Fourier Transform Infra Red (FTIR) spectrometer (spectral
range from 2 to 14 μm).
The GER 3700 spectrometer has a spectral sample interval of 1.5 nm over the
range 350-1050 nm (spectral resolution 3 nm); 6.5 nm over the range 1050-1900
nm (spectral resolution 11 nm); and 9.5 nm from 1900 to 2500 nm (spectral
resolution 16 nm). Two measurements were required in order to determine the
reflectance of the rock samples: the spectral response of a reference sample and
the spectral response of the sample. The reflectance spectrum was computed by
dividing the spectral response of each rock sample by that of the reference
sample.
The Spectrum GX FTIR spectrometer is capable of collecting spectra in the
near and mid-infrared region with a spectral resolution of better than 1.5 nm. The
Spectrum GX has a microscope accessory with a liquid nitrogen cooled detector
that can be used in either transmittance or reflectance mode. The solid sample
3
was finely pulverized with pure, dry Potassium Bromide (KBr), the mixture was
pressed in a hydraulic press to form a transparent pellet, and the spectrum of the
pellet measured. Potassium Bromide is commonly used for infrared transmission
windows within FTIR spectrophotometers because KBr has no absorptions in the
infrared above 0.4 μm.
In order to explore the spectral signatures of rock samples, a combination
(figure 3) of different data analysis methods (least square modelling, nonlinear
smoothing, and principal component analysis) has been applied. This way, the
spectral signatures of rock samples are related to their distinct mineralogical
compositions.
Reflection spectra are commonly dominated by surface effects and scattering
phenomena that can soften spectral signatures. The source strength is controlled
by sunlight in the reflective region and target temperature in the emissive region
and in both cases the atmosphere contaminates the spectra. Even in the lab the
amount of light that hits the sample controls the intensity of return.
First the data is smoothed with a running median smoother (4253H) and
decimated. 4253H consists of a running median of 4, then 2, then 5, then 3
followed by Hanning. Hanning is a running weighted average, the weights being
1/4, 1/2 and 1/4. Nonlinear smoothers were used instead of linear smoothers, such
as running means because they are resistant to outliers and remove narrow
“spikes” (figure 3(a)). Since the intensity of reflected/emitted radiation is directly
proportional to the incident ‘light’, the observations were converted to a logarithmic
form to overcome the multiplicative effect of the ‘light’ source. This logarithmic
transformation helped to better visualize trends in the data set (figure 3(b)). Then
the data is modeled by a combination of the second degree polynomial trend plus
sinus and cosines terms of wavelengths (figure 3(c)). The model contains a
constant term that adjusts for individual reflectance level differences. Subtraction
of additive model removes multiplicative effect of illumination (figure 3(d)).
Discrimination is based on the difference in spectral shape. Therefore we
standardized the amplitudes of each sample by subtracting the median across all
wavelengths and divided
by
the
standard
deviation across wavelengths
to make the samples comparable.
A principal component analysis (PCA) was performed to isolate independent
components in the spectra. Principal component analysis transforms a number of
correlated variables into a smaller number of uncorrelated variables called
principal components and possibly isolates spectra typical of shale and sandstone
rock types. The first principal component accounts for most of the variance in the
spectra and each succeeding component accounts for decreasing percentages of
the variance (Davis 1986). In our case because the number of variables is large
only the first PCs with eigenvalues contributing with more than 1% to the total
variance were considered.
3.2. Ground-based Infrared Thermal Imaging
There are two principal types of detectors that are used for thermal imaging—
photovoltaic and thermal. Photovoltaic IR detectors produce electric current in
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proportion to the number of incident photons that are shorter than a threshold
wavelength. Thermal detectors make use of the changes in material properties,
most commonly resistance, as absorbed light heats the lattice of the detector
material (Matthews 2004).
Photovoltaic arrays are more sensitive—by an order of magnitude or more—
than thermally-based detectors. However a major drawback to these detectors is
that they must be cooled to cryogenic temperatures (77 K). To maintain these very
low temperatures, the detectors are enclosed in a Dewar with a window
transparent at the required infrared wavelengths. However, such detectors are not
yet available for the large public at wavelengths higher than 11 µm.
Thermal detectors have a significant advantage over photovoltaic types: they
do not require cryogenic cooling. While less sensitive than photovoltaic detectors,
microbolometer pixels will readily respond to a temperature change of less than
0.1° C (Matthews 2004). Uncooled microbolometer arrays are now commonly
available in commercial imaging systems.
Multi-spectral images of the outcrop at Big Rock have been acquired using a
conventional digital camera for the visible range and a PV320 digital camera for
the thermal infrared interval (2-14 μm). The PV320 has an uncooled
microbolometer focal plane array detector. Radiometric calibration of the PV320
camera is done using internal blackbody source references. This method does not
account for the intervening atmosphere emitting radiant energy into the
instantaneous field of view (IFOV) of the sensor system or absorbing energy
emitted from the ground before it reaches the detector. Therefore the data must be
at a high enough pixel resolution to discriminate.
The radiometric, spatial and spectral resolutions of the thermal infrared imaging
system control the detection and mapping of geologic features at different scales.
There is a trade-off between resolution and noise amplification: the poorest value
of resolution corresponds to the maximum value of noise, and decreasing the
noise necessarily produces a higher resolution. There is no way that both
quantities can be improved simultaneously (Milman 1999). Therefore slicing the
spectrum into narrower bands can give more information about surface
composition, but sacrifices resolution.
In our case we were concerned about the individual shale layers which
typically have a thickness of less than 10 - 15 cm. The question was whether or
not the signal from a pixel of 10 by 10 cm and a band pass of 200 nm will be
strong enough to be recorded at the camera sensor.
The thermal band and the three visible bands were co-registered and displayed
in Red-Green-Blue (RGB) colour space to create false colour images that are
useful for highlighting lithologic variation of the outcrop.
Discrimination of different lithology based on the spectral characteristics was
also made using other image processing techniques, such as principal component
analysis. The principal component transformation is effective in enhancing
information present in the scene when there is high correlation between bands.
Therefore it is commonly used to compress multi-spectral data sets. Each
successive principal component image accounts for a progressively smaller
proportion of the variation of the original multi-spectral dataset. Since principal
5
components are orthogonal (uncorrelated) the spectral differences between
different types of rocks may be more apparent in the PC images than in individual
bands.
4. Results
4.1. Spectral Analysis
4.1.1. Analysis of the Reflectance Spectrum
Reflectance spectra of 51 samples (34 sandstones and 17 shales) collected from
Big Rock were measured with a GER 3700 spectrometer. Repeated
measurements have been done for each sample and the results compared. Apart
from an overall albedo change (due to variations in light intensity and to the
roughness of surfaces which cause scattering to occur) the spectra did not
significantly differ (figure 4(a)).
In order to investigate the spectral characteristics of the two types of rocks the
data was modeled using a combination of second degree polynomials and Fourier
series of order 15 that were ulterior removed.
The principal component analysis applied to the residual helped to identify
regions over the short-wave infrared region (SWIR) where sandstone and shale
samples can be discriminated. Since the number of variables is large we will look
at a smaller number of components which will provide the highest explained
variance (table 1). Each observation is converted to a principal component score
by projecting it onto principal component axes. Scatter plots of sandstone and
shale principal component scores show evidence of clustering (figure 5(a)).
Principal component transformation computes a correlation between each
wavelength with each PC to determine how each wavelength is associated with
each component (figure 5(b)). First and sixth principal components show that
wavelengths at about 1.9 μm and 2.2 μm are responsible for differences between
samples.
Since quartz does not have absorption features over visible and near infrared
(Clark 1999) we infer that the spectral characteristics present in the spectral
curves of sandstones are due to the matrix. We did not make any petrographic
analysis, but Jordan et al. (1993) did mention the presence of about 2 to 15%
matrix in their sandstone samples collected from the quarry. This explains the
spectral similarity of the sandstone and shale over the reflective part of the infrared
spectrum.
Shale can be identified spectroscopically based on their characteristic H 2O and
OH absorptions in the spectral region 1.8-2.5 μm. The combination cation–OHbend plus OH stretch produces absorption features near 2.2 to 2.3 μm that are
very diagnostic of all clays (Clark et al. 1990). Also they show strong absorption
features at about 1.4 μm and 1.9 μm. However, strong atmospheric absorption at
these wavelengths due to the presence of water and carbon dioxide and scattering
6
from the surface induce noise that can hinder the extraction of desired information.
Also is well known that weathering and surface roughness dramatically reduce the
band contrast of most materials (Kirkland et al. 2000; Salisbury and Wald 1992;
Salisbury et al. 1987).
When reflectivity values from the spectral curves were converted to brightness
values (from 0 to 255) and the ratio of the two bands (1.9 μm /2.2 μm) calculated it
was inferred that the resulting ratio image will have a low contrast due to the fact
that sandstone and shale will have very close brightness values (129 vs. 128).
Even with a min-max contrast stretch the contrast will not significantly increase.
Also the presence of vegetation in the scene (low brightness values in the SWIR
region) has to be considered. This implies that the sand and shale will appear
identical in the ratio image even if they have different brightness values because
they have similar slopes of their spectral reflectance curves. Therefore these
wavelengths (1.9 μm and 2.2 μm) have not been further considered for spectral
discrimination.
4.1.2. Analysis of the Emmitance Spectrum
Emission spectra of 15 samples (7 sandstones and 8 shales) were measured with
a Spectrum GX FTIR spectrometer. When light of a specific wavelength hits a
particular molecule in the rock the molecule starts vibrating and re-radiates at the
same wavelength of light. This is the process of absorption and emission. The
wavelengths of light that cause molecular vibrations occur in the infrared region.
Every molecule has its own characteristic frequency of vibration. This means that
the infrared light emitted by vibrating molecules can be used to identify them.
The silicate rocks show the typical emissivity minimum at wavelengths of 8 to
12 μm. There is a linear relationship between decreasing silica and increasing
wavelength for the emission minimum. The more silica is present in the rock the
shorter the wavelength where the emissivity minimum occur. Thermal emission
spectroscopy could be used to discriminate among shale and sandstone based on
characteristic absorption bands in these spectral regions.
Laboratory emission spectra of collected samples displayed in Figure 6 shows
that both sandstones and shale have a broad, deep absorption band between 8
µm and 10 µm, with the spectral curves of sandstones shifted to the left compared
to shale spectra. Data was modelled using a combination of second degree
polynomials and Fourier series of order 15 that were ulterior removed.
Based on the principal component analysis wavelengths at 11.8, 12.03, 12.16,
and 13.8 μm have been identified (figure 7) were sandstone and shale can be
discriminated. The first PCs with eigenvalues contributing with more than 1% to
the total variance were considered (table 2). Scatter plots of sandstone and shale
principal component scores show evidence of clustering (figure 7(a)). Particular
PCs differ at particular spectral bands (figure 7(b)).
Overall shale has a higher emissivity compared to sandstone, but always some
overlap occurs between the spectral curves of sandstone and shale samples
therefore a ratio image will be more appropriate for enhancing one of the rock
type. Laboratory measurements show a spectral contrast between the bands
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considered for rationing to be about 5%, except for the sandstone at wavelengths
of 12.03 μm and 13.8 μm which is about 10 to 14%.
Due to the inherent noise in the field (atmospheric attenuation, instrument
noise) it is quite possible that even a 10% spectral contrast is low enough and the
two individual bands will look very similar. In order to test this, narrow band filters
(bandwidth ~250 nm) centred at 12.03 and 13.8 μm were considered to image the
outcrop with a digital thermal infrared camera. It has been proved after taking the
images with the thermal camera using the filters that the selected infrared bands
were too narrow and the signal not strong enough to allow for imaging the outcrop
(the signal-to-noise ratio was too low). The radiometric resolution of the infrared
camera is 12 bits and the integration time is 16 milliseconds. At such a low
exposure time the acquisition of the thermal images with the narrow bandpass
filters has not been possible. Therefore a wide band (2-14 μm) has been used for
the infrared interval.
4.2. Ground-based Thermal Imaging
The aim of this study was to assess how well sandstone may be detected versus
shale in the deep-water sedimentary succession at Big Rock using ground-based
multi-spectral imaging. The information contained in the three visible channels
(red, green, and blue) and a wide thermal infrared band (2-14 μm) has been used
to identify lithological units on outcrop. The thermal channel has been used
because surface temperature distribution may contain relevant information about
rock distribution in the scene. Weathering of sandstone in outcrops due to the
presence of water makes the sandstone darker which makes it harder to
distinguish when occurs together with shale. Since the three visible bands - red,
green and blue- are highly correlated to each other the thermal infrared band has
been used to enhance the contrast between the sandstone and shale in the scene.
Close-range normal colour and infrared images have been acquired at two
locations on the outcrop; based on this they have been named the southeast (SE)
and the northwest (NW) images. Co-registration of normal colour images with the
thermal images has been done using white plaster reflectors (diameter = 12 cm).
We used about 5 reflectors for each image. Discrimination of different lithologies
based on the spectral characteristics has been made using image processing
techniques, such as principal component analysis. A significant amount of shadow
is present in each of the visible images (figure 8). Since the shadows tend to be
classified as a separate class and also the reflectors (high reflectivity in all three
visible bands) a principal component analysis was also performed after the
shadows and reflectors have been removed from the scene. Therefore they
haven’t been considered in the classification.
The principal component transformation was applied to all four bands (red,
green, blue, and thermal). False colour images have been created using the first
three principal components. The last one (the fourth PC) has not been considered
8
since it is the most noisy and also contains the least variation in the data (figures 9
and 11).
Since the three visible bands are highly correlated with each other, the
transformation was also applied only to the highly correlated red, green and blue
bands. Different combinations of the first two principal components and the
thermal band produced better images compared to the case when all four bands
were considered (figures 9 and 11).
Since neither one of the distributions is symmetrical, some data
transformations (taking the logarithm in base 10, taking the square root or rising
the intensity value at each pixel at power 1.5) have been performed to make the
distributions look more Gaussian. The best transformed image for each band has
been chosen for the principal component analysis.
For the NW part of the outcrop the logarithmic transformed images of the
visible and thermal bands (figure 10) have been considered for the principal
component analysis. For the SE part of the outcrop neither one of the
transformations helped. However in the SE image a higher amount of shadow was
present and it had to be removed before performing the principal component
transformation (figure 11).
A close view of the SE outcrop image (figure 12 (a)) reveals the details of the
interbedded pattern of shale and sandstone layers. Thinner layers of shale (cm
thick) have a rougher texture when compared to sandstone, but still they bare
similar spectral characteristics which make it somehow difficult for separating
them. Appling a principal component transformation to the original bands (red,
green, blue, and thermal) and combining the best principal components into a
false colour image helps to better visualize the layering of strata (figure 12 (b) and
(c)) since different lithologies, as well as reflectors and shadows are displayed with
different colours.
5. Discussions
The methodology and analysis presented in this study can be used for any type of
rocks taken in consideration their spectral characteristics. Different types of
infrared cameras can be used to correspond to the interval of the electromagnetic
spectrum were diagnostic features for that type of rock are present.
5.1. Using different types of cameras
To collect the infrared images we used a PV320 thermal infrared camera. This
was relatively accessible equipment having a low spatial and spectral resolution,
but in the future more sensitive cameras like the ones with photovoltaic sensors
should be used. For this study we took close images of the outcrop (from a
distance of several meters) that correspond to an area of about 2m x 3m. In order
to image a larger area of the outcrop the pictures are to be taken from a further
distance which will affect the spatial resolution especially if we think of centimeter
thick shale layers and thin beds of sandstone (tens of centimeters thick). This and
the fact that sandstone and shale occur together with intraformational breccia
which is a mixture of sandstone and shale might affect the way they are displayed
9
in the thermal bands since they have similar spectral signatures. Registration
procedures should be considered carefully for allowing to mosaic pictures taken
from the outcrop into a more comprehensive image of the whole exposure. Due to
the steepness of the cliff faces it was practically impossible to put reflectors on the
walls of the quarry to make the registration process easier. Another matter to be
considered is the proper overlapping of real colour and infrared images. Since the
two types of images are taken at different times and with different types of
cameras a proper overlap of the two is very tedious and time consuming. Time can
be saved by using more expensive cameras with both RGB and infrared channels
which allow for automatic registration between the two images. If this methodology
is combined with the 3-D real photo mapping technique improved models of
outcrops can be obtained with a better three dimensional visualization of the
lithologies, geometries and heterogeneities associated with these.
5.2. Appling this methodology to different lithologies
The sandstone and shale exposed at Big Rock have a similar chemical
composition and therefore similar spectral signatures. Even so the analysis used
in this study helped in discriminating them (figure 12). Since the response at the
infrared camera is mainly controlled by the chemical compositions of rocks this
method can also be used in carbonate outcrop studies where limestone and
dolomite have similar colours, but significant spectral difference. Another example
will be mapping magmatic intrusive bodies especially were the rock colours are
similar, but the spectral signal is different.
6. Conclusions
The two end members (sandstone and shale) chosen for our classification were
quite similar to each other regarding their chemical and therefore their spectral
characteristics. However the procedure developed in this study helped in
discriminating shale and sandstone at the outcrop of Big Rock. Thermal data
allowed separation of rock types with differing thermal properties, but with similar
reflectance characteristics. These encouraging results have demonstrated the
utility of high spatial resolution multi-spectral data as an important tool in geologic
mapping. This methodology can also be applied to any type of rocks such as
carbonates and magmatic rocks.
Acknowledgements
This study benefited from a GCSSEPM Ed Picou Fellowship Grant for Graduate
Studies in the Earth Sciences. The authors would like to thank to Raed Aldouri,
University of Texas at El Paso for providing the GER 3700 spectrometer for
reflectivity measurements and to Mike Sampson from University of Texas at Dallas
for running the emission spectra. The thermal infrared camera was provided by
10
Electrophysics Corporation. Our thanks go also to Jeff Leake for his help with
running the Velocity software.
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Figure caption
Figure 1. Atmospheric transmission over the ultra violet (UV), visible and infrared
(IR) part of the electromagnetic spectrum. Gases responsible for atmospheric
absorption bands are indicated (modified from Floyd, 1997)
Figure 2. Location of the outcrop at Big Rock Quarry (BRQ). The outcrop belt is
located along the north bank of the Arkansas River in North Little Rock, Arkansas.
The exposure is oriented at different angles and is up to 60 m high and 1 km long
(Y is north, and X is east). Locations from where the infrared pictures have been
taken are indicated on the virtual outcrop by the two rectangles.
Figure 3. Procedure developed to explore the spectral signature of sandstone and
shale samples from Big Rock Quarry (here applied to the spectral curve of an
individual shale sample). (a) Raw data (blue) is smoothed with the running median
smoother (4253H) and then decimated (red). (b) Data is converted to a logarithmic
form (green) to overcome the multiplicative effect of the light source. A second
degree polynomial (red) is fit to each log-transformed spectral curve to separate
trends in illumination and reflectivity from spectral details. (c) Trend components
are subtracted from the observations, the amplitude standardized and a mean
spectrum (black) estimated. Fourier series of order 15 (red) models the mean
spectrum after the linear trend is removed. (d) Fourier series model is removed
from each spectrum (green) and the amplitudes are scaled again (red).
Figure 4. Procedure developed to explore the spectral signature of sandstone and
shale samples over the reflective part of the electromagnetic spectrum. (a)
Reflectivity spectra of shale and sandstone samples covering visible and near
infrared wavelengths from 600 to 2400 nm. Each curve represents spectral
characteristics of individual sandstone and shale samples. (b) Data is converted to
a logarithmic form after smoothing with a non-linear smoother (4253H) and
decimation. (c) Residual left after fitting a second degree polynomial to each
spectral curve. (d) Fourier series of order 15 models residuals left after the trend
components are subtracted from the observations. Spectral differences enhanced
in this graph are due to a different mineralogical composition of sandstone and
shale samples.
Figure 5. Principal component analysis applied to the reflective part of the
spectrum. (a) Scatter plots of principal component scores. Each observation was
converted to a principal component score by projecting it onto the principal axes.
Due to their spectral similarity over the visible and near infrared part of the
electromagnetic spectrum it is difficult to discriminate sandstone vs. shale, but
some trends can be noticed on the scatter plots of the scores of the first principal
component. (b) Loading of wavelengths on the first six principal components.
Loadings are weights associated with wavelengths on each component and show
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how much correlation is between that PC and a particular wavelength.
Wavelengths at 1880 nm have high loadings on the first and sixth principal
components.
Figure 6. Procedure developed to explore the spectral signature of sandstone and
shale samples over the thermal part of the electromagnetic spectrum. (a) Emission
spectra of shale and sandstone samples covering thermal infrared wavelengths
from 3 to 14 µm. Each curve represents spectral characteristics of individual
sandstone and shale samples. (b) Data is converted to a logarithmic form after
smoothing with a non-linear smoother (4253H) and decimation. (c) Residual left
after fitting a second degree polynomial to each spectral curve. (d) Fourier series
of order 15 models residuals left after the trend components are subtracted from
the observations. Spectral differences enhanced in this graph are due to a
different mineralogical composition of sandstone and shale samples.
Figure 7. Principal Component Analysis of the emission spectra. (a) Principal
Component Scores. Each observation was converted to a principal component
score by projecting it onto the principal axes. Scatter plots of the first principal
component show evidence of clustering. (b) Loading of wavelengths on the first six
principal components. Loadings are weights associated with wavelengths on each
component and show how much correlation is between that PC and a particular
wavelength. Wavelengths at 10 to 12 µm have high loadings on the first and forth
principal components.
Figure 8. Reflectors and shadows highlighted on the outcrop images taken at Big
Rock. (a) SE outcrop image with reflectors (left) highlighted in white and shadows
(right) in black (b) NW outcrop image with reflectors (left) highlighted in white and
shadows (right) in black (reflectors diameter = 12 cm).
Figure 9. Principal Component Analysis applied to the NW outcrop image. (a)
Original images have been registered to each other and the normal colour image
resampled so the number of pixels will correspond to the number of pixels in the
thermal image (see reflectors for scale; diameter = cm) (b) Principal component
transformation applied to all four bands (red, green, blue, thermal) (c) Principal
component transformation applied only to the highly correlated visible bands (d)
Principal component transformation applied to the log transformed images (e)
Normal and false colour images of the outcrop From left the first one is a highresolution, normal colour image (RGB); the second one is a combination of the
first three principal components in (b) (green = sandstone, blue = shale, pink =
shadows, black = reflectors); the third image is a combination of the first two
principal components in (c) and the thermal band (purple = sandstone, blue =
shale, orange = shadows, green = reflectors) and the forth one combines the first
three principal component images in (d) (dark green = sandstone, blue = shale,
pink = shadows, yellow-green = reflectors).
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Figure 10. Transformed images and the corresponding histograms. Each of the
histograms shows the pixel distributions in each of the original red, green, blue,
and thermal images before and after performing different transformations (raising
the intensity value at each pixel at power 1.5, estimating the square root or taking
the logarithm in base 10) to make the distributions look more Gaussian.
Figure 11. Principal Component Analysis applied to the SE outcrop image. (a)
Original images have been registered to each other and the normal colour image
resampled so the number of pixels will correspond to the number of pixels in the
thermal image (b) Principal component transformation applied to all four bands
(red, green, blue, and thermal). (c) Principal component transformation applied
only to the highly correlated visible bands. (d) Principal component transformation
applied to all four bands after shadows and reflectors have been removed. (e)
Normal and false colour images of the outcrop. From left the first one is a normal
colour image (RGB); the second one is a combination of the first three principal
components in (b) (light blue = sandstone, dark blue = shale, light green =
shadows, pink = reflectors); the third image is a combination of the first two
principal components in (c) and the thermal band (purple = sandstone, light blue =
shale, orange = shadows, dark blue = reflectors) and the forth one combines the
first three principal component images in (d) (pink = sandstone, red = shale, light
green = shadows and reflectors).
Figure 12. Close-up images (RGB and false colours) of the outcrop displayed in
Figure 11 showing layers of sandstone interbedded with shale (a) Normal (RGB)
colour image (reflectors diameter = 12 cm; sandstone = ss; shale = sh) (b)
Combination of the first three principal components obtained from the principal
component transformation applied to all four bands - red, green, blue, and thermal;
(greenish brown = sandstone, light blue = shale, light green = shadows, red =
reflectors) (c) Combination of the thermal band and the first two principal
components obtained from the principal component transformation applied only to
the highly correlated visible bands (purple = sandstone, light blue = shale, pink =
shadows, dark blue = reflectors).
Table 1. Statistics for the principal component analysis. The first 23 eigenvalues of
the covariance matrix are considered here in descending order, with the first one
accounting for the highest percentage of total variance. Note that these first 23
components account for over 99% of the total variance, with only 7 of them
contributing to more than 90% of the total variance.
Table 2. Statistics for the principal component analysis. Only the first 8
eigenvalues of the covariance matrix are shown here in descending order, with the
first one accounting for the highest percentage of total variance. Note that these
first 8 components account for over 99% of the total variance.
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