Peak Frequency and Peak Frequency Magnitude Volumes
Introduction
In
this 2part post, a workflow is described on how to create and visualize Peak
Frequency and Peak Frequency by Magnitude volumes. This workflow provides an
enhanced visualization of spectral differences over different lithology and can
be used as a seismic facies classification tool, based on dominant frequency.
The Discrete Frequency volumes can be generated in the Frequency Decomposition
tool using either Constant Q, Constant Bandwidth or the High Definition
Frequency Decomposition within GeoTeric.
Generating
Peak Frequency volumes, using discrete frequencies, allows for delineating subtle depositional and
structural patterns in a manner similar to RGB blending of Frequency
Decomposition volumes. While RGB blend is limited to 3 input volumes, the Peak
Frequency volume can use as many discrete frequencies as desired allowing better
coverage of the spectrum and mapping of subtle frequency variations.
The resulting volume maps, shows for
each voxel, the dominant frequency (frequency with the maximum amplitude). This
provides better understanding of the reservoir heterogeneity as frequencies can
be correlated with thickness and lithology.
Interpretation of
Peak Frequency VolumesFigure 2  Comparison between Envelope (left) and Peak Frequency Volume (right).
The
resulting Peak Frequency volume is shown on the right in Figure 2, compared
with the Envelope volume on the left. One of the main characteristics extracted
from Frequency Decomposition volumes, is the correlation between bed thickness
and frequency (Partyka et al., 1999; Khonde and Rasogi, 2013). Therefore, a Peak
Frequency volume can be interpreted as an estimation of the reservoir
thickness. In the Stybarrow reservoir, it is known that, lower frequencies
correspond to thicker sands, while higher frequencies correspond to the erosional
shale filled channels. As can be seen in the Peak Frequency volume, reservoir
heterogeneity is controlled by erosional channels (1 and 3), and faults
blocks (2 and 4). The bright spot (5)
seen on the envelope can be explained by constructive interference, while best
reservoir properties (thickness and lithology) are found at locations 2 and 4 characterized by lower frequencies.
Those
results can be validated by published inversion results O’Halloran G., et al., 2008 and Glinsky et al., 2005; and 4D monitoring
interpretation – Duncan et al., 2013.
In Part 1 of the post, it is demonstrated how to generate and choose discrete frequencies, create a Peak
Frequency volume and generate the corresponding
1D colour bar for optimal visualization. Part 2 will demonstrate how to create a Peak Frequency by Magnitude volumes.
Part 1  Peak
Frequency Volume
Discrete Frequency volumes
It is recommended to perform noise attenuation and spectral balancing before generating the discrete frequency volumes. Spectral balancing accounts for the loss of energy of higher frequencies generating a flatter spectrum.
Figure 3 
Spectral Balancing
It is
possible to generate discrete frequency magnitude volumes using
any of the frequency decomposition tools available within GeoTeric. The
discrete frequency magnitude volumes can be generated from Constant Bandwidth
and Constant Q Frequency Decomposition
tool under the Normal Preview selection.
On the Data Preview tab it is possible to select the discrete frequency
volumes of interest by marking the adjacent boxes. Give the volumes a name and it will be
followed by the data selected
Note:
Frequency Decomposition tool in GeoTeric provides an option to generate Mode
and Mean frequency volumes. Those volumes provide continuous frequency
readings. While our interest in generating a volume with discrete values for
facies classification and magnitude modulation.
High Definition Frequency Decomposition
To generate discrete frequency volumes using
HDFD go to Stratigraphic > HDFD and Select the spectrally balanced volumes as input. Select central frequencies and press Generate
3D blend. To generate more than three volumes choose different frequencies and
repeat this step until the desired number of discrete frequencies is achieved.
It is recommended to keep even spacing between central frequencies. For
example: 2030405060 Hz.
Peak Frequency volume
With the discrete frequency volumes scaled, open
Workflows >Batch Processing Framework>Processes>Volume Maths
>Parser.
Under
expression type a conditional expression that will assign the central frequency
to the voxels were the corresponding volume has the maximum magnitude. In this
case we have 7 discrete frequency volumes:
(im1>im2 & im1>im3
& im1>im4 & im1>im5 & im1>im6 & im1>im7)*2000 +
(im2>im1 & im2>im3
& im2>im4 & im2>im5 & im2>im6 & im2>im7)*2667 +
(im3>im1 & im3>im2
& im3>im4 & im3>im5 & im3>im6 & im3>im7)*3333 +
(im4>im1 & im4>im2
& im4>im3 & im4>im5 & im4>im6 & im4>im7)*4000 +
(im5>im1 & im5>im2
& im5>im3 & im5>im4 & im5>im6 & im5>im7)*4667 +
(im6>im1 & im6>im2
& im6>im3 & im6>im4 & im6>im5 & im6>im7)*5333 +
The
value after * represents the central frequency, multiplied by 100, to convert Hz
value to integers that would fit the bit rate of the volume (in this case
16bit). The ranges are selected to
maximize the interval assigned to each frequency. Example – 33,33 Hz * 100 =
3333.
Give
the output volume a name and press Run Workflow to generate the volume.
Below,
the peak frequencies are displayed on a horizon, using an inverted Spectrum
colour map. The colour map is inverted to have red corresponding to low
frequency and blue to higher. However to
we need a discrete colour map to properly visualise the peak frequencies.
Create New Colour map
Please follow the link http://blog.geoteric.com/2013/12/createnewgeotericcolourmaps.html to view the complete information on creating
new colour map in GeoTeric. Here a brief case will be illustrated to create a
colour map that will be used for Peak Frequency and Peak Frequency by Magnitude
volumes. This colour map uses hue to
represent the Peak Frequency and saturation to represent its magnitude. A text editor will be needed for part of this
process.
In GeoTeric we need to convert this 2D colour map to a
linear (1D ), where
discrete intervals described by the hue will represent a frequency and the
changes in saturation along this interval will represent magnitude. To do this
we need to select colours to represent the frequency and define a saturation
interval.
It is better illustrated with the example below:
For the central frequency volumes created in the previous
step we define the following intervals.
Table 1 – Central Frequency and Interval Values
Frequency

20 Hz

26,67 Hz

33,33 Hz

40 Hz

46,67 Hz

53,33 Hz

60 Hz

Min value

1333

2001

2668

3334

4001

4668

5334

Max value

2000

2667

3333

4000

4667

5333

6000

Theoretically
intervals are chosen to maximize the range assigned to each frequency. In this
case the volume corresponding to 33,33 Hz will be mapped to the range from 2667
to 3333. This interval will be used for modulation by amplitude as shown ahead.
Here smaller magnitudes will start at the “Min value ”
for each interval and maximum amplitudes at the “Max value” for each interval:
For this step a simpler
colour map could be created that assigns a single colour for each interval.
However we will need the colour modulation for the next steps and creating one
single colour map rather than two can save some time.
In order to create the colour map we
need to convert the interval for each frequency from values to percentages. The
volume generated in the previous step has a data range from 0 to 8191. The
values below 1333 and above 6000 will set to black because they do not have
corresponding frequency volumes and will have no values in the histogram as
will be shown below. Also it is
important to consider the colour map binning, a color map has 9bits (512
bins), and therefore to have correct values, the min and max ranges should
be limited by nearest bins. This assures that in each interval, the min and max
value falls in the corresponding colour bin.
Table 2  Values Ranges
Hz

2000

2667

3333

4000

4667

5333

6000


Min

0

1345

2017

2673

3345

4017

4673

5345

6017

Max

1344

2016

2672

3344

4016

4672

5344

6016

8192

Range

1344

671

655

671

671

655

671

671

2175

%

16.41

8.19

8.00

8.19

8.19

8.00

8.19

8.19

26.55

Table 3 – Colour map file script
<colourmap name="PeakFreq Amplitude (7 volumes)">

Name
that is displayed in GeoTeric

<!(1)>#BLACK
<range width="16.41">
<point>
0.0 0.0 0.0
</point>
<point>
0.0 0.0 0.0
</point>
</range>

First block covering the smallest values. –
0 to 1332  Black
Range in percentage
Start color – Red Green Blue – 0=minimum saturation
1=maximum saturation.
End color – Red Gree Blue.

<!(2)> #RED
<range width="8.19%">
<point>
0.2 0.0
0.0
</point>
<point>
1.0 0.0
0.0
</point>
</range>

Second block – 1333 to 2000 – Red
Range in percentage
Start color – Red Green Blue – 0=minimum
saturation 1=maximum saturation.
End color – Red Gree Blue.

…

Subsequent ranges

</colourmap>

Close color map

The final colour bar has the following
design:
Figure 7 Resulting colour map. To account for values range of the Peak
Frequency volume black interval are added.
And when applied to the volume has the
following histogram for the example volume:
Figure
8 Histogram of Peak Frequency Volume
The horizon with the peak
frequencies displayed with the new colour map.
Figure 9  Peak Frequency Volume with the corresponding colour bar.
The weak contrast between
reservoir internal and external area can be explained as having similar bed
thickness distribution. Adding magnitude modulation to the Peak Frequency,
facilitated its interpretation and adds information on amplitude variations
within each peak frequency. This will be addressed in the next blog post.
(By Pavel Jilinski)
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