Geometric Attributes: Program nonparallelism MEASURING ...mcee.ou.edu/aaspi/documentation/Geometric_Attributes-non...Geometric Attributes: Program nonparallelism Attribute-Assisted

Geometric Attributes: Program nonparallelism

Attribute-Assisted Seismic Processing and Interpretation May 31, 2021 Page 1

MEASURING CHAOTIC VS. CONFORMAL REFLECTORS – PROGRAM nonparallelism

Contents Computation Flow Chart ..................................................................................................... 1

Output file naming convention ........................................................................................... 2

Motivation ........................................................................................................................... 2

Theory ................................................................................................................................. 4

Dip Deviation ................................................................................................................... 4

Amplitude or energy gradient deviation ........................................................................ 6

Total Deviation ................................................................................................................ 7

Invoking the nonparallelism GUI ........................................................................................ 7

Example 1: Great South Basin, New Zealand ...................................................................... 9

Example 2: Offshore Louisiana, USA ................................................................................. 12

References ........................................................................................................................ 19

Computation Flow Chart



Seismic facies such as salt domes, mass transport complexes, and karst collapse features, are usually easier identified by their parallelism of reflector dips, chaotic reflections, and high energy reflections on facies edges. To map these properties of seismic facies, we introduce 3D nonparallelism attributes that highlight lateral variation of parallelism of reflectors and their energy. The nonparallelism attributes provide quantitative measures of reflector dips by extracting statistical components of the 3D seismic amplitude volume.

Output file naming convention Program nonparallelism will always generate the following output files:

Output file description File name syntax

Vector dip deviation from average value

dip_deviation_unique_project_name_suffix.H

Amplitude/energy deviation from average value

gradient_deviation_unique_project_name_suffix.H

Combined deviation of vector dip and amplitude gradient from average values

total_deviation_unique_project_name_suffix.H

Program log information nonparallelism_unique_project_name_suffix.log

program error/completion information

nonparallelism_unique_project_name_suffix.err

where the values in red are defined by the program GUI. The errors we anticipated will be written to the *.err file and be displayed in a pop-up window upon program termination. These errors, much of the input information, a description of intermediate variables, and any software trace-back errors will be contained in the *.log file.

Motivation Dip attribute, measured reflector dipping angle, is significant to differentiate one complex deposition facies from surrounding facies. There are many dip computation algorithms including trace-by-trace cross-correlation (Bahorich and Farmer, 1995), the complex trace analysis (Luo et al., 1996; Barnes, 1996), discrete semblance scans (Marfurt et al., 1998), the gradient structure tensor (Bakker, 2002), the plane-wave destruction (Claerbout, 1992; Fomel, 2002), the predictive painting (Fomel, 2010), and the ratio of smoothed instantaneous wavenumber to smooth instantaneous frequency (Barnes, 2007). In the last few decades, to obtain better lateral resolution of seismic attributes, implementation of local dip to other attribute computation became quite common.



When asked “which dip is useful for machine learning in differentiating seismic facies?”, it could be some kind of continuity dip measurement rather than a specific dip or a dip component. The first statistical measurement of reflector dips was first proposed by Barnes (2002) and measures “parallelism” (or more precisely, deviation from parallelism) which is estimated by the standard deviation of vector dip. Reflector convergence and reflector rotation are also the statistical measures of structure (Marfurt and Rich, 2010). Lateral changes in reflector dips can be measured by curvature or aberrancy, while vertical changes in dips are measured by reflector convergence. In both cases, the strength of these anomalies rather than their strike or azimuth is the differentiating factor. Another kind of seismic attributes in seismic facies analysis is the amplitude attribute, which measures the magnitude or strength of reflectors in seismic amplitude volumes. Derivative approaches to measure amplitude variability are mean amplitude, root mean square (RMS) amplitude, and average amplitude. By Employing Hilbert Transform, one can compute instantaneous envelope and frequency, amplitude volume transform, and other complex trace amplitude attributes to measure amplitude vertical variation. For measuring lateral variation of amplitude, an alternative approach is to compute amplitude gradient along inline- and crossline-axis. When asked “which amplitude is useful for machine learning”, it could be the amplitude attribute that can exhibit either sharp edges of different facies, or strong amplitude contrast between each facies. Marfurt (2006) computed the gradients of peak amplitude of principal-component eigenvectors as coherent amplitude gradients, rather than original amplitude gradients calculated along the geometry of seismic data. Qi et al. (2014) found that the coherent amplitude gradients and its second derivatives of the coherent amplitude gradient are sensitive to subtle lateral amplitude discontinuities such as small (less than 1/4 wavelength) karst collapse features, and joints.



Theory

Dip Deviation Because most 3D data volumes are time-migrated, most dip computations (such as those used in Radon transforms) are computed in terms of s/m or s/ft. Subsequent curvature and aberrancy computations need these dips to be in m/m or ft/ft. For depth-migrated or depth-stretched data this is the expected result; for time-migrated data, we use a simple (constant) velocity in program dip3d and dip3d_gst to provide a (crude) conversion from time to depth. The output of these latter programs is posted in degrees from the horizontal, θx and θy where

tan , and

tan .

x

y

zp

x

zq

y

= =

= =

(1)

The values p and q work well for moderate values of dip but can become quite large for the steep dips that can occur in depth-migrated data volumes. For this reason, we will use the unit normal, n, to dipping reflector planes in our subsequent computations:

( )

( )

( )

1/22 2 2

1/22 2 2

1/22 2 2

,1

, and1

1.

1

x

y

z

pn

p q

qn

p q

np q

=+ +

=+ +

=+ +

(2)

The accuracy of the dip estimation is greatest where the energy is maximum. We therefore weight the three components of the normal nk by an appropriate measure of energy, RMS amplitude, or envelope, ej, at the jth voxel to compute the mean components of the unit normal within a J-voxel analysis window:

1

1

J

j kj

j

k J

j

j

e n

e

=

=

=

. (3)

Given these values, we can find the energy weighted standard deviation of vector dip about its mean to be:

( )1/2

32

1 1

1

J

j kj k

j k

J

j

j

e n

e

= =

=

− =

n , (4)

which in degrees is simply 1

dip sin −=n . (5)





Theory (continued)

Amplitude or energy gradient deviation For relatively conformal reflectors, the amplitude or energy gradient is often a measure of thinning or thickening, or of the lateral change in impedance contrast within a formation with features above or below it. We wish to differentiate such “organized” lateral changes in energy from chaotic changes, such as seen within salt domes, karst collapse, gas chimneys, over-pressured shales, and some areas of mass transport deposits. In program similarity3d, the orientation of the gradient is defined as the gradient of the first eigenvector, which physically represents a map of the energy of the traces that formed the analysis window. The gradient, g, measures the lateral variation in seismic energy (or alternatively RMS amplitude) along structural dip. Because the gradient perpendicular to the reflector is dominated by the time variation of the seismic wavelet, it is ignored. For steep dips, the gradient needs to be compensated by the increasing length of the reflector between adjacent traces. If ξ defines the distance along the reflector in the x-z plane, and η the distances along the reflector in the y-z plane, then

cos , and

cos .

x x

y y

g g

g g

=

= (6)

As with the dip deviation calculation, we first compute the two mean gradient components:

1

1 J

k kj

j

gJ

=

= , (7)

where there is no need to weight by the energy since the gradients were computed as a measure of the lateral change in energy. The amplitude gradient deviation is then

( )1/2

22

1 1

J

kj k

j k

gradient

g

J

= =

− =

. (8)



Invoking the nonparallelism GUI Program nonparallelism is found on the aaspi_util GUI under the Geometric_Attributes tab:

Theory (continued)

Total Deviation The covariance matrix provides a means to compare changes in the analysis window of the unit normal dip vector n and the amplitude gradient vector g. Because the dip is measured in degrees and the gradient in either mV/m or mV/ft we need to normalize both measurements by their RMS values for the entire volume, Rn and Rg, computed previously in programs dip3d and similarity3d, giving

23 2

1/2

1 1n n g

1/2

11

222

1/2

1 g1 n g

1/2

1

kj k kj k kj k

j jk k

JJ

mm

mm

kj kkj k kj k

jkk

J

m

m

n n ge e

R R R

e J e

gn ge

RR R

JJ e

= =

==

==

=

− − −

= − − −

C1

J

j=

, (9)

Where Rn=sin(Rdip). Note that that upper left element of this matrix is the energy-weighted normal deviation, while the lower right element is the amplitude gradient deviation. We define the total deviation as the first eigenvalue of equation 9. If we rewrite C as

a b

c d

=

C , (10)

the first eigenvalue λ1 is

( ) ( ) ( )1/2

2

1

4

2

a d a d ad bc

+ + + − − = . (11)



The following GUI appears:

The first step to (1) define input an energy or RMS amplitude measure to weight the dip computation. Here we use the coherent RMS amplitude computed from program similarity3d. Next, (2) define the inline and crossline structural dip file names computed from program dip3d, then (3) define the inline and crossline energy or RMS amplitude gradient computed from program similarity3d. Place a checkmark in (4) to compute dip deviation attribute and in (5) to compute the gradient deviation attribute. The default analysis window sizes (6) are double those used previously to compute the dip components in program dip3d. Finally, clicking (7) will



execute the process where your main window will show results such as those below that are saved in the *.log file:

Example 1: Great South Basin, New Zealand Example 1 is computed for the GSB subvolume used in much of the geometric and spectral attribute documentation. The input volumes are those used in the previous description of the GUI. Co-rendering the dip deviation and seismic amplitude provides the following image:



Note the stronger deviation (in red) about the U-shaped syneresis features at t=1.45 s and about the progradation at t=1.72 s. The highly parallel features at t=1.3 s appear as blue. A time slice through the progradation at t=1.72 s looks like this



where we note significant dip deviation about the faults as well. Next, examine the same line show previously, but now with the amplitude gradient deviation co-rendered with the original seismic amplitude:

The corresponding time slice at t=1.72 s looks like this



The two gradients exhibit similar features. However, this similarity is because of the geology, not because of the mathematics. In this example, faults in the lower right corner of the two time slices exhibit both a rapid variation in dip and amplitude. Likewise, the progradation also exhibit changes in dip and amplitude.

Example 2: Offshore Louisiana, USA



Figure 1. (a) Time slice at t = 1.22 s, and (b) vertical slice along line AA’ through the seismic amplitude volume.

Our first example is from Gulf of Mexico. We identify salt features of dip, amplitude, and their covariation, which using the nonparallelism. Figure 1. (a) Time slice at t = 1.22 s, and (b) vertical slice along line AA’ through the seismic amplitude volume. Red polygons indicate salt diapirs voxels Figure 2, 3, and 4 show the nonparallelism attributes. Note that the deviation of vector dip (Figure 2a and 2b), and the deviation of energy gradient (Figure 3c and 3d) attributes highlight chaotic salt areas and high energy salt boundaries respectively. However, the covariance of vector dip and energy gradient (Figure 4e and 4f) attribute express both chaotic and high energy features, which shows the merged anomalies from the first two attributes. Note that the deviation of vector dip and the covariance of vector dip and energy highlight salt dome, but also express “salt and pepper” anomalies.



Figure 2(a) Time slice at t = 1.22 s, and (b) vertical slice along line AA’ through the deviation of vector dip



Figure 3 (a) Time slice at t = 1.22 s, and (b) vertical slice along line AA’ through the deviation of energy gradient.



Figure 4 (a) Time slice at t = 1.22 s, and (b) vertical slice along line AA’ through the covariance of vector dip and energy gradient.

The second example is from Fort Worth Basin. Figure 5 shows a time slice at t=0.72 s through the seismic amplitude volume, where carbonate is the dominant formation. We interpret and pick large karst collapse features by yellow polygons. Figure 6, 7, and 8 shows the three nonparallelism attributes. Note, the deviation of vector dip (Figure 6) exhibits karst edges and reflector flexures between the layers of Barnett Shale and Ellenburger formation. The deviation of energy gradient (Figure 7) highlights high energy collapse features and small karst features, which of size is smaller



than ¼ wavelength and showing as scatter lighting dots. The covariance of vector dip and energy (Figure 8) exhibits incoherent karst edges and faults that are like anomalies in coherence.

Figure 5. Time slices at t = 0.72 s through the seismic amplitude volume mapping karst collapse features on Fort Worth Basin. Note yellow polygons indicate karst collapse features that are also painted facies of interest for this dataset.



Figure 6. Time slices at t = 0.72 s through the deviation of vector dip.

Figure 7. Time slices at t = 0.72 s through the deviation of energy gradient.



Figure 8. Time slices at t = 0.72 s through the covariance of vector dip and energy.

References Bahorich, M. S., and Farmer, S. L., 1995, 3-D seismic discontinuity for faults and stratigraphic

features: The Leading Edge, 14, no. 10, 1053–1058. Bakker, P., 2002, Image structure analysis for seismic interpretation: Ph.D. dissertation,

University of Delft. Barnes, A. E., 1996, Theory of two-dimensional complex seismic trace analysis: Geophysics, 61,

264–272. Barnes A. E., 2003, Shaded relief seismic attribute: Geophysics, 68, 1281–1285. Barnes A. E., 2007, A tutorial on complex seismic trace analysis: Geophysics, 72, W33-W43. Claerbout, J. F., 1992, Earth soundings analysis: Processing versus inversion: Blackwell Scientific

Publications. Fomel, S., 2010, Predictive painting of 3-D seismic volumes: Geophysics, 75, A25–A30. Luo, Y., W. G. Higgs, and W. S. Kowalik, 1996, Edge detection and stratigraphic analysis using 3-D

seismic data: 66th Annual International Meeting, SEG, Expanded Abstracts, 324–327. Marfurt, K. J., and R. L. Kirlin, 2000, 3-D broadband estimates of reflector dip and amplitude:

Geophysics, 65, no. 1, 304–320. Marfurt, K. J., and J. R. Rich, 2010, Beyond curvature: Volumetric estimates of reflector rotation

and convergence: 80th Annual International Meeting, SEG, Expanded Abstracts, 1467–1472.



Qi, J., B. Zhang, H. Zhou, and K. J. Marfurt, 2014, Attribute expression of fault-controlled karst — Fort Worth Basin, TX: Interpretation, 2, SF91–SF110.

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Geometric Attributes: Program nonparallelism MEASURING ...mcee.ou.edu/aaspi/documentation/Geometric_Attributes-non...Geometric Attributes: Program nonparallelism Attribute-Assisted