OW Attributes

Landmark PostStack Family Reference Manual

Trace Attributes

PostStack converts conventional traces into trace and complex attributes. You can output the converted data directly to a seismic datafile and use it for interpreting in SeisWorks. Or you can use the trace data for the next process in the flow.

If your goal is to extract attribute horizons from the complex trace data with PAL, you do not have to output the data to a disk file. The program holds the converted data in memory and uses it for input to the attribute extraction. After each trace is processed through the flow, the memory is purged of the complex trace data. To take advantage of this disk-saving option, toggle off all the Output Data options in PostStack/PAL.

In This Chapter:

• “Overview” on page 162

• “Instantaneous Attributes” on page 166

• “General Attributes” on page 193

• “Math Attributes” on page 199

• “Reflection Pattern Attributes” on page 205

• “References” on page 227

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PostStack Family Reference Manual Landmark

Overview

This section lists the trace attributes calculated, the methodology used, and the concept of a complex trace.

Trace Attributes Calculated

Trace attributes are contained under three main categories as listed below.

Instantaneous (Complex)

• Quadrature Trace (page 166)• Reflection Strength (page 166)• Phase (page 171)• Frequency (page 173)• Apparent Polarity (page 177)• Bandwidth (page 179)• Quality Factor (page 179)• Dominant Frequency (page 180)• Amplitude Acceleration (page 180)• Response Phase (page 177)• Response Frequency (page 184)• Perigram (page 186)• Cosine of Phase (page 188)• Perigram ∗ Cosine of Phase (page 190)

General

• Integration (page 193)• Differentiation (page 194)• Energy Half-Time (page 195)• Arc Length (page 196)• RMS Amplitude

Math

• Absolute Amplitude (page 199)• Log Base e (page 200)• Log Base 10 (page 200)• Exponential Base e (e**Amp) (page 201)• Exponential Base 10 (10**Amp) (page 202)• Power (Amp**Power) (page 203)

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Reflection Patterns

• Amplitude Variance (page 206)• Azimuth (page 207)• Dip (page 209)• Divergence (page 211)• Hummocky (page 213)• Parallelism (page 215)• Shaded relief (page 217)• Similarity (page 221)• Spacing (page 224)

You can calculate any of these trace attributes using Data Attributes. and selecting the desired attribute. There are no parameters for data attribute calculation.

Methodology

Complex trace analysis separates amplitude and phase information. The data attribute options provide different ways of viewing and combining the extracted amplitude and phase information.

Complex trace data is calculated following the procedure. Input data is converted to the frequency domain by performing a Fast Fourier Transform (FFT). To prevent undesirable data wraparound effects, significant data padding is used before applying FFTs.

The Concept of a Complex Trace

The complex trace consists of a real component (the conventional seismic trace) and an imaginary component (the quadrature trace):

F t( ) f t( ) ih t( )+=

where f(t) is the recorded traceh(t) is the quadrature tracei is the square root of -1.

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The quadrature trace can be uniquely determined from the recorded trace using the Hilbert transform (Bracewell 1965):

In practice, is a 90o phase-shifted version of . All other complex trace attributes are derived from the quadrature trace and the recorded trace.

Derivation of Four Data Attributes

The recorded trace can be expressed in terms of a time-dependent amplitude and a time-dependent phase , as follows:

The quadrature trace is then

and the complex trace is

If and are known (remember can be derived from using the Hilbert transform), one can solve for and :

is called “reflection strength,” and is called “instantaneous phase,” after Bracewell (1965).

h t( )f t( )

where ∗ denotes convolution.

∗h t( ) 1πt-----= f t( )

h t( ) f t( )

f t( )A t( ) θ t( )

f t( ) A t( ) θ t( )cos=

h t( )

h t( ) A t( ) θ t( )sin=

F t( )

F t( ) f t( ) ih t( )+=

F t( ) A t( ) θ t( ) iA t( ) θ t( )sin+cos=

F t( ) A t( )eiθ t( )=

f t( ) h t( ) h t( ) f t( )A t( ) θ t( )

A t( ) f2 t( ) h2 t( )+ F t( )= =

θ t( ) h t( ) f t( )⁄[ ]tan 1∠=

A t( ) θ t( )

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Then, taking the derivative of instantaneous phase yields “instantaneous frequency”:

Taner et al (1979) first described the significance of the quadrature trace and introduced reflection strength, instantaneous phase, and instantaneous frequency to the geophysical community.

Practical Use

The algorithms for computing complex trace attributes are designed to provide exact values for each time sample. In practice, the specific values are not as important as the trends in the attribute. These trends can be readily seen when complex trace data is displayed in Seismic View or when an attribute horizon is extracted via PAL and displayed in Map View. An interpreter tends to use the complex trace attributes to infer geologic significance from the data, not to extract specific attribute values.

Generally you will want to consider several different complex trace attributes for the area of interest. “The various attributes reveal more as a set than they do individually,” Taner et al (1979) note. “Features often are anomalous in systematic ways on various displays.”

ω t( ) dθ t( )dt

-------------=

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Instantaneous Attributes

PostStack calculates the following Instantaneous Attributes. These are the complex trace attributes. All the instantaneous measurements are associated with an instant of time rather than an average over a time interval.

To deduce any stratigraphic meaning from the seismic data before estimating the instantaneous parameters, the amplitude and frequency content of the seismic signal must be preserved in each processing step. Any variation in the shape of the basic waveform that is not attributable to the subsurface geology must be eliminated. Multiples and all types of random noise limit the reliability of the results.

Quadrature Trace

The quadrature component is calculated by performing a Hilbert transform on the recorded trace:

A quadrature trace is identical to the recorded trace but phase-shifted by 90°. It can be thought of as representing potential energy while the recorded trace represents the kinetic energy of particles moving in response to the seismic wave. Quadrature trace is used as the basis for all other seismic attribute calculations.

Uses

Since quadrature data is simply the input data phase-rotated by 90°, it contains no new information, but it gives you another perspective. Because of the phase rotation, peaks and troughs from the input data appear as zero crossings in the quadrature data, and zero crossings from the input data appear as peaks and troughs in the quadrature data. The difference in wavelet appearance may be enough to highlight certain features that were obscured on the recorded data.

where ∗ denotes convolution f(t) is the recorded traceh(t) is the quadrature trace.

∗h t( ) 1πt-----= f t( )

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Also, a comparison of the quadrature data and the recorded data may indicate that neither is zero phase and a phase rotation is needed. You can analyze and correct phase problems with Seismic Balance, or you can use the phase rotation option in PostStack.

Furthermore, quadrature data may help you understand and check other trace attributes since all complex trace attributes are merely different mathematical combinations of the recorded trace and the quadrature trace.

Example

A comparison of recorded seismic data and quadrature data is shown on the next page.

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In the recorded seismic data, the gas-oil contact (flat horizon) corresponds to a large peak event. In the quadrature data, it corresponds to a zero crossing, which is simply a 90° phase rotation of the peak. Note that the peak energy is pulled upwards in time because of this -90° phase shift.

Reflection Strength

Instantaneous amplitude, or reflection strength, is the square root of the total energy of the seismic signal at an instant of time. Reflection strength can then be thought of as amplitude independent of phase. It is

-128 +127

-128 +127

Quadrature

-128 +127

recorded seismic data


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the envelope of the seismic trace. For each time sample, reflection strength is calculated as follows:

Therefore, reflection strength is always positive and always in the same order of magnitude as the recorded trace data.

Uses

Reflection strength is an effective tool to identify bright and dim spots.It provides information about contrasts in acoustic impedance. Lateral changes in reflection strength are often associated with major lithologic changes or with hydrocarbon accumulations. Gas reservoirs, in particular, frequently appear as high-amplitude “bright spot” reflections.

Sharp changes in reflection strength may be associated with faults or depositional features such as channels. Reflection strength is also useful in identifying subcropping beds and may aid in distinguishing one massive reflector, such as an unconformity, from a composite group of reflectors.

Reflection strength also provides a means of detecting and calibrating thin-bed tuning effects, which may result from the constructive and destructive interference of reflector wavelets.

Example

An example of recorded seismic data and reflection strength data for the same section is shown below. Interpreted time horizons appear at

√ (recorded trace)2 + (quadrature reflection

Illustrations in this chapter

Throughout this chapter, the same area of interest and same time horizons are shown on recorded seismic data and on various types of complex trace data. These illustrations were created by doing the data conversion in PostStack (which generates a .3dv file of the complex trace data) and displaying the complex trace .3dv in SeisWorks.

In these examples from the Roar gas field in the Danish Central Graben, the uppermost horizon is the Top Chalk reflector. Beneath it, a flat spot (associated with a gas-oil fluid contact) and an interpreted unconformity are visible (Abatzis and Kerr 1991).


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the same location on the reflection strength data as on the recorded data.

Reflection strength is a measure of the magnitude of the amplitude response, regardless of sign. Peaks and troughs in the recorded seismic data both correspond to high amplitudes in the reflection strength display. Note that reflection strength contains only positive values, and its maximum value can exceed the maximum value seen in the recorded trace data.

In this example, the gas reservoir corresponds to a zone of high reflection strength values. The gas-oil contact can be seen to correspond to a local reflection strength high. At the edges of the reservoir, tuning effects are evident as the Top Chalk reflector and

+1270

-128 +127

0 +127


Reflection Strength


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gas-oil contact combine into a single, composite reflection strength maximum.

Phase

The instantaneous phase is a measure of the continuity of events on a seismic section. The temporal rate of change of the instantaneous phase is the instantaneous frequency.

Phase describes the angle between the phasor (a rotating vector formed by the real and imaginary components of the time-series) and the real axis as a function of time. Therefore, it is always a number between -180° and +180°.

Instantaneous phase data has a discontinuous, sawtooth appearance caused by the sudden phase-wrapping from +180° to -180°. For a more normal looking display, you can use cosine of phase (page 188). Taking the cosine of instantaneous phase essentially unwraps the data.

Uses

Instantaneous phase tends to enhance weak coherent events because it is independent of reflection strength. It emphasizes the continuity of events and is therefore helpful in revealing faults, pinchouts, angularities, channels, fans, and internal depositional geometries. Phase displays often reveal sedimentary layering patterns and thus can help you in identifying seismic sequence boundaries.

In certain gas reservoirs, instantaneous phase may be used to identify and map phase reversals, which are indicative of gas content. This attribute can also be used to detect and calibrate thin-bed tuning effects, which may result from the constructive and destructive interference of reflector wavelets.

Example

A comparison of recorded seismic data and instantaneous phase data is shown on the next page.


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On the recorded seismic data the gas-oil contact (flat horizon) consistently tracks a maximum. On the instantaneous phase data, this interface corresponds with a phase value of 0° (trough-to-peak zero crossing).

The polarity reversal in Top Chalk, evidenced in the recorded data by a change from a trough along the top of the reservoir to a peak beyond the edges of the reservoir, is also apparent in the instantaneous phase data. Above the gas-oil contact, Top Chalk tracks along the point of phase wrapping (+180° to -180° phase). Below the gas-oil contact, the changing fluid content results in a change in phase for Top Chalk. The reflector now tracks at 0° phase.

+127

-128 +127

-180 +180

Instantaneous Phase

-128 +127



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In general terms, as recorded seismic data moves from a peak to a trough, the instantaneous phase changes from 0° to +180°. At the trough, the phase wraps from +180° to -180°. In the instantaneous phase display on the previous page, the instances of phase wrapping can be clearly seen wherever the trace crosses from positive to negative phase. As the recorded data moves from a trough to a peak, the instantaneous phase changes from -180° to 0°.

Any horizon that has been snapped to an onset type should reveal a constant phase angle in an instantaneous phase display. In general, horizons picked on peaks and troughs in the normal seismic display will be displayed at zero crossings and at points of phase wrapping, respectively, in the instantaneous phase display.

Regardless of the amplitude value at the peak or trough, the magnitude of the instantaneous phase will always be the same (0° for peak amplitudes, ±180° for troughs). In other words, instantaneous phase tends to equalize weak and strong events and thus makes it easier to track weak, coherent events.

Frequency

Frequency represents the rate of change of instantaneous phase as a function of time. It is a measure of the slope of the phase trace and is obtained by taking the derivative of the phase. Values may range from -Nyquist frequency to +Nyquist frequency; however, most instantaneous frequencies will be positive.

+180-180

+180-180

0-128 +127

maximum

minimum

zero (-/+)

zero (+/-)

0

Amplitude Trace Instantaneous Phase Trace

(-128) (+127)

phase wrapping


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Uses

Instantaneous frequency can provide information about the frequency signature of events, the effects of absorption and fracturing, and depositional thickness.

Low-frequency shadows may be associated with reflectors below gas sands, condensate, and oil reservoirs. Generally this shift to lower frequencies occurs only on reflectors immediately beneath the producing zone; deeper reflectors appear normal. Also, loss of higher frequencies may indicate the onset of formation pore fluid overpressure.

Instantaneous frequency also provides a means of detecting and calibrating thin-bed tuning effects, which may result from the constructive and destructive interference of reflector wavelets.

Because it represents a value at a point rather than averaged over an interval, instantaneous frequency can reveal abrupt changes that would otherwise get lost in the averaging process. Such changes could indicate pinchouts or the edges of hydrocarbon-water interfaces. Instantaneous frequency is, therefore, a good check-and-balance to use in combination with other measurements.

Example

A comparison of instantaneous phase and instantaneous frequency data is shown on the next page.


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In the instantaneous phase display, the slope of the phase trace changes with time. The time between any two troughs varies down the trace, even though the phase always moves between -180 and +180. The measure of the slope of the phase trace is the derivative of the phase. The steepness of that slope is a measure of the frequency at that point in the trace.

Since instantaneous frequency is the slope of the instantaneous phase, negative values are possible and valid. The instantaneous frequency will never have a value greater than the Nyquist frequency, or the reciprocal of twice the sample rate.

-180 +180

-Nyquist +Nyquist

Instantaneous Frequency

-180 +180

Instantaneous Phase


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Spikes in the instantaneous frequency display correspond to minimums in the reflection strength data, as shown below. Small changes in amplitude in these areas can result in relatively large slope changes and are seen as spikes in the instantaneous frequency display. These spikes are essentially noise.

In the Roar field example, a slight lowering in instantaneous frequency occurs below the thickest part of the reservoir. At the edges of the reservoir, where the Top Chalk reflector intersects the flat gas-oil contact, the instantaneous frequencies remain high. The lower frequencies beneath the reservoir are likely due to gas absorption effects.

-Nyquist +Nyquist

0 +127

-Nyquist +Nyquist


0 +127

Reflection Strength


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Apparent Polarity

Apparent polarity is defined as the sign of the recorded trace where the reflection strength trace has a local maximum. This calculation assumes a zero-phase wavelet and assigns a positive sign when the reflection coefficient is positive or a negative sign when the reflection coefficient is negative.

The value of a time sample corresponding to a local maximum (m) on the reflection strength trace is computed as

This value is held constant and applied to all time samples until the next local maximum occurs. As a result, apparent polarity displays have a blocky appearance. Compare apparent polarity with response phase, where instantaneous phase values are applied between minima; and with response frequency, where instantaneous frequency values are applied between minima.

Apparent polarity measurements are extremely sensitive to data quality.

Uses

Apparent polarity can sometimes help you distinguish between different types of amplitude anomalies. As Taner et al (1979) point out, “Bright spots associated with gas accumulations in clastic sediments usually have lower acoustic impedance than surrounding beds and hence show negative polarity for reservoir top reflections and positive polarity for reflections from gas-oil or gas-water interfaces (often called ‘flat spots’).”

Example

A comparison of recorded seismic data, reflection strength data, and apparent polarity data is shown on the next page.

Valuem ReflectionStrengthm Signm×=


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0 +127

Apparent Polarity

-128 +127

-128 +127

0 +127


Reflection Strength


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In the recorded seismic data, the gas-oil contact (flat horizon) corresponds to the center of a zone with large amplitudes and positive polarity. In the apparent polarity display, this interface is even more prominent since the effect of apparent polarity is to highlight both the dominant amplitude and the polarity of the event.

The Top Chalk reflector exhibits negative apparent polarity above the reservoir and positive apparent polarity beyond the edges of the reservoir. The change is due to the changing fluid content. The gas-oil contact exhibits large, positive apparent polarity values. Note that our example agrees with Taner et al’s (1979) statement that tops of gas reservoirs often have negative polarity and gas-oil contacts, positive polarity.

Bandwidth

Instantaneous bandwidth (t) is defined as absolute value of the time rate of change of the natural logarithm of the instantaneous amplitude, a(t), divided by 2 :

This might be better considered a measure of half bandwidth. Instantaneous bandwidth has units of Hertz and can take any value from 0 to Nyquist. Typically it has about half the value of instantaneous frequency and only rarely exceeds instantaneous frequency.

Uses

Instantaneous bandwidth is used in quantifying amplitudes by their sharpness rather than by their magnitude. Sharper amplitude changes give rise to greater bandwidth.

Quality Factor

Instantaneous quality factor q(t) is defined as the instantaneous frequency f(t) divided by twice the instantaneous bandwidth (t):

σ

π

σ t( ) 12π------ d

dt----- a t( )ln a' t( )

2πa t( )----------------=⋅=

σ

q t( ) f t( )2σ t( )-------------=


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Instantaneous quality factor is dimensionless. Typical values range from 1 to 5; anomalous values are either much larger or less than 0.5.

Uses

Instantaneous quality factor is useful for identifying similar waveforms and anomalies caused by wavelet interference.

Dominant Frequency

Instantaneous dominant frequency fd(t) is defined as the square root of the sum of the squares of the instantaneous frequency f(t) and the instantaneous bandwidth (t):

Dominant frequency has units of Hertz with values that range from 0 to Nyquist frequency and occasionally larger. It is always positive and at least as large as instantaneous frequency.

Uses

Instantaneous dominant frequency is used as a replacement for instantaneous frequency, because it is less susceptible to the problem of spikes and a better measure for tracking reflection spacing.

Amplitude Acceleration

Instantaneous amplitude acceleration (t) is defined as the second derivative of the logarithm of the reflection strength. It is scaled to have units of Hz/s. Like all second-order attributes, it is wildly variable and hence should be interpreted qualitatively and not quantitatively. In particular, it can have huge values, and tends to spike at the same places where instantaneous frequency spikes. As a result, scaling this attribute can be difficult.

Uses

At a workshop at the 1997 Dallas SEG convention, T. Taner touted the merits of this attribute, arguing that it can reveal detail in the amplitude

σ

fd t( ) f2 t( ) σ2+ t( )=


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of the data that was not before apparent. Oliveros and Radovich (1997) and Radovich and Oliveros (1998) employ this attribute as the basis for a 3D instantaneous continuity computation. Amplitude acceleration in fact can in fact highlight some discontinuities, and can reveal thin beds that cannot be found on other common displays. It produces a display that looks rather like a noisy “cosine of the phase” display, but with additional features that complement the cosine of the phase. It appears especially good at helping distinguish areas of continuous reflectivity from areas of chaotic or hummocky reflectivity.

Response Phase

The concepts of response phase and response frequency were taken by Bodine (1984) from signal analysis and applied to geophysical waveform analysis. Response phase attempts to extract physically meaningful phase information about the localized seismic wavelet.

Response phase is defined as the instantaneous phase calculated at the peak of the amplitude envelope (reflection strength). The algorithm computes the instantaneous phase at each envelope peak, then applies that value to every sample between minima in the amplitude envelope trace. As a result, a response phase trace has a blocky appearance. Compare response phase with apparent polarity, where reflections strength values are applied between minima; and with response frequency, where instantaneous frequency values are applied between minima.

Uses

A response phase display will emphasize the dominant phase characteristics of the reflectors. Response phase is also useful for detecting phase changes associated with lateral fluid content or even lithologic changes.

Bodine (1986) suggests that response phase and response frequency may be used to distinguish between pay zones and nonpay zones with similar amplitude response. He gives the example of two seismic bright spots. One with low frequency and -90° was a gas reservoir; the other with high frequency and +90° was merely a tight streak.

Example

A comparison of instantaneous phase, reflection strength, and response phase follows. In both the instantaneous phase and response phase


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displays, the gas-oil contact (flat horizon) generally exhibits a phase of 0° (trough to peak zero-crossing).

The phase reversal of the Top Chalk reflector is not clearly exhibited in the response phase display. The reason for this can be seen by examining the reflection strength data. Top Chalk does not correspond to a local reflection strength maximum; therefore, the response phase information is associated with adjacent reflectors.


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0 +127

Reflection Strength

+180-180

+180-180

Response Phase

-180 +180

Instantaneous Phase


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Response Frequency

The concepts of response frequency and response phase were taken by Bodine (1984) from signal analysis and applied to geophysical waveform analysis. Response frequency attempts to extract physically meaningful frequency information about the localized seismic wavelet.

Response frequency is defined as the instantaneous frequency calculated at the peak of the amplitude envelope (reflection strength). The algorithm computes the instantaneous frequency at each envelope peak, then applies that value to every sample between minima in the amplitude envelope trace. As a result, a response frequency trace has a blocky appearance. Compare response frequency with response phase, where instantaneous phase values are applied between minima; and with apparent polarity, where reflection strength values are applied between minima.

Uses

Response frequency has much the same uses as instantaneous frequency. However, a response frequency display may be more interpretable in areas where the instantaneous frequency displays are quite noisy.

Response frequency will emphasize the dominant frequency characteristics of the reflectors. This data may be useful in detecting the effects of frequency absorption related to fluid content, fracturing, or changing depositional environments.

Example

A comparison of instantaneous frequency, reflection strength, and response frequency is shown on the next page.

Note the slight lowering of response frequency values beneath the thicker parts of the reservoir. At the edges of the reservoir and off the reservoir, response frequency remains high and relatively constant. The higher response frequency values at the edge of the reservoir are due to reduced absorption as the gas column thins.


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0 +127

Reflection Strength

+Nyquist Nyquist

Response Frequency

-Nyquist +Nyquist

-Nyquist +Nyquist



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Perigram

Perigram is the amplitude envelope (reflection strength) with the dc component removed. Gelchinsky and his colleagues suggested that such a display would make the locations of energy maxima more obvious in the seismic section (Gelchinsky et al 1985, Shtivelman et al 1986).

The low-frequency component of the reflection strength is calculated as follows:

Then that low-frequency component, A (t), is subtracted from the reflection strength, A (t), to produce the perigram, g (t):

Uses

Perigram has essentially the same uses as reflection strength; but because perigram data has both positive and negative values, it can be analyzed with the standard color maps and can be subjected to trace mixing or other data enhancement processes. Reflection strength data, because it is only positive, is not suitable for many types of analysis and processing.

Example

A comparison of the amplitude envelope (reflection strength) and the perigram is shown on the next page.

A t( ) 1T∆

------- A τ( ) τdt T 2⁄∆∠( )t T 2⁄∆+( )∫=

g t( ) A t( ) A t( )∠=


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The waveform on each trace in the perigram display is identical to its corresponding trace in the reflection strength display. The perigram data is just shifted towards zero relative to the reflection strength data.

Because the above example is centered on a high-energy zone, the majority of the amplitudes are positive. A display of a broader area would exhibit an equal amount of positive and negative values.

In the perigram display, as in the reflection strength display, the gas reservoir corresponds to a zone of large, positive values. The gas-oil contact corresponds to a local perigram peak.

+1270

Perigram

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0 +127

Reflection Strength


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Cosine of Phase

The cosine of the instantaneous phase, described as the “normalized trace” by Gelchinsky et al (1985), is another useful data attribute.

The recorded trace, we defined earlier as the product of amplitude and phase:

The cosine of the instantaneous phase is then derived by

In other words, the recorded trace, , is divided by the reflection strength, .

A cosine of phase display looks like data processed with a short-gate automatic gain control (instantaneous AGC). Reflections are enhanced and appear very similar in this display because of high-amplitude modulation. The trace values for the cosine of phase, before scaling and clipping of amplitudes, will range from -1 to +1.

Uses

Cosine of phase has essentially the same uses as instantaneous phase, but it offers a significant advantage. Cosine of phase data does not exhibit the discontinuous wrapping of instantaneous phase data. Instead, it smoothly oscillates between positive and negative values. Consequently, cosine of phase data can be more easily analyzed using traditional color maps and can be processed for data enhancement.

Example

A comparison of instantaneous phase data and cosine of phase data is shown on the next page.

f t( ) A t( ) θ t( )cos=

θ t( )cos f t( )A t( )----------=

f t( )A t( )


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The time range for a complete cycle is the same on the cosine of phase data as it is on the instantaneous phase data. The cosine function gives the cycle a smoother shape, which may impact the appearance of events in the seismic display.

The gas-oil contact can be readily tracked as a positive polarity event on the cosine of phase data. Furthermore, the termination of this interface against the Top Chalk reflector can also be clearly seen. The polarity reversal in Top Chalk due to changing fluid content is also apparent. Above the gas-oil contact, Top Chalk tracks a large, negative cosine of phase value; below the gas-oil contact, it tracks a large, positive cosine of phase value.

Cosine of Phase

-1 +1

-180 +180

Instantaneous Phase


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Perigram ∗ Cosine of Phase

The product of the perigram and the cosine of phase yields yet another useful type of complex trace, as suggested by Shtivelman et al (1986).

The recorded trace, we defined earlier as the product of amplitude and phase:

In other words, the recorded trace, , is equal to the reflection strength, , multiplied by the cosine of phase, .

The product of the perigram and the cosine of phase is a variation on the above expression. Recall the definition of perigram:

The product of the perigram and the cosine of phase is defined as

if

and

if

Combining the previous expressions, we get

if

and

if

In other words, whenever the perigram values are positive, the product of the perigram and the cosine of phase is equal to the input data, , multiplied by a trace scalar, , that is slightly less than one. When perigram values are negative, the amplitudes are set to zero. The composite effect is to zero essentially half of the data samples, corresponding to the lower reflection strength amplitudes.

f t( ) A t( ) θ t( )cos=

f t( )A t( ) θ t( )cos

g t( ) A t( ) A t( )∠=

G t( ) g t( ) θ t( )cos= g t( ) 0>

G t( ) 0= g t( ) 0≤

G t( ) A t( ) A t( )∠[ ] θ t( )cos=

G t( ) f t( ) 1 A t( )∠ A t( )⁄[ ]= g t( ) 0>

G t( ) 0= g t( ) 0≤

f t( )1 A t( )∠ A t( )⁄[ ]

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Calculating perigram ∗ cosine of phase thus exploits the separation of the recorded data into amplitude (perigram) and phase (cosine of phase) data. The less energetic half of the amplitude data is removed. Then the amplitude and phase data are recombined by multiplication to produce the final product. Note that if the low-energy data were not removed, then the multiplication would essentially reproduce the input recorded data.

Uses

A perigram ∗ cosine of phase display emphasizes high-amplitude, continuous events. This type of data and its extracted attributes have many of the same uses as reflection strength data. Bright spots associated with gas sands, for example, will often be dramatically highlighted when surrounding low-energy reflectors are reduced to zero.

Example

A comparison of cosine of phase, perigram, and perigram ∗ cosine of phase displays is provided on the next page.

Zeros in the perigram ∗ cosine of phase display occur where the perigram attribute is negative. Some of these muting effects can be seen above the reservoir. The reservoir itself is a high-energy zone; therefore, most of the reflectors exceed the muting threshold. On a display showing a larger area, you would find half the data had been set to zero.


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Cosine of Phase

-1 +1

Perigram ∗ Cosine of Phase

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Perigram

-128 +127


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General Attributes

General attributes are transforms in which each output sample is some combination of either samples before or samples after.

PostStack calculates the following four General Attributes.

Integration

Integration integrates the trace using Fourier transform. This is done by transforming the trace, dividing each frequency by (2*Pi*freq*sqrt(-1)), and zeroing the zero frequency component (removing dc). This gives a result similar to the simple (trace(i) = trace(i) + trace (i-1)), but has a more accurate 90 degree phase response at all frequencies. The frequency domain method is also not dependent on dc biases caused by small amplitude variations of the first few samples.

Integration produces an output trace in which each output sample value is the sum of the original samples, including this original sample.

Uses

If we assume that the seismic trace is a low frequency estimate of reflectivity, we can derive an estimate of acoustic impedance from the integrated trace attribute using the following formula:

where

This means we can get a high frequency estimate of acoustic impedance by using the Integration attribute followed by the math attribute Exponential Base e. This differs from normal acoustic impedance in that a low frequency component is not present.

Acm Ac1 e

Tnn 1=

m

∑×=

IntegratedTracem Tn

n 1=

m

∑=

Ac1 firstreflectioncoefficient=

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Example

An example of Integration is shown below:

Differentiation

Differentiation differentiates the trace using Fourier transform: (trace(i) = trace(i) - trace(i-1)). This is implemented in the same manner as integration, but each frequency is multiplied by the quantity (2*Pi*freq*sqrt(-1)), rather than divided by it.

In other words, Differentiation describes a trace value as the difference between the preceding sample and the succeeding sample divided by the difference in time. The calculation is done in the frequency domain.

Uses

Many useful attributes result from applying Differentiation to the instantaneous attributes such as Instantaneous Phase or Instantaneous Frequency, or to volume attributes such as Dip and Azimuth.

Example

An example of Differentiation is shown below:

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Energy Half-Time

This process computes the energy half-time, the proportion of time required for the energy contained within a time interval to build up to one-half of the total energy contained within the entire interval. One of several windowed attributes, this attribute gives the energy distribution in the analysis window.

Uses

Changes in energy half-time spatially should be related to possible facies changes.

Parameter

There is only one parameter to set in the Data Attribute - Energy-Half-Time dialog box that appears:


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Sliding time Window (ms)Specifies the length in milliseconds of the sliding window.

Example

An example of Energy Half-Time is shown below:

Arc Length

Arc Length is a scaled measure of the total excursion of a seismic trace in a window. To illustrate, imagine a seismic trace plotted in wiggle-trace format. Then imagine that a string is placed on the trace such that the string follows every wiggle. The Arc Length of the trace is then defined as the total length of the string stretched out. The length does not account for any smooth wiggle appearance. It only measures the distance from sample to sample. The formula is:

where:

a(i) = amplitude at the ith sample T = sample period N = number of samples in the window

S 1NT------- a i 1+( ) a i( )∠[ ] 2 T2+

i 1=

N

∑=


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Uses

Changes in arc length spacially indicates frequency and/or amplitude changes, which may be indicative of different facies or changes in attenuation in the seismic data.

Parameter

There is one parameter to set in the Data Attribute - Arc Length dialog box that appears:

Sliding Time Window (ms)Specifies the length in milliseconds of the sliding window. The arc length is computed for every sample from the samples in this window.

Example

An example of Arc Length is shown below:


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RMS Amplitude

RMS amplitude provides a scaled estimate of the trace envelope. Like energy half-time and arc length, it is computed in a time window whose length is set by the user. If this window has N samples, then the RMS amplitude RMS at the center of the window is given by:

Uses

RMS amplitude resembles reflection strength, but is smoother (depending on the window length). However, there is usually no particular reason to favor it over reflection strength. If the smoother nature is desirable, then prefer a smoothed reflection strength instead.

Parameters

There is one parameter to set in the Data Attribute - RMS Amplitude dialog box that appears:

Sliding Time Window (ms)Specifies the length in milliseconds of the sliding window. The RMS amplitude is computed for every sample from the samples in this window.

∑=

≡N

iiRM x

Nx

1

2S

1


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Math Attributes

Math Attributes apply mathematical operations or transforms to prepare traces for further processes. More than one attribute can be applied. For example, if a trace near zero phase is first integrated with the Integration attribute, then followed by the Exponential Base e attribute, the result should look like an estimate of acoustic impedance.

PostStack calculates the following six Math Attributes.

Absolute Amplitude

Absolute Amplitude replaces all samples with the absolute value of the original sample.

Uses

With application of the Absolute Amplitude attribute, zones of high acoustic impedance change become more visible.

Example

An example of the Absolute Amplitude attribute is shown below:

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Log Base e

Log Base e computes the Loge of the absolute value of every sample of the original trace, and retains the sign of the original trace. This tends to bring the high amplitudes down more than the low amplitudes. For example, Loge(10) = 2.302, whereas Loge(5) = 1.609.

Uses

A useful attribute can result from applying the Log Base e or Log Base 10 transform on the Absolute Amplitude transform for bad trace zone detection or depth of penetration analysis.

Example

An example of the Log Base e attribute is shown below:

Log Base 10

Log Base 10 computes the log10 of the absolute value of every sample on the trace, and retains the original sign. This tends to bring high amplitudes down more than low amplitudes. For example, Log10(10) equals 1, whereas Log10(5) is approximately 0.7.

Uses

The Absolute Amplitude transform followed by the Log Base e or Log Base 10 transform may show depth of penetration (time).

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Example

An example of the Log Base 10 attribute is shown below:

Exponential Base e (e**Amp)

Exponential Base e raises the number e to a power equal to the absolute value of the trace sample. If the absolute value of the trace sample exceeds 80, the sample is clipped to 80 to avoid floating overflow upon exponentiation. After exponentiation, the original sign is given to the new sample.

Uses

This attribute would be used after the Integration attribute to compute an estimate of acoustic impedance.

Example

An example of the Exponential Base e attribute is shown below:


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Exponential Base 10 (10**Amp)

Exponential Base 10 raises the number 10 to a power equal to the absolute value of the trace sample. If the absolute value of the trace sample exceeds 32, the sample is clipped to 32 to avoid floating overflow upon exponentiation. After exponentiation, the original sign is assigned to the new sample.

Uses

This transform may be used in place of Exponential Base e raised to the integrated trace transform for an estimate of acoustic impedance.

Example

An example of the Exponential Base 10 attribute is shown below:


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Power (Amp**Power)

Power raises the absolute value of each trace sample to a user-specified number (power). The absolute values may be clipped so that exponentiation will not result in a floating overflow. After each sample is raised to the power, the original sign is retained.

Uses

This transform may be used to further separate high amplitudes from low amplitudes.

Parameter

There is only one parameter to set in the Data Attribute - Power dialog box that appears:


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PowerSpecifies the power to which the absolute value is to be raised.

Example

An example of the Power attribute is shown below:


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Reflection Pattern Attributes

A set of 3D attributes that measure various patterns in the data. All of these are computed as complex seismic trace attributes, and therefore can be instantaneous or local.

Defining the Window

Although larger window sizes produce smoother attributes, they take longer to process. Therefore, take care when defining your window size.

Weighting preferentially favors values close to the window center over values near the window boundaries, reducing edge effects.

Number of traces and Number of lines must be appropriate for the window size. Generally, Number of lines should as large as the number of lines in the window, and Number of traces should be as large as the number of traces in the window. However, the code work, although less effectively, for a minimum number of lines given by:

Minimum input number of lines = number of lines in window/2 + 1

That is, for 7 lines in the analysis window, input at least 4 lines.

A similar relation holds for the minimum number of traces.

Time to Depth Conversion

Unless seismic data is already in depth, most reflection pattern attributes (all except amplitude variance and azimuth) require a velocity input. Velocity is used for time to depth conversions to correctly scale the attributes.

You can either input a TDQ Velocity model or create a suitable 1D Velocity function: t1,v1,t2,v2,t3,v3,... (Time units are ms and velocity units are m/s or ft./s)

Time-to-depth conversion here correctly scales the attributes. It does not account for changes in reflection orientation that result from a true time to depth conversion. These conversions are strictly correct for a 1D velocity model. For better results, run PostStack's time-to-depth conversion prior to the reflection pattern attributes. If you run this process, a velocity model is not required. For rather simple layer-cake

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velocity models, or when qualitative results are all that is needed, these conversions are sufficient.

Dip and azimuth are particularly affected by details of the velocity structure, though the other reflection pattern attributes are less sensitive. (Azimuth, though it doesn't require velocity input in any case, is nonetheless sometimes greatly altered by true time-to-depth conversions.)

Amplitude variance

Reflection amplitude variance is how much seismic amplitude varies from the average amplitude within an analysis window.

Uses

Use to compare between different datasets with different amplitude levels.

Parameters

.

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Resolution

Local attributes Local attributes are smoother and more stable than instantaneous attributes. That is, they are free of spikes. However, they take several times longer to compute, depending upon the window size.

Amplitude variance is normalized by the average amplitude.

InstantaneousNot as smooth or stable as local attribute but runtime is much faster.

Window Size for Local Averaging

Number of TracesThe default is 3.

Number of LinesThe default is 3.

Number of SamplesThe default is 5.

Azimuth

Reflection azimuth is measured in degrees from north.

Uses

Azimuth reveals structural units and details, complementing reflection dip and continuity attributes.


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Parameter

Resolution


This attribute is weighted by instantaneous power (reflection strength squared).



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Advanced Parameters

Output range (in degrees)The output range defaults to 180º to +180º. However, you can choose an output range between 0º to 360º.

Dip

Reflection dip is the angle between a reflection and the horizontal measured in degrees.

Uses

Dip is useful in revealing structural details, much like continuity attributes.


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Parameters

Resolution



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Advanced Parameters

Dip Magnitude/Directional DipToggle Dip Magnitude or Directional Dip and enter the dip direction (degrees from N).

Time/Depth Conversion Uses Toggle between velocity function or velocity model. You can either input a TDQ Velocity model or create a suitable 1D Velocity function: t1,v1,t2,v2,t3,v3,... (Time units are ms and velocity units are m/s or ft./s).

Divergence

Reflection divergence is the degree to which succeeding reflections in a sequence diverge consistently from one another. Divergent reflections


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are characterized by constant azimuth and increasing dip with depth. Divergence is best recognized on a moderate to large scale.

Uses

Divergent reflections can for example, signify channel edges.

Parameters


Number of Traces


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The default is 3.



Advanced Parameters


Hummocky

Reflection hummockiness is the degree to which reflections in a window exhibit waviness in both the inline and crossline directions. Hummockiness is best recognized on a moderate to large scale.

Uses

Hummocky reflections can help delineate the types and thickness of sedimentary units.


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Parameters




Number of Samples


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The default is 5.

Advanced Parameters


Parallelism

An attribute that quantifies how parallel reflections are within a multi-dimensional window. Parallelism is a measure of the variance of the dips and azimuths from the average direction. The more uniform the dips and azimuths, the greater the parallelism, and the more variance in the dips and azimuths, the less the parallelism.

Uses

Highly parallel stratigraphy indicates sedimentation in a low-energy environment, suggesting shale. Nonparallel stratigraphy indicates sedimentation in a high-energy environment, which could suggest sands.


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Parameters

Resolution




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Advanced Parameters


Shaded relief

PostStack s shaded relief attribute represents seismic reflections as apparent topography. This facilitates geologic understanding by revealing structural and stratigraphic details hidden in seismic data and presenting them in a familiar and intuitive display.

Shaded relief combines reflection dip and azimuth into apparent topography. Hence, it contains the same information as the common dip-azimuth attribute, the difference being in how the information is presented. Dip-azimuth shows dip and azimuth together with dip determining the shading of the display and azimuth determining its color.


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Uses

Shaded relief complements other attributes, such as continuity. Both shaded relief and continuity reveal details hidden in the data, but continuity highlights faults and other discontinuities, whereas shaded relief shows changes in reflector orientation. There is also a difference of directionality, for most attributes reveal structures in all directions, whereas shaded relief is directional, enhancing features perpendicular to the illumination direction while suppressing those that are parallel. As a result, shaded relief displays should be created in pairs with orthogonal illumination directions so as to capture all features. This directionality is useful, as it makes a powerful directional filter of shaded relief, enabling you to selectively highlight certain trends while hiding others.


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Parameters


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Resolution








Sun Position (in degrees)

These parameters as well as the Advanced Parameters describe where the light is coming from that shines on the data to produce shaded relief. Enter the values for Elevation above Horizontal and Azimuth from True North.

Advanced Parameters

Surface Type


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Since shaded relief makes a time slice look like apparent topography, this surface type option allows you to select the type of topography (dry or wet). The same information is shown by all choices, but sometimes a wet surface can enhance subtle features better.Toggle between the following surface types:

• Dull is a surface that scatters light like a dry surface. For example, desert is a dull surface. This is called specular reflection.

• Intermediate is a surface that scatters light somewhere between the desert and polished marble.

• Shiny is a surface that scatters light like a wet surface. For example polished marble.

Surface ReflectanceToggle on the type of surface reflectance from the following choices: Uniform, Amplitude, or Spacing. Further character can be added by selecting amplitude or reflection spacing for the surface reflectance. This allows either of these two stratigraphic attributes to be combined with the structural information of the shaded relief.

Vertical ExaggerationEnter the vertical exaggeration of the model. This value enhances the slopes in the data so as to improve the contrast in the shaded relief.


Similarity

Similarity is a stratigraphic attribute that quantifies the variance of the reflection spacing, dip, and azimuth together within the analysis window. Similarity is much like parallelism with the additional factor of reflection spacing. Similarity is also rather like a 3D bandwidth measure scaled to have units of feet or meters, and which may be thought of as a kind of diameter of a zone of similar reflections. Larger values imply greater similarity; smaller values imply dissimilarity.


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Similar reflections are characterized by relatively constant dip and azimuth as well as constant reflection spacing; dissimilar reflections are characterized by high variance in dip and azimuth or in reflection spacing, or in both. Similarity has the uses as reflection parallelism and continuity.

Uses

Similar stratigraphy indicates sedimentation in a low-energy environment, suggesting shale. Dissimilar stratigraphy indicates sedimentation in a high-energy environment, which could suggest sands.


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Parameters




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Advanced Parameters


Spacing

The distance between two succeeding reflections measured perpendicularly to the reflections and starting and ending on points of common phase. Computed as a wavelength with units of ft. or m.

Uses

Reflection spacing is the 3D counterpart to instantaneous frequency, which is a 1D trace attribute.


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Parameters

Velocity

Unless the seismic data is already in depth, most reflection patterns attributes require suitable velocity input for on-the-fly conversions to depth. The two exceptions are amplitude variance and azimuth, which do not require velocity input.

You can choose an existing TDQ velocity model or create a single 1D velocity function.


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References

Taner and Sheriff (1977) and Taner et al (1979) are two classic articles on the derivation and use of complex trace attributes. These and the other articles listed below are recommended for more information on complex trace analysis.

Abatzis, I., and J. Kerr, 1991. New spatial visualization techniques in tectonic and stratigraphic interpretation optimize reservoir delineation of the Roar Field, Danish North Sea. SEG Expanded Abstracts.

Albu, I., and A. Papa, 1992. Application of high-resolution seismics in studying reservoir characteristics of hydrocarbon deposits in Hungary. Geophysics, v. 57, p. 1068-1088.

Bahorich, M. S., and S. R. Bridges, 1992. Seismic sequence attribute map (SSAM). SEG 62nd Annual International Meeting, October, New Orleans.

Barnes, A.E., 2000, Attributes for automating seismic facies analysis: 70th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 553-556.

Barnes, A. E., 1991. Instantaneous frequency and amplitude at the envelope peak of a constant-phase wavelet (short note). Geophysics, v. 56, p. 1058-1060.

Barnes, A.E., 1993. Instantaneous bandwidth and dominant frequency with applications to seismic reflection data: Geophysics, 58, 419-428.

Barnes, A. E., 1992. The calculation of instantaneous frequency and instantaneous bandwidth (short note). Geophysics, v. 57, p. 1520-1524.

Bodine, J. H., 1984. Waveform analysis with seismic attributes. SEG 54th Annual International Meeting, December, Atlanta.

Bodine, J. H., 1986. Waveform analysis with seismic attributes. Oil & Gas Journal, v. 84, no. 24, p. 59-63.

Bondar, I., 1992. Seismic horizon detection using image processing algorithms. Geophysical Prospecting, v. 40, p. 785-800.

Bracewell, R. N., 1965. The Fourier transform and its applications. New York, McGraw-Hill, p. 268-271.

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Gelchinsky, B., E. Landa, and V. Shtivelman, 1985. Algorithms of phase and group correlation. Geophysics, v. 50, p. 596-608.

Neidell, N.S., 1991. Could the processed seismic wavelet be simpler than we think? Geophysics, v. 56, p. 681-690.

Oliveros, R.B., and Radovich, B.J., 1997, Image-processing display techniques applied to seismic instantaneous attributes on the Gorgon gas field, North West Shelf, Australia: 67th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 2064-2067.

Radovich, B.J., and Oliveros, R.B., 1998, 3-D sequence interpretation of seismic instantaneous attributes from the Gorgon field: The Leading Edge, 17, 1286-1293.

Robertson, J. D., and H. H. Nogami, 1984. Complex seismic trace analysis of thin beds. Geophysics, v. 49, p. 344-352.

Robertson, J. D., and D. A. Fisher, 1988. Complex seismic trace attributes. The Leading Edge, v. 7, no. 6, p. 22-26.

Shtivelman, V., E. Landa, and B. Gelchinsky, 1986. Phase and group time sections and possibilities for their use in seismic interpretation of complex media. Geophysical Prospecting, v. 34, p. 508-536.

Taner, M. T., and R. E. Sheriff, 1977. Application of amplitude, frequency, and other attributes to stratigraphic and hydrocarbon determination, in C. E. Payton, ed., Seismic stratigraphy: Applications to hydrocarbon exploration. AAPG Memoir 26, p. 301-327.

Taner, M. T., F. Koehler, and R. E. Sheriff, 1979. Complex seismic trace analysis. Geophysics, v. 44, p. 1041-1063.

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Documents

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