Spectral Decomposition

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Long Window Analysis

• The geology is unpredictable.• Its reflectivity spectrum is therefore white/blue.

Long Window AnalysisReflectivityr(t)

Fourier Transform

Amplitude

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Waveletw(t)

Noisen(t)

Seismic Traces(t)

Amplitude Amplitude Amplitude

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TIMEDOMAIN

FREQUENCYDOMAIN

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Short Window Analysis

• The non-random geology locally filters the reflecting wavelet.• Its non-white reflectivity spectrum represents the

interference pattern within the short analysis window.

Short Window Analysis

WaveletOverprint

Reflectivityr(t)

Fourier Transform

Amplitude

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Waveletw(t)

Noisen(t)

Seismic Traces(t)

Amplitude Amplitude Amplitude

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TIMEDOMAIN

FREQUENCYDOMAIN

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Spectral Interference

• The spectral interference pattern is imposed by the distribution of acoustic properties within the short analysis window.

Spectral Interference

Source WaveletAmplitude Spectrum

Thin Bed ReflectionAmplitude Spectrum

Thin BedReflection

ReflectedWavelets

SourceWavelet

Thin Bed

ReflectivityAcousticImpedance

Temporal Thickness

FourierTransform

FourierTransform

Amplitude Amplitude

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Temporal Thickness1

The Tuning Cubex

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Interpret

3-D Seismic Volume

Subset

Compute

Animate

Interpreted3-D Seismic Volume

Zone-of-InterestSubvolume

Zone-of-InterestTuning Cube(cross-section view)

Frequency Slicesthrough Tuning Cube(plan view)

Prior to Spectral Balancing

• The Tuning Cube contains three main components:– thin bed interference,– the seismic wavelet, and– random noise

Multiply

Tuning Cube

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freqx

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freqx

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Seismic Wavelet NoiseThin Bed Interference

++Add

Short Window Analysis

WaveletOverprint

Reflectivityr(t)

Fourier Transform

Amplitude

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Waveletw(t)

Noisen(t)

Seismic Traces(t)

Amplitude Amplitude Amplitude

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TIMEDOMAIN

FREQUENCYDOMAIN

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Spectral Balancing

xy

freq

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freq

Split Spectral Tuning Cubeinto Discrete Frequencies

Tuning Cube

Spectrally BalancedTuning Cube

Gather Discrete Frequenciesinto Tuning Cube

Independently NormalizeEach Frequency Map

Frequency 1 Frequency 2 Frequency 3 Frequency 4 Frequency n

Frequency 1 Frequency 2 Frequency 3 Frequency 4 Frequency n

Frequency Slicesthrough Tuning Cube(plan view)

Spectrally BalancedFrequency Slicesthrough Tuning Cube(plan view)

After Spectral Balancing

• The Tuning Cube contains two main components:– thin bed interference, and– random noise

Tuning Cube

xy

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freqx

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NoiseThin Bed Interference

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Real Data Example

• Gulf-of-Mexico, Pleistocene-age equivalent of the modern-day Mississippi River Delta.

Gulf of Mexico Example 10,000 ft

Channel “A”

Channel “B”

Fault-Controlled Channel

Point Bar

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Amplitude

analysis window length = 100ms

Response Amplitude

Gulf of Mexico Example 10,000 ft

North-South Extentof Channel “A” Delineation

Channel “A”

Channel “B”

Fault-Controlled Channel

Point Bar

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Amplitude

analysis window length = 100ms

Tuning Cube, Amplitude at Frequency = 16 hz

Gulf of Mexico Example 10,000 ft

North-South Extentof Channel “A” Delineation

Channel “A”

Channel “B”

Fault-Controlled Channel

Point Bar

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Amplitude

analysis window length = 100ms

Tuning Cube, Amplitude at Frequency = 26 hz

Hey…what about the phase?

• Amplitude spectra delineate thin bed variability via spectral notching.

• Phase spectra delineate lateral discontinuities via phase instability.

Phase Spectrum

Phase

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Amplitude Spectrum

Amplitude

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Thin Bed Reflection

FourierTransform

Faults

10,000 ft

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-180

Phase

Gulf of Mexico Example

Response Phase

Faults

10,000 ft

N

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-180

Phase

analysis window length = 100msGulf of Mexico Example

Tuning Cube, Phase at Frequency = 16 hz

analysis window length = 100ms

Faults

10,000 ft

N

180

-180

Phase

Gulf of Mexico Example

Tuning Cube, Phase at Frequency = 26 hz

Summary

• Spectral decomposition uses the discrete Fourier transform to quantify thin-bed interference and detect subtle discontinuities.

• For reservoir characterization, our most common approach to viewing and analyzing spectral decompositions is via the “Zone-of-Interest Tuning Cube”.

• Spectral balancing removes the wavelet overprint.• The amplitude component excels at quantifying thickness

variability and detecting lateral discontinuities.• The phase component detects lateral discontinuities.