Team 6:Deducing Rock Properties from

Spectral Seismic DataMentor Jiajun Han, CGG

Maria-Veronica Ciocanel, Brown UniversityHeather Hardeman, University of CalgaryDillon Nasserden, Simon Fraser University

Byungjae Son, University of North Carolina, GreensboroShuai Ye, Texas A & M University

ProblemThe aim of our investigations is to find evidence for subsurface reservoirs and valleys from geological data.

Spectral decomposition, which is called time-frequency decomposition, characterize the change in frequency of a seismic signal.

Methods

Short-Time Fourier Transform (STFT)

Continuous Wavelet Transform (CWT)

• Synchrosqueezing Transform (SST)

• Basis Pursuit (BP)

Seismic Attributes

Envelope of seismic trace:

𝐸𝐸 𝑡𝑡 = 𝑇𝑇2(𝑡𝑡) + 𝐻𝐻𝑇𝑇2(𝑡𝑡) The first and second time derivative of the envelope The phase attribute:

𝜃𝜃 𝑡𝑡 = arctan(𝐻𝐻𝑇𝑇 (𝑡𝑡)𝑇𝑇 (𝑡𝑡)

)

The first and second time derivative of the phase attribute

Reservoir Data Set

Post-stack data Pre-stack data

Post-stack Results – standard attributes

Attributes for the reservoir post-stack data: First derivative of the envelope (left) and second derivative of the envelope (right)

Post-stack Results – amplitude and phase attributes

Constant frequency slices obtained by CWT for the amplitude (left) and phase (right) attributes at frequency approx. 5 Hz and 3 Hz respectively.

Post-stack Results – amplitude and phase attributes

Constant frequency slices obtained by SST with regards to the amplitude (left) and phase (right) attributes at frequency approx. 60 Hz (left) and 55 Hz (right).

Valley Data Set

Post-stack data

Post-Stack Results – standard attributes

Attributes for the valley post-stack data: First derivative of the envelope (left) and second derivative of the envelope (right)

Post-Stack Results – phase attribute

Constant frequency slices obtained with BP (basis pursuit) for the phase attribute at approx27 Hz (left), and 32 Hz (right)

Preliminary/Future Work

Look into AVO (amplitude vs offset) analysis in order to identify bright spots for hydrocarbon reservoirs

Identify ways to use spectral decomposition information for pre-stack data analysis

Determine if frequency information from t-f analysis can provide insight into distinguishing between P and S-waves

Pre-stack Results – AVO, A-B attributesP and S-Wave Velocities

Unlike density, seismic velocity involves the deformation of a rock as a function of time. This leads to two different types of velocities:

(1) P-wave (2) S-wave

If q > 0°, an incident P-wave will produce both P and S reflected andtransmitted waves. This is called mode conversion.

Mode Conversion of an Incident P-Wave

Reflected P-wave = RP(θ1)

Reflected S-wave = RS(θ1)

Transmitted P-wave = TP(θ1)

Incident P-wave

Transmitted S-wave = TS(θ1)

VP1 , VS1 , ρ1

VP2 , VS2 , ρ2

θ1

φ1

θ1

θ2

φ2

q16

AVO method

• AVO (Amplitude versus Offset) method ---- Interpret the amplitudes of the P-waves as a function of offset, or angle, which contain implied information about the S-waves.

• Converting from offset to angle domain

• To extract S-wave type information from P-wave reflections at different offsets ----(Wiggins’ Form of the Aki-Richards Equation)

: where,sintansin)( 222 θθθθ CBARP ++=

.21,24

21,

21

22

p

P

P

S

S

S

P

S

p

P

p

P

VVC

VV

VV

VV

VVB

VVA ∆

=∆

−

∆

−

∆=

∆+

∆=

ρρ

ρρ

An example of evaluated attributes A and B

Pre-stack Preliminary Results

Attributes 𝑻𝑻𝟏𝟏 (left) and 𝑻𝑻𝟐𝟐 (right) at approx. 40 Hz as a function of time and offset. BP was performed with a Ricker wavelet dictionary.