SEISMIC ATTRIBUTE ANALYSIS USING COMPLEX TRACE SIGNALS

-BySOMAK HAJRA

M.Sc.-Tech APPLIED GEOPHYSICS2012MC0093

SEISMIC ATTRIBUTES-AN INTRODUCTION

“Seismic Attributes are all the information obtained from seismic data, either by direct measurements or by logical or experience based reasoning”.

Seismic attributes may also be defined as all of the measured, computed or implied quantities obtained from the seismic surveys which provide a link between rock properties and seismic data.

E.g. Reflection strength, apparent polarity, instantaneous frequency, instantaneous phase etc.

CLASSIFICATION OF ATTRIBUTES PRE-STACK - AVO, velocity &

azimuthal variations. INSTANTANEOUS – Trace

envelope, instantaneous frequency & phase.

PHYSICAL - These relate to physical qualities & quantities like lithology & wave propagation.

WINDOW- summarizing information from vertical window of data.

FOURIER- obtained in freq. domain through Fourier analysis, like spectral decomposition.

POST-STACK – Attributes of CDP stacked/ migrated data.

WAVELET – Instantaneous frequency at the peak of the envelope equals the mean frequency of the wavelet amplitude spectrum.

GEOMETRICAL - Geometrical attributes describe the spatial and temporal relationship of all other attributes & include lateral information's like dip and azimuth.

MULTI-TRACE- calculated using more than one seismic traces to give lateral variations in data.

E.g. Volumetric curvature, dip etc.

FLOWCHART SHOWING BRIEF CLASSIFICATION OF ATTRIBUTES

WHAT IS A COMPLEX TRACE?Complex trace analysis

treats a seismic trace as a real part of analytical signal:

F(t)=f(t)+jf*(t), where j= √-1

The quadrature component f*(t) is determined either by a linear convolution (Hilbert Transform) or by a phasor representation.

If Y(t) be the time-varying signal composed of real & imaginary parts, we have:

COMPONENTS OF A COMPLEX TRACE If A(t) & θ(t) be the

Amplitude & time-dependent phase respectively, then the real seismic trace can be written as:

f(t)= A(t).cos θ(t)

So, f*(t)=A(t).sin θ(t)

Thus, F(t)=

A(t).e^(jθ(t))

ANALYSIS OF SEISMIC ATTRIBUTESSINGLE TRACE TYPE

Seismic attributes which are calculated using single seismic trace as input.

The classes of seismic attributes are: Horizon (loop) Horizon A •Peak amplitude •Duration •Symmetry Sample (volume, instantaneous) •Amplitude •Time •Frequency Interval •Average amplitude •Maximum (Minimum) Duration •Isochron

COLOUR CODING OF SEISMIC ATTRIBUTES

REFLECTION STRENGTH

Reflection strength is the amplitude of the envelope & is given by the equation:

A(t)=|F(t)|= √{(f(t)^2)+(f*(t)^2)}The envelope represents the

instantaneous energy of the signal and is proportional in its magnitude to the reflection coefficient.

The envelope is useful in highlighting discontinuities, changes in lithology, faults, changes in deposition, tuning effect, and sequence boundaries.

Hydrocarbon accumulations, like gas, shows high amplitude reflections or, ‘bright spots’.

INSTANTANEOUS PHASE Instantaneous phase is the angle of

lag or lead of the harmonic components of a seismic pulse with respect to a reference.

For example, a zero-phase wave would be symmetric whereas a 90° phase wave would be perfectly asymmetric.

It is represented as: θ(t)= arc tan [f*(t)/f(t)]Phase is independent of amplitude

but is related to instantaneous frequency and hence makes weakly coherent events clearer.

It is also the best indicator of lateral continuity.

INSTANTANEOUS FREQUENCY It is the time derivative of instantaneous

phase & is represented as: W(t)= d θ(t)/dtReflection events are composite of individual

reflections from a number of closely spaced reflectors, the superposition of which produces a characteristic frequency pattern.

Variations like pinch-outs or hydrocarbon-water interfaces tend to change the instantaneous frequency value more rapidly.

A low frequency shift (“low frequency shadow”) occurs due to reflections from reflectors below gas sands, condensates or oil reservoirs.

The adjacent seismic (a) & the corresponding frequency(b) section shows low frequency anomaly at shallow depths indicating presence of shallow gas.

WEIGHED AVERAGE FREQUENCY APPARENT POLARITYWeighed average frequency

emphasizes the frequency of stronger reflection events & smoothes irregularities caused by noise.

It is given by the equation:

where, freq(t)=w(t-T) & env (t)=A(t-T).L(T) L(T) being the low pass

filter. It is an excellent tool for

enhancing reflection continuity.

Apparent polarity is the sign of f(t) when A(t) is maximum and are especially sensitive to data quality.

‘Bright Spots’ associated with gas accumulations show negative polarity for reservoir top reflections.

‘Flat Spots’ associated with reflections from gas-oil or gas-water interfaces show positive polarity.

The +ve or –ve sign is assigned assuming a zero phase wavelet.

SOME OTHER DERIVED ATTRIBUTES Amplitude Derivative (RE)=dA(t)/dt which highlights the change in

reflectivity and is also related to the absorption of energy. Second Derivative of Envelope (DDE)=d2A(t)/dt2 which indicates all

reflecting interfaces visible within seismic band-width showing sharpness of events & changes in lithology.

Cosine of Instantaneous Phase C(t)=cos θ(t) which gives detailed visualization of bedding configurations.

Instantaneous Acceleration AC(t)=d(F(t))/dt which accentuates bedding differences.

Thin Bed Indicator TB(t)=F(t)-F’(t) which highlights the location where the instantaneous frequency jumps in the reverse direction due to very close reflectors, i.e., thin beds. Computed from large spikes of instantaneous frequency, indicating overlapped events.

Instantaneous Bandwidth B(t)={d(E(t))/dt}/2*pi*E(t). It shows overall effects of absorption and seismic character changes.

Instantaneous Q=pi*(instantaneous frequency) * (envelope)/derivative of envelope. It May indicate liquid content by ratio of pressure versus shear wave section Q factors.

Relative Acoustic Impedance which calculates the running sum of the trace to which a low cut filter is applied. It is an indicator of impedance changes, in a relative sense.

MULTI-TRACE TYPESeismic attributes which are calculated using more than a single seismic trace as input are known as multi-trace type.It is based on the correlation of two or more seismic traces.

SPECTRAL DECOMPOSITIONThe spectral analysis is a procedure that decomposes a time series into a spectrum of cycles of different lengths. It is also known as frequency domain analysis. The spectral analysis describes the distribution of the power at a specific frequency of a signal, based on a finite set of data. It replaces the single input trace with a gather of traces corresponding to the spectral decomposition of the input attribute. Creating spectral decomposition attributes enables us to illuminate the structures with different frequency bands to see if any of them gives us better resolution.

In spectral decomposition we use complex traces.Basically a single trace is convolved with the first realwavelet to get the real trace for the first frequency, andthe input trace is convolved with the first wavelet ofthe imaginary part to get the imaginary trace. Then acomplex trace attribute is constructed, such asenvelope, phase, etc. This step is repeated for eachfiltered wavelet operating on the same trace and obtainband limited traces.

CONCLUSION Our increasing reliance on seismic data requires that we extract

the most information available from the seismic response. Seismic attributes are important because they enable interpreters to extract more information from seismic data. Applications of attributes include:

Hydrocarbon play evaluation, prospect identification and risking, reservoir characterization, well planning and field development.

Description of shape or other characteristics of a seismic trace over specific intervals or at specific times.

They are used for qualitative analysis (e.g., data quality, seismic facies mapping) and quantitative analysis (e.g., net sand, porosity prediction).

It may be noted that these attributes are very useful tools analysis of a single attribute may not provide a conclusive definitive information. Instead, useful conclusions can be drawn by using a combination of attributes together.

THANK YOU

REFERENCES: D. Subrahmanyam & P. H. Rao, Seismic Attributes- A Review;

International Conference & Exposition on Petroleum Geophysics; Pg-398 M. T. Taner, F. Koehler, and R. E. Sheriff, Geophysics; Complex Seismic

Trace Analysis; 44 (6), 1041 (1979). doi:10.1190/1.1440994 M. Turhan Taner, SEISMIC ATTRIBUTES S. M. Rahman; Constraint of Complex Trace Analysis for Seismic

Data Processing; J. Sci. Res. 3 (1), 65-73 (2011) Schroeder, Using Seismic Attributes ;AAPG http://en.wikipedia.org/wiki