Seismic inverse Q filtering

Key takeaways

Seismic inverse Q filtering belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Seismic inverse Q filtering to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Seismic inverse Q filtering from memory before moving on to harder problems.

Reference excerpt

Seismic inverse Q filtering is a data processing technology for enhancing the resolution of reflection seismology images. Q is the anelastic attenuation factor or the seismic quality factor, a measure of the energy loss as the seismic wave moves.

Basics Seismic inverse Q-filtering employs a wave propagation reversal procedure that compensates for energy absorption and corrects wavelet distortion due to velocity dispersion. By compensating for amplitude attenuation with a model of the visco-elastic attenuation model type, seismic data can provide true relative-amplitude information for amplitude inversion and subsequent reservoir characterization. By correcting the phase distortion due to velocity dispersion, seismic data with enhanced vertical resolution can yield correct timings for lithological identification. However, Wang's outline of the subject is excellent and to follow his path, inverse Q filtering can be introduced based on the 1-D one-way propagation wave equation. He introduce this equation:.

d U ( r , w ) d r − i k ( w ) U ( r , w ) = 0 ( 1.1 ) {\displaystyle {\frac {dU(r,w)}{dr}}-ik(w)U(r,w)=0\quad (1.1)}

where U(r,w) is the plane wave of radial frequency w at travel distance r, k(w) is the wavenumber and i is the imaginary unit. Reflection seismograms record the reflection wave along the propagation path r from the source to reflector and back to the surface. With this approach Wang assumes that the plane wave U(r,w) has already been attenuated by a Q filter through travel distance r. We must have this in mind when we go to the step of finding a solution of (1.1). It is necessary that the initial U(r,w) either is already created by a forward synthetic Q-filtering process or taken directly from seismic surface data. Wang has introduced this concept in chapter 5 in his book. I think it is necessary to have this in mind also when the inverse theory is developed. Equation (1.1) has an analytical solution given by

U ( r + △ r , w ) = U ( r , w ) exp ⁡ ( i k ( w ) △ r ) ( 1.2 ) {\displaystyle U(r+\bigtriangleup r,w)=U(r,w)\exp(ik(w)\bigtriangleup r)\quad (1.2)}

Kolsky's attenuation-dispersion model The wavenumber k(w) is an important variable in the solution (1.2). To obtain a solution that can be applied to seismic k(w) must be connected to a function that represent the way U(r,w) propagates in the seismic media. This functions can be regarded as a Q-model. The Kolsky Model is used extensively in seismic inverse Q-filtering. The model assumes the attenuation α(w) to be strictly linear with frequency over the range of measurement:

α = | w | ( 2 c r Q r ) ( 1.3 ) {\displaystyle \alpha ={\frac {|w|}{(2c_{r}Q_{r})}}\quad (1.3)}

And defines the phase velocity as:

1 c ( w ) = 1 c r ( 1 − 1 π Q r l n | w w r | ) ( 1.4 ) {\displaystyle {\frac {1}{c(w)}}={\frac {1}{c_{r}}}(1-{\frac {1}{\pi Q_{r}}}ln|{\frac {w}{w_{r}}}|)\quad (1.4)}

Where cr and Qr are the phase velocity and the Q value at a reference frequency wr. For a large value of Qr >>1 the solution (1.4) can be approximated to

1 c ( w ) = 1 c r | w w r | − γ ( 1.5 ) {\displaystyle {\frac {1}{c(w)}}={\frac {1}{c_{r}}}|{\frac {w}{w_{r}}}|^{-\gamma }\quad (1.5)}

where

γ = ( π Q r ) − 1 {\displaystyle \gamma =(\pi Q_{r})^{-1}}

… excerpt ends here. Continue reading the full article.

Illustrations

Seismic inverse Q filtering illustration

Worked examples

Example 1 — a first encounter with Seismic inverse Q filtering

Start with the simplest possible case. Write down what Seismic inverse Q filtering claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Seismic inverse Q filtering before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Seismic inverse Q filtering ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Seismic inverse Q filtering

In research: Seismic inverse Q filtering appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Seismic inverse Q filtering in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Seismic inverse Q filtering is common in secondary-school and first-year university syllabi. It links to neighbouring topics Geophysics, Seismology measurement, so understanding it makes those chapters shorter.
In everyday life: Look for Seismic inverse Q filtering outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Seismic inverse Q filtering in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Seismic inverse Q filtering means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Seismic inverse Q filtering out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Seismic inverse Q filtering in simple terms?

Seismic inverse Q filtering is a data processing technology for enhancing the resolution of reflection seismology images. Q is the anelastic attenuation factor or the seismic quality factor, a measure of the energy loss as the seismic wave moves.

Why does Seismic inverse Q filtering matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Seismic inverse Q filtering?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Seismic inverse Q filtering.