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Idea for a useful model of land data
By Jon Claerbout, 2016
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job interview question:
“On what important truth do very few people agree with you?”
--Peter Thiel
In the 1980s the oil industry moved off shore.
Drilling got a whole lot more expensive.
Seismology got a whole lot cheaper. Hooray!
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In the 1980s the oil industry moved off shore.
Drilling got a whole lot more expensive.
Seismology got a whole lot cheaper. Hooray!
Now the industry is going back on shore.
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In the 1980s the oil industry moved off shore.
Drilling got a whole lot more expensive.
Seismology got a whole lot cheaper. Hooray!
Now the industry is going back on shore. Oh, oh!
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In the 1980s the oil industry moved off shore.
Drilling got a whole lot more expensive.
Seismology got a whole lot cheaper. Hooray!
Now the industry is going back on shore. Oh, oh!
Should we start thinking about land data?
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Land data: Too noisy!
"All models are wrong,
but some are useful."
George Box, 1919-2013 British statistician
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Land data: Too noisy!
Noise = (modeled - field) data
Field data is repeatable.
Our modeled data is far from field data.
"All models are wrong,
but some are useful."
George Box, 1919-2013 British statistician
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Land data: Too noisy!
Noise = (modeled - field) data
Field data is repeatable.
Our modeled data is far from field data.
"All models are wrong,
but some are useful."
George Box, 1919-2013 British statistician
10
Land data: Too noisy!
Noise = (modeled - field) data
Field data is repeatable.
Our modeled data is far from field data.
"All models are wrong,
but some are useful."
George Box, 1919-2013 British statistician
11
Land data: Too noisy!
Noise = (modeled - field) data
Field data is repeatable.
Our modeled data is far from field data.
"All models are wrong,
but some are useful."
George Box, 1919-2013 British statistician
12
Land data: Too noisy!
Noise = (modeled - field) data
Field data is repeatable.
Our modeled data is far from field data.
"All models are wrong,
but some are useful."
George Box, 1919-2013 British statistician
13
Land data: Too noisy!
Noise = (modeled - field) data
Field data is repeatable.
Our modeled data is far from field data.
Is there a simple heart in this mess?
"All models are wrong,
but some are useful."
George Box, 1919-2013 British statistician
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x
t
hyperbola
Vee
What is the earth model and the path of the rays?
x
z
Data
Model
Vee
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x
t
hyperbola
Here is the easy part of the earth model.
x
z
Data
Model
Vee
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x
t
hyperbola
Vee
What is the earth model and the path of the rays?
x
z
Data
Model
Vee
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x
t
hyperbola
Vee
Here is the earth model and the path of the rays.
x
z
Data
Model
Vee
Secondary source:
- road
- river
- etc
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x
t
hyperbola
Vee
Here is the earth model and the path of the rays.
x
z
Data
Model
Vee
Secondary source:
- road
- river
- etc
Do you know of any data that looks like this?
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from BEI
hyperbolas
Ground roll
Backscattered
ground roll
400 m = 0.4 km offset
1 sec
dx = 3.4 m
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from BEI
hyperbolas
Ground roll
Backscattered ground roll
400 m = 0.4 km offset
1 sec
dx = 3.4 m
300 m/s
130 m/s
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from BEI
400 m = 0.4 km offset
1 sec
dx = 3.4 m
Ground roll
Ground roll, slower, shallower
Ground roll, slower, shallower
Deeper penetration
Backscatter has slower velocity
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Stack of nested Vee’s.
Each layer has a Vee
hanging down, (1) slow, and (2) high frequency (3) damped.
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Each layer has its own Vee
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Wind noise
Signal generated noise. Because of spatial aliasing, neighboring traces differ from their neighbors.
Shot generated ground roll
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Area of interest sprinkled with many tiny Vees.
CLAIM: Weak Vee’s are everywhere, peaked at all time and space locations.
Stack of nested Vee’s.
Each layer has a Vee
hanging down, (1) slow, and (2) high frequency (3) damped.
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Area of interest sprinkled with many tiny Vees.
Backscatter
Another backscatter?
Another backscatter?
Weak observational support of the idea that Vee’s are everywhere, peaked at all time and space points.
Less breakup
More breakup
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Forward modeling: How would you start?
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Forward modeling: How would you start?
I would take some marine data and corrupt it in the manner that land data is corrupted by surface wave scattering.
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Forward modeling: How would you start?
I would take some marine data and corrupt it in the manner that land data is corrupted by surface wave scattering.
A line of random numbers along the surface, each number blasting a shower of Vee’s beneath it, each Vee scaled by the marine reflector at its apex.
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Inversion:
Need a decent estimate of the Vee filter shape.
Better yet, its inverse filter.
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This Vee is an impulse response in the (t,x)-plane.
What does its inverse filter look like?
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The adjoint is a starting guess of the inverse. That’s the time reverse.
More precisely, since the wavelet is a smooth function of time, the inverse will be rough (inverse spectrum).
Vee’s collapse
To spikes.
Exciting!
This Vee is an impulse response in the (t,x)-plane.
What does its inverse filter look like?
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The Vee’s are everywhere, but they interfere so much we don’t see the individual Vee’s.
So how do we estimate them, and their inverse?
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The Vee’s are everywhere, but they interfere so much we don’t see the individual Vee’s.
So how do we estimate them, and their inverse?
2-D spectral...
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The Vee’s are everywhere, but they interfere so much we don’t see the individual Vee’s.
So how do we estimate them, and their inverse?
2-D spectral factorization!
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Area of interest loaded with many tiny Vee
stacks.
After finding the spectrum in the area of interest we eliminate all but the Vee’s part of the spectrum by deleting the fast stuff and keeping the slow.
Then: spectral factorization
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More added 4/2017
At an internal presentation I was asked:
At an internal presentation I was asked:
At an internal presentation I was asked:
At an internal presentation I was asked:
I’ll parameterize surface scattering with lines, not points.
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Very old data.
Sign bit.
Tons of explosives.
Nevada test site.
200 miles away.
Sign bit data.
Survey line perpendicular
to the line of propagation.
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V sketches
Statics...
on the deep reflections?
on the surface scatterers?
Too early to say.
Lots more things to think about:
Why can’t we eliminate all the Vee’s with an (f,k) filter?
Why can’t we eliminate all the Vee’s with an (f,k) filter?
Because they are spatially aliased, even at 3.4 meter trace spacing, so steep events might look gentle.
Why can’t we eliminate all the Vee’s with an (f,k) filter?
Because they are spatially aliased, even at 3.4 meter trace spacing,
so steep events might look gentle.
But, an (f,k) wedge filter is a good way to begin. It defines conventional processing --- that which we want to beat.
Why can’t we eliminate all the Vee’s with an (f,k) filter?
Because they are spatially aliased, even at 3.4 meter trace spacing,
so steep events might look gentle.
But, an (f,k) wedge filter is a good way to begin. It defines conventional processing --- that which we want to beat.
Remember: PEFs are easily nonstationary.
Why can’t we eliminate all the Vee’s with an (f,k) filter?
Because they are spatially aliased, even at 3.4 meter trace spacing,
so steep events might look gentle.
But, an (f,k) wedge filter is a good way to begin. It defines conventional processing --- that which we want to beat.
Remember: PEFs are easily nonstationary.
Remember: PEFs can deal with spatial aliasing.
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“On what important truth do
very few people
agree with you?”
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“On what important truth do
very few people
agree with you?”
I believe we are close to a new model for land data.
It’s a model that has a manageable inverse.
It’s a model that acknowledges spatial aliasing.
Synthetics can be made in weeks (not months) of coding.
3-D is not much harder than 2-D.
We will recognize features of these synthetics in much field data.
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On what important truth do
very few people
agree with me?
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On what important truth do
very few people
agree with me?
Let’s answer this question.
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On what important truth do
very few people
agree with me?
Will anyone here
work a month with me
building some synthetics?
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The end
A useful model for land data?
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What about statics corrections?
“Static” refers to time-invariant time shift of a seismic trace. Statics means many of the traces have shifts, apparently randomly.
The data shown here shows little evidence of statics.
In reality, statics will occur, sometimes with and sometimes without the land data noise that I am proposing.
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from BEI
steep Vee’s
400 m = 0.4 km offset
1 sec
dx = 3.4 m
Ground roll
Ground roll
Ground roll, slower, shallower
Ground roll, slower, shallower
backscatter
backscatter?
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A data space holding two spikes and two copies of a PEF. That PEF is a convolution of two PEFs each killing one dip.
That data space divided by the PEF. One wave is aliased.
Fly Sketch
How to mark up your computer screen while telling a story.
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FlySketch from Flying Meat
It’s free !
Better it should not be free, so you could rely on it always remaining available, and a better typing mode developed.
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