notebook.community

Edit and run



In [1]:

    
10+10









    Out[1]:





20



In [2]:

    
import math



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math.sqrt(20)









    Out[3]:





4.47213595499958



In [4]:

    
%%file modeling.scons

# Model with two spikes
Flow('model',None,
     '''
     spike n1=250 n2=50 nsp=2 k1=50,100 k2=40,10 |
     ricker1 frequency=10 | put v0=1 dv=0.1
     ''')

Flow('data','model','veltran adj=n x0=0.1 dx=0.01 nx=80')
Result('data','grey title=Data')









    



Writing modeling.scons

Section

List

Link: See Madagascar

Explanation for the modeling part

We create a model in time-velocity space $(t_0,v)$, then we model data by spreading in time-diatance space $(t,x)$ over hyperbolas $t(x) = \sqrt{t_0^2 + \frac{x^2}{v^2}}$.



In [5]:

    
from m8r import view



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view('data')









    Out[6]:

Let us go back to thr time-velocity space.

If $\mathbf{L}$ is a linear operator, $\mathbf{L}^T$ is the adjoint operator.

The dot-product test is

$\mathbf{d}^T\,\mathbf{L}\,\mathbf{m} = \mathbf{m}^T\,\mathbf{L}^T\,\mathbf{d}$



In [8]:

    
%%file adjoint.scons

Flow('tran','data','veltran adj=y nv=100')
Result('tran','grey title="Velocity Transform" ')









    



Writing adjoint.scons



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view('tran')









    Out[9]:



In [10]:

    
!ls









    



Fig            data.png       tran.png
SConstruct     data.rsf       tran.rsf
Untitled.ipynb model.rsf
adjoint.scons  modeling.scons



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%%file mute.scons

Flow('data1','tran','cut max2=0.5 | veltran adj=n x0=0.1 dx=0.01 nx=80')
Result('data1','grey title=Noise')

Flow('data2','data data1','add scale=1,-1 ${SOURCES[1]}')
Result('data2','grey title=Signal')









    



Writing mute.scons



In [12]:

    
view('data1')









    Out[12]:



In [13]:

    
view('data2')









    Out[13]:



In [16]:

    
!sfdottest sfveltran nv=100 mod=tran.rsf dat=data.rsf









    



sfdottest:  L[m]*d=68864.5
sfdottest: L'[d]*m=68864.7



In [19]:

    
%%file inversion.scons

# Run inversion using Conjugate Gradients

Flow('inv','data tran',
     'conjgrad veltran mod=${SOURCES[1]} nv=100 niter=10')
Result('inv','grey title="Velocity Transform (Inverse)" ')

Flow('idata1','inv','cut max2=0.5 | veltran adj=n x0=0.1 dx=0.01 nx=80')
Result('idata1','grey title=Noise')

Flow('idata2','data idata1','add scale=1,-1 ${SOURCES[1]}')
Result('idata2','grey title=Signal')









    



Overwriting inversion.scons



In [18]:

    
view('inv')









    Out[18]:



In [20]:

    
view('idata1')









    Out[20]:



In [21]:

    
view('idata2')









    Out[21]:



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