finite difference seismic modelling

Consider the 2D seismic modelling experiment with modeling building with both velocity and density, source generating, observation geometry with both streamer and ocean bottom setting and finite difference wave modelling output both observed data and time slice QC.

Download Experiment

1. We create a velocity model and a density model, and store them as two vectors data and rho in the file data/vel.sg. The two models sampled in 10 meters in both lateral and depth directions. The model has a dipping water bottom and a flat subsurface reflector.

from experiment import *

Process('vel', None,
	'''
	sgcreate data.s0=-1000 data.ds=10 data.ns=600 nx=900
	| sgfieldmath lateral:f="-1000+jx*10" 
	  ref1:f="100+(lateral>0)*0.1*lateral"  ref2:f="2000"
	| sgfieldmath rho:F="1.225+998*(atan(data.time/50)/PI+0.5)"
	  data="340+1160*(data.time>=0)"
	| sgfieldmath rho="rho+500*(data.time>=ref1)+1500*(data.time>=ref2)"
	| sgattribute index=lateral
	  dx:f=10 nx:i=900 ox:f=-1000 ny:i=1
	''')

To QC the synthetic velocity and density model, we use the Figure SCons command.

Figure('./vel.png', 
	'''
	sgplotps top.label="Lateral (m)" data.image=bwr rho.image=owb
	''')

As the data has two vectors, it automatically generate a figure with two plots.



2. We create a source of Ricker wavelet with peak frequency 30Hz. The source is planning to be fired at 3000m in lateral position and 10 meter deep in the water.

Process('source',None,
	'''
	sgcreate data.ns=2000 data.ds=0.002 data.s0=-0.3
	| sgfieldmath index.rename=fldr sz:f=10 sx:f="3000"
	  gy:f=0 sy:f=0 data="ricker(30*data.time)"
	''')

The QC is as simple as

Figure('./source.png',	'sggraphps ')



3. Now we create two observation geometries: a hydrophone streamer on the water surface, and a geophone array on the water bottom, and store them as two columns in a single dataset data/rr.sg.

Process('rr', None,
	'''
	sgcreate data.ns=300 data.ds=10 data.s0=2000 nx=2
	| sgfieldmath index.rename=rl 
	  gx:F=data.time gz:F="(jx==0)*10+jx*(100+data.time*0.1)"
	| sgwindow remove=data
	''')

To QC the receivers and source location, we overlay their positions on the density model.

Figure('ss', 'source',
	'''
	sgfieldout fields=sz,sx
	| sggraphps yreverse=y x=sx y=sz
	  sz.style="*" sz.color="FF0000"
	  xmin=-1000 xmax=7990 ymin=-1000 ymax=4990
	''')


Figure('rr', 'rr',
	'''
	sgresamp dt=200
	| sgfieldmath color:i="jx"
	| sggraphps yreverse=y x=gx y=gz
	  gz.style=. gz.color=color
	  xmin=-1000 xmax=7990 ymin=-1000 ymax=4990
	''')

Figure('./obs.png', 'vel ss.ps rr.ps',
	'''
	sgplotps --default=rho rho.top.label="Lateral (m)"
	  rho.image=bwr rho.image.bar=right
	| sgoverlayps ${SOURCES[1:]}
	''')



4. At last, we do the finite difference wavefield modelling. It has three inputs: the source, the velocity model, and the observation geometry. All of them are stored in the same format, supported by the sigclear-soig.

Process('data wfd', 'source vel rr',
	'''
	sgwefd we=awe2 vel=${SOURCES[1]} vel.vp=data
	  out.grid=${SOURCES[2]} out.grid.vects=gz,gx
	  wfd=${TARGETS[1]} 
	''')

It outputs two files, the observed data and the wavefield snapshot. Both the outputs are stored in the .sg format, the same as the input datasets, The observed data of hydrophones and geophones in two subgroups respectively. We can QC it

Figure('./data.png',
	'sgplotps data.image=seismic multicol=subgroup')



The QC time slice data data/wfd.sg of the FD process has multiple groups, related to wavefield snapshots on each time slice. sgplotps automatically generates a movie, with each page for a slice group.

Figure('./wfd.gif',
	'''
	sgwindow time.min=-0.001 time.max=3.2
	| sgplotps out.title="@group"
	''')

The movie for the time slice QC is as follows.



Finite difference methods need to handle five kinds of data, velocity model, source, observation geometry, observed data and QC time slice. Developers may pay lots of attention on the data accessing, and on the relative parameters for them. However, with sigclear-soig, developers can use the universal API to access all of them, and their relative parameters are stored together with the data.