Examples

Datuming is a simple example of an operator that can be written using WEI. The wavefield at a given surface is recursively downward-continued in depth using a mixed-domain (f-k,f-x) operator using a relation like

$$\mathcal W\left({z+\Delta z} \right)= \mathcal W\left(z \rig... ...partial k_z}{\partial s} \right\vert _{s=s_o}\Delta s\Delta z}.$$ (7)

The library is first called to initialize the functional operators

  call weidtm_init(SLin=weislxN_init	&
  ,                WCin=weimwcN_init	&
  ,                FKin=weiwem3_init	&
  ,                FXin=weissf3_init	),

where

• SLin represents the slowness operator;
• WCin represents the mixed-domain wavefield-continuation operator, a multi-reference slowness operator in this example;
• FKin represents the (f-k) operator, full 3-D prestack in this example;
• FXin represents the (f-x) operator, split-step Fourier in this example.

After initialization, the main datuming operator is called:

  stat = weidtm(adj,add,D,U &
  ,                SLop=weislxN &
  ,                WCop=weimwcN &
  ,                FKop=weiwem3 &
  ,                FXop=weissf3 ),

where D and U are tags to the files storing the wavefield at the surface and at depth, respectively. Other parameters from the command line control the execution of the program (Appendix A).

A second example of operator that can be written in WEI is a modeling/migration pair. In this case, the main operator requires, in addition to the 4 functional operators used for datuming, a 5^th operator for the imaging condition. As we have done before, the WEI operator is first initialized

  call weimig_init(SLin=weislsN_init	&
  ,                WCin=weimwcN_init	&
  ,                FKin=weiwem3_init	&
  ,                FXin=weissf3_init	&
  ,                IGin=weihcig_init	),

and then executed

  stat = weimig(adj,add,R,D &
  ,                SLop=weislsN &
  ,                WCop=weimwcN &
  ,                FKop=weiwem3 &
  ,                FXop=weissf3 &
  ,                IGop=weihcig ).

Figure 2 shows the result of migrating the Marmousi synthetic using seven reference velocities. The main program, makefile, and parameter file are listed in Appendix A.

 

marm
Figure 2 The top panel shows the Marmousi velocity model. The bottom panel shows the migrated image using WEI. The main program, makefile, and parameter file are listed in Appendix A.