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Research Scenarios

To test Jag during its development, we implemented a small set of research scenarios:

Figure 3
The signal at the upper left is a random reflectivity series. We compute the lower left signal by convolving the reflectivity series with a 16 point Ricker wavelet, which is shown in the upper right. We compute the lower right wavelet by inverting for an unknown 16 point wavelet given the two traces on the left. The CG solver finds the same zero-phase Ricker wavelet.

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The code fragment progDecon[*] is the main routine of the deconvolution problem. The class instantiates two Rsf. One contains a random time series, the other one the result of a convolution of the time series with a 16 point Ricker wavelet. Next the program instantiates an internal convolution operator. Since we are going to use a Conjugate Gradient solver, we create a positive-definite operator by recasting the operator and vectors according to the normal equations
{\bf A x} &=& {\bf b} \nonumber \\ {\bf A'A x} &=& {\bf A' b}. \nonumber \end{eqnarray}
Finally, we instantiate a CG solver, solve for the unknown wavelet, and write the wavelet to a file. Figure 3 shows the input and the result of the inversion.


 * <BR><!-#include file="./"-><BR>

/** * I solve b = M x for x. * M is a known convolution operator of the time series m (reflectiviy). * x is an unknown filter (wavelet). * b is a known time series (seismic trace). * * I create the normal equations: b_L = M'b and L = M'M and * call a CGSolver to solve M'b = M'M x or b_L = L x. */ public class IcafDecon { public static void main(String[] args) { Rsf trace = new Rsf("./trace.H"); Rsf rflct = new Rsf("./rflct.H");

hasAdjoint icaf = new IcafFactory(rflct, trace.getSpace()); Vector traceNormal = icaf.adjoint().image(trace); CompoundLinearOperatorAdjoint icafNormal = new CompoundLinOpAdj(icaf, icaf.adjoint()); // Create an initial wavelet Rsf wave = (Rsf) icafNormal.getDomain().newMember();; // Solve with CG solver and default solver settings new CGSolver().solve(icafNormal, traceNormal, wave); // Write wave.write(System.out); } }

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Stanford Exploration Project