Non-linear seismic trace matching to well logs

1. A method of filtering seismic data, the method comprising:

calculating, from an input seismic trace comprising negative and positive samples, a nonlinear compression trace using a plurality of the positive samples from the input seismic trace;

calculating a nonlinear rarefaction trace using a plurality of the negative samples from the input seismic trace; and

deriving a multi-component matching filter to fit a plurality of samples from the input seismic trace, nonlinear compression trace, and nonlinear rarefaction trace to a reference trace,

wherein calculating a nonlinear compression trace using a plurality of the positive samples from the input seismic trace comprises selecting the positive samples S i >0 from the input seismic trace, and calculating a nonlinear compression sample Q i =ƒ(S i ) for each positive sample, wherein ƒ(x) is a nonlinear function, and

wherein calculating a nonlinear rarefaction trace using a plurality of the negative samples from the input seismic trace comprises selecting the negative samples S i <0 from the input seismic trace, and calculating a nonlinear rarefaction sample Z(i)=ƒ(S i ) for each negative sample, and

wherein deriving a multi-component matching filter comprises minimizing the function

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wherein the multi-component matching filter comprises an adjusted normal trace filter F 1 , a compression filter F 2 , and a rarefaction filter F 3 .

2. The method of claim 1 , further comprising filtering a second seismic trace, comprising negative and positive samples, using the multi-component matching filter.

3. The method of claim 2 , wherein filtering a second seismic trace comprises:

calculating, from the second seismic trace, a second nonlinear compression trace using a plurality of the positive samples from the second seismic trace;

calculating a second nonlinear rarefaction trace using a plurality of the negative samples from the second seismic trace; and

applying the multi-component matching filter to the second seismic trace, second nonlinear compression trace, and second nonlinear rarefaction trace.

4. The method of claim 1 , wherein the reference trace is a well log trace, and the input seismic trace represents data gathered for subsurface formations in the vicinity of the well bore from which the well log trace was gathered.

5. The method of claim 4 , wherein the well log comprises measured or calculated data as a function of well depth, comprising at least one of sound velocity, density, porosity, liquid saturation, acoustic impedance, and reflectivity.

6. The method of claim 1 , wherein ƒ x =|x| 1+r −|x|.

7. The method of claim 6 , wherein 0<r≦1.

8. A method of filtering seismic data, the method comprising:

calculating, from an input seismic trace comprising negative and positive samples, a nonlinear compression trace using a plurality of the positive samples from the input seismic trace;

calculating a nonlinear rarefaction trace using a plurality of the negative samples from the input seismic trace;

deriving a multi-component matching filter to fit a plurality of samples from the input seismic trace, nonlinear compression trace, and nonlinear rarefaction trace to a reference trace; and

filtering a second seismic trace, comprising negative and positive samples, using the multi-component matching filter;

wherein filtering a second seismic trace comprises:

calculating, from the second seismic trace, a second nonlinear compression trace using a plurality of the positive samples from the second seismic trace;

calculating a second nonlinear rarefaction trace using a plurality of the negative samples from the second seismic trace; and

applying the multi-component matching filter to the second seismic trace, second nonlinear compression trace, and second nonlinear rarefaction trace;

wherein the reference trace is a well log trace, and the input seismic trace represents data gathered for subsurface formations in the vicinity of the well bore from which the well log trace was gathered;

wherein the well log comprises measured or calculated data as a function of well depth, comprising at least one of sound velocity, density, porosity, liquid saturation, acoustic impedance, and reflectivity;

wherein calculating a nonlinear compression trace using a plurality of the positive samples from the input seismic trace comprises selecting the positive samples S i >0 from the input seismic trace, and calculating a nonlinear compression sample Q i =ƒ(S i ) for each positive sample, wherein ƒ(x) is a nonlinear function;

wherein calculating a nonlinear rarefaction trace using a plurality of the negative samples from the input seismic trace comprises selecting the negative samples S i <0 from the input seismic trace, and calculating a nonlinear rarefaction sample Z(i)=ƒ(S i ) for each negative sample;

wherein ƒ x =|x| 1+r −|x|;

wherein 0<r≦1; and

wherein deriving a multi-component matching filter comprises minimizing the function

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wherein the multi-component matching filter comprises an adjusted normal trace filter F 1 , a compression filter F 2 , and a rarefaction filter F 3 .