# Difference between revisions of "Dictionary:Convolutional model"

Chrisdinneen (talk | contribs) (Fixed Equations) |
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The concept that a seismic trace ''f''(''t'') can be represented by the convolution of an embedded (equivalent) wavelet ''w''(''t'') with a reflectivity function ''r''(''t'') plus random noise ''n''(''t''): | The concept that a seismic trace ''f''(''t'') can be represented by the convolution of an embedded (equivalent) wavelet ''w''(''t'') with a reflectivity function ''r''(''t'') plus random noise ''n''(''t''): | ||

− | <center><math>f(t)=w(t)\ | + | <center><math>f(t)=w(t)\ast r(t)+n(t) </math></center> |

This model is a consequence of the concept that each reflected wave causes its own effect at each geophone (or hydrophone) independent of what other waves are affecting the geophone and that the geophone response is simply the sum (linear superposition) of the effects of all the waves. The model can be modified to allow for propagation effects such as absorption. The convolutional model is implied in most seismic processing and interpretation. | This model is a consequence of the concept that each reflected wave causes its own effect at each geophone (or hydrophone) independent of what other waves are affecting the geophone and that the geophone response is simply the sum (linear superposition) of the effects of all the waves. The model can be modified to allow for propagation effects such as absorption. The convolutional model is implied in most seismic processing and interpretation. |

## Revision as of 10:07, 24 February 2015

The concept that a seismic trace *f*(*t*) can be represented by the convolution of an embedded (equivalent) wavelet *w*(*t*) with a reflectivity function *r*(*t*) plus random noise *n*(*t*):

This model is a consequence of the concept that each reflected wave causes its own effect at each geophone (or hydrophone) independent of what other waves are affecting the geophone and that the geophone response is simply the sum (linear superposition) of the effects of all the waves. The model can be modified to allow for propagation effects such as absorption. The convolutional model is implied in most seismic processing and interpretation.