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Here we relate the basic theoretical statement
of geophysical inverse theory
to the basic theoretical statement
of separation of signals from noises.
A common form of linearized geophysical inverse theory is
inverse theory

| |
(7) |

| (8) |

We choose the operator to be an identity
and we rename the model to be signal .Define noise by the decomposition of data into signal plus noise,
so
.Finally, let us rename the weighting (and filtering) operations
on the noise and
on the signal.
Thus the usual model fitting becomes
a fitting for signal-noise separation:
| |
(9) |

| (10) |

** Next:** SIGNAL-NOISE DECOMPOSITION BY DIP
** Up:** Nonstationarity: patching
** Previous:** Which coefficients are really
Stanford Exploration Project

4/27/2004