# Friendly multiples

The phrase "friendly multiples" was coined by O'Doherty and Anstey (1971)^{[1]} to denote the many peg-leg multiples which arise naturally from a propagating wavefront, as it traverses many sedimentary layers. Because each peg-leg is reduced in amplitude by two reflection coefficients, such multiples have very low amplitude, individually. But, since they typically have the same algebraic sign, they typically reinforce each other hence were called "friendly".

The peglegs are delayed, relative to the primary, thus extending the pulse, in effect enhancing the lower frequencies; this is called
Stratigraphic filtering^{[2]}^{[3]}.
Although its effect is similar to absorption; this relative loss of high frequencies is a purely elastic effect, it is also called "apparent attenuation".

The accumulation of many of these peg-leg multiples progressively shifts most of the energy from the primary to the propagating superposition of these "friendly multiples". The events usually seen on workstation screens are these "friendly multiples"; the so-called "primary" is usually just the initial first break. It arrives with a velocity which is the inverse of the average slowness in the overburden, whereas *maximum* amplitude arrives with the velocity given by Backus averaging.

## References

- ↑ O'Doherty, R. F. and Anstey, N. A., 1971. Reflections on Amplitudes: Geoph. Prospg., 19, 430.
- ↑ Banik, N.C., Lerche, I., & Shuey, R.T. 1985. Stratigraphic Filtering, Part I: Derivation of the O'Doherty-Anstey Formula. Geophysics, 50, 2768.
- ↑ Banik, N. C. , I. Lerche, J. R. Resnick, and R. T. Shuey, 1985. Stratigraphic filtering, Part II: Model spectra. GEOPHYSICS. VOL. 50(12) P. 2775-2783.