Maximum likelihood estimation of the ratio of the velocities of

Details Maximum likelihood estimation of the ratio of the velocities of Maximum likelihood estimation of the ratio of the velocities of

1981-02-11

1983-12-20

Moskowitz, Nelson

Communications, electrical: acoustic wave systems and devices

Seismic prospecting

Land-reflection type

367 75, 364421, G01V 136

Patent

active

044221657

ABSTRACT:
Maximum likelihood estimation theory is applied to the determination of the ratio of P-wave velocity to S-wave velocity (V.sub.p /V.sub.s) from P-wave and S-wave seismic sections obtained along the same line of exploration. For a certain statistical model, the optimal estimator for V.sub.p /V.sub.s is determined, and shown to be equivalent to maximizing the simple mathematical correlation between P-wave and stretched S-wave seismogram segments. The maximum likelihood method provides a data-dependent formula for the mean square error associated with the V.sub.p /V.sub.s estimate. Alternatively, the latter formula provides a measure of the V.sub.p /V.sub.s information contained in the data. The information measure also provides optimal weighting for computing multitrace V.sub.p /V.sub.s averages, and provides for the determination of the statistical error in such averages. The performance of the maximum likelihood estimator and its attendant information measure are demonstrated on synthetic and real seismograms.

REFERENCES:
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patent: 3514585 (1970-05-01), Horsworthy
patent: 3571788 (1971-03-01), Bachus et al.
patent: 3629800 (1971-12-01), Schneider
patent: 4203161 (1980-05-01), Johnson et al.
patent: 4241429 (1980-12-01), Bloomquist et al.
patent: 4244026 (1981-01-01), Dickey
Nations, "Lithology . . . Wave Transit Time Relationships", 6/5/74, pp. 3-8, 15th Annu. Logg. Symp. of SPWLA, Texas.

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