Maximum likelihood estimation of seismic reflection coefficients

Journal Article · Tue Oct 01 04:00:00 EDT 1985 · Geophys. Prospect.; (United States)

DOI:https://doi.org/10.1111/j.1365-2478.1985.tb00781.x· OSTI ID:6056397

Ozdemir, H

A seismic trace is modeled as a moving average (MA) process both in signal and noise: a signal wavelet convolved with a reflection coefficient series plus colored random noise. Seismic reflection coefficients can be estimated from seismic traces using suitable estimation algorithms if the input wavelet is known and vice versa. The maximum likelihood (ML) algorithm is used to estimate the system order and the reflection coefficients. The system order is related to the arrival time of the latest signal in a complex seismic reflection event. The least-squares (LS) method does not provide such information. The ML algorithm makes assumptions only about the Gaussian nature of the noise. It is better suited for seismic applications since the LS method inherits the white noise assumption. The Gauss-Newton (G-N) and Newton-Raphson (N-R) optimization algorithms are used to obtain the ML and the LS estimates. Reflection coefficient estimations are affected by the choice of sampling rate of seismic data. Theoretically, the optimum choice in system identification is the Nyquist rate. Experience with synthetic data confirms the theory. In practice, good estimates of reflection coefficients are possible only up to certain pulse separations (or, equivalently, orders). This is mostly due to numerical problems with the optimization algorithms used and partly due to the limited bandwidth of seismic signals. Good estimates from data simulated using three airgun array pulses recorded with 6-128 Hz filter setting are possible up to about 40.0 ms pulse separations. Successful estimations from pinchout and thin layer simulations and well controlled offshore ''bright-spots'' are given.

• Research Organization: Istanbul Teknik University, Tesvikiye, Istanbul
• OSTI ID: 6056397
• Journal Information: Geophys. Prospect.; (United States), Journal Name: Geophys. Prospect.; (United States) Vol. 33:6; ISSN GPPRA
• Country of Publication: United States
• Language: English

Related Subjects

58 GEOSCIENCES
580203* -- Geophysics-- Geophysical Survey Methods-- (1980-1989)
FUNCTIONS
GAUSS FUNCTION
GEOPHYSICAL SURVEYS
LEAST SQUARE FIT
MATHEMATICAL MODELS
MAXIMUM-LIKELIHOOD FIT
NOISE
NUMERICAL SOLUTION
REFLECTION
SEISMIC SURVEYS
SEISMIC WAVES
SIGNALS
SURVEYS