Derivation of Layer Parameters of an Elastic Medium From Reflection Coefficient Matrices*

Aminzadeh, F.

doi:10.1111/j.1365-2478.1984.tb00741.x

Cited by 2 publications

(1 citation statement)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Meadows & Coen (1986) developed a technique for inversion in anisotropic medium. This technique is based on the state-space approach developed by Shiva & Mendel (1983) and Aminzadeh (1984).…”

Section: Introductionmentioning

confidence: 99%

Generalized non-linear elastic inversion with constraints in model and data spaces

Carrion

1989

Geophysical Journal International

View full text Add to dashboard Cite

Seismic data are non-linearly related to model parameters such as seismic velocities. However, seismic inversion is usually considered in a linear approximation. Such techniques as the Born inversion were recently applied to seismic data.Non-linear inversion is more complicated and involves extensive calculations. Non-linear inversion was developed in the frame work of an unconstrained optimization procedure. It uses as a priori information an initial model and probability distribution functions in the data and model spaces (This a priori information is called 'soft' bounds).In this paper, we propose a new technique for solving a constrained non-linear inversion. This technique will allow us to use a priori information not only in terms of 'soft' bounds, but 'hard' bounds as well (usually giving more stable and accurate solutions).Non-linear inversion is considered as an iterative procedure which involves a dual transform at each iteration. A dual transform allows for considering the problem in terms of the Lagrangian multipliers. The number of Lagrangian multipliers is equal to the number of available data and thus, significantly reduces the dimension of the problem (this is true for underdetermined problems only). However, the most important property of the dual transform is that it allows us to consider a constrained problem as an unconstrained problem.Another important property is that proper constraints incorporate small-wave numbers in the generalized inversion. It is shown that conventional (unconstrained non-linear inversion) is a special case of the constrained non-linear inversion developed in this paper if the truncation operator is represented by the identity matrix.

show abstract

Section: Introductionmentioning

confidence: 99%

Generalized non-linear elastic inversion with constraints in model and data spaces

Carrion

1989

Geophysical Journal International

View full text Add to dashboard Cite

show abstract

Full waveform inversion of reflection data

Singh¹,

West²,

Bregman³

et al. 1989

J. Geophys. Res.

View full text Add to dashboard Cite

The theory of a direct inversion method to obtain the P and S wave seismic velocities and the density of a horizontally, finely layered elastic medium from vertical and horizontal component plane wave seismograms in the tau‐p (slant stacked) domain has been developed. The method is based on the downward continuation method of Bube and Burridge (1983), but plane wave seismograms with a range of ray parameters are used simultaneously to obtain the velocity and density profiles. A corrected acoustic approximation of the elastic case has also been developed with which one may obtain a model of the P wave velocity and density from vertical component seismic recordings. However, it requires the S wave velocity to be estimated a priori, for instance as a fixed fraction of the P wave velocity. Many direct inverse methods, including the Bube and Burridge procedure followed here, may lack stability when implemented numerically, specially when they are applied to real data which necessarily are band limited at both low and high frequencies. The possibility of a stable implementation of our methods has been investigated, firstly by using synthetic data for layered acoustic media containing a full range of low frequencies. In this case, the inverted velocity and density profiles are in good agreement with the test models. Secondly, the indeterminacy associated with the lack, in practice, of low frequencies has been studied, and a method has been devised to estimate the missing low‐frequency data from travel time information. Finally, the inversion algorithm has then been applied to high‐quality marine seismic reflection data obtained by the North Atlantic Transect (NAT) group in the deep ocean using an expanding spread profile (ESP). In this test, only the P wave velocity profile was estimated independently, because the move‐out data cannot provide low‐frequency information about density. Also, the “source wavelet” of the seismic system had to be estimated from the seismic recordings. A stable and plausible estimate of the velocity variation was obtained. Unfortunately, no independent measurement of this velocity structure is available with which to verify the method's accuracy.

show abstract

Derivation of Layer Parameters of an Elastic Medium From Reflection Coefficient Matrices*

Cited by 2 publications

References 4 publications

Generalized non-linear elastic inversion with constraints in model and data spaces

Generalized non-linear elastic inversion with constraints in model and data spaces

Full waveform inversion of reflection data

Contact Info

Product

Resources

About