# Inversion of seismic reflection data in the acoustic approximation

@article{Tarantola1984InversionOS, title={Inversion of seismic reflection data in the acoustic approximation}, author={Albert Tarantola}, journal={Geophysics}, year={1984}, volume={49}, pages={1259-1266} }

The nonlinear inverse problem for seismic reflection data is solved in the acoustic approximation. The method is based on the generalized least‐squares criterion, and it can handle errors in the data set and a priori information on the model. Multiply reflected energy is naturally taken into account, as well as refracted energy or surface waves. The inverse problem can be solved using an iterative algorithm which gives, at each iteration, updated values of bulk modulus, density, and time source…

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## References

SHOWING 1-10 OF 18 REFERENCES

### LINEARIZED INVERSION OF SEISMIC REFLECTION DATA

- Geology
- 1984

This is the first of a series of papers giving the solution of the inverse problem in seismic exploration. The acoustic approximation is used together with the assumption that the velocity field has…

### INTEGRAL FORMULATION FOR MIGRATION IN TWO AND THREE DIMENSIONS

- Geology
- 1978

Computer migration of seismic data emerged in the late 1960s as a natural outgrowth of manual migration techniques based on wavefront charts and diffraction curves. Summation (integration) along a…

### TWO‐DIMENSIONAL AND THREE‐DIMENSIONAL MIGRATION OF MODEL‐EXPERIMENT REFLECTION PROFILES

- Geology
- 1974

Processed reflection data over 3D models demonstrate that 3-D migration eliminates many of the lateral correlation ambiguities caused by “sideswipes” and “blind structures".

### Quantitative Seismology: Theory and Methods

- Geology
- 1980

This work has here attempted to give a unified treatment of those methods of seismology that are currently used in interpreting actual data and develops the theory of seismic-wave propagation in realistic Earth models.

### Seismic waves and sources

- Geology
- 1981

1 Classical Continuum Dynamics.- 1.1. The Stress Dyadic and Its Properties.- 1.2. Geometry of Small Deformations.- 1.3. Linear Elastic Solid.- 1.4. The Field Equations.- 1.5. Lagrangian Formulation.-…

### Generalized Nonlinear Inverse Problems Solved Using the Least Squares Criterion (Paper 1R1855)

- Mathematics
- 1982

We attempt to give a general definition of the nonlinear least squares inverse problem. First, we examine the discrete problem (finite number of data and unknowns), setting the problem in its fully…

### Toward a unified theory of reflector mapping

- Geology
- 1971

Schemes for seismic mapping of reflectors in the presence of an arbitrary velocity model, dipping and curved reflectors, diffractions, ghosts, surface elevation variations, and multiple reflections…

### Robust Modeling With Erratic Data

- Geology
- 1973

An attractive alternative to least‐squares data modeling techniques is the use of absolute value error criteria. Unlike the least‐squares techniques the inclusion of some infinite blunders along with…

### Methods of theoretical physics

- Physics
- 1937

Allis and Herlin Thermodynamics and Statistical Mechanics Becker Introduction to Theoretical Mechanics Clark Applied X-rays Collin Field Theory of Guided Waves Evans The Atomic Nucleus Finkelnburg…