Inversion of prestack field data: An application to 1‐D acoustic media

Hindlet, Francois; Kolb, Pierre

doi:10.1190/1.1892168

Cited by 4 publications

(3 citation statements)

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“…Non-linear acoustic inversion of real data for laterally invariant media have been reported by Hindlet and Kolb (1988) and by Pica, Diet and Tarantola (1990). Hindlet and Kolb (1988) used a finite-difference method to model the data. They estimated both reflectivity and velocity starting with a low-frequency inversion and then gradually increasing the bandwidth.…”

Section: Introductionmentioning

confidence: 84%

“…demonstrated on synthetic data that this difficulty could be overcome by starting the inversion with low-frequency data, followed by a step-wise increase of the frequency content. Hindlet and Kolb (1988) succeeded in applying this technique to real data, while Pica, Diet and Tarantola (1987) encountered some difficulties. These difficulties might be related to the poor signal-to-noise ratio often found in the low-frequency band of real data.…”

Section: Estimation Of T H E Earth Modelmentioning

confidence: 99%

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MULTI‐OFFSET ACOUSTIC INVERSION OF A LATERALLY INVARIANT MEDIUM: APPLICATION TO REAL DATA¹

Helgesen¹,

Kolb²

1993

Geophysical Prospecting

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HELGESEN, J. and KOLB, P. 1993. Multi-offset acoustic inversion of a laterally invariant medium: application to real data. Geophysical Prospecting 41,517-533.The aim of seismic inversion methods is to obtain quantitative information on the subsurface properties from seismic measurements. However, the potential accuracy of such methods depends strongly on the physical correctness of the mathematical equations used to model the propagation of the seismic waves. In general, the most accurate models involve the full non-linear acoustic or elastic wave equations. Inversion algorithms based on these equations are very CPU intensive. The application of such an algorithm on a real marine CMP gather is demonstrated. The earth model is assumed to be laterally invariant and only acoustic wave phenomena are modelled. A complete acoustic earth model (P-wave velocity and reflectivity as functions of vertical traveltime) is estimated. The inversion algorithm assumes that the seismic waves propagate in 2D. Therefore, an exact method for transforming the real data from 3D to 2D is derived and applied to the data. The time function of the source is estimated from a vertical far-field signature and its applicability is demonstrated by comparing synthetic and real water-bottom reflections. The source scaling factor is chosen such that the false reflection coefficient due to the first water-bottom multiple disappears from the inversion result. In order to speed up the convergence of the algorithm, the following inversion strategy is adopted: an initial smooth velocity model (macromodel) is obtained by applying Dix's equation to the result of a classical velocity analysis, followed by a smoothing operation. The initial reflectivity model is then computed using Gardner's empirical relationship between densities and velocities. In a first inversion step, reflectivity is estimated from small-offset data, keeping the velocity model fixed. In a second step, the initial smooth velocity model, and possibly the reflectivity model, is refined by using larger-offset data. This strategy is very efficient. In the first step, only ten iterations with a quasi-Newton algorithm are necessary in order to obtain an excellent convergence. The data window was 0-2.8 s, the maximum offset was 250 m, and the residual energy after the first inversion step was only 5% 517 518 JAN HELGESEN AND PIERRE KOLB of the energy of the observed data. When the earth model estimated in the first inversion step is used to model data at moderate offsets (900 m, time window 0.0-1.1 s), the data fit is very good. In the second step, only a small improvement in the data fit could be obtained, and the convergence was slow. This is probably due to the strong non-linearity of the inversion problem with respect to the velocity model. Nevertheless, the final residual energy for the moderate offsets was only 11 %.The estimated model was compared to sonic and density logs obtained from a nearby well. The comparison indicated that the present algorithm can be used to estimate normal i...

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Section: Introductionmentioning

confidence: 84%

Section: Estimation Of T H E Earth Modelmentioning

confidence: 99%

MULTI‐OFFSET ACOUSTIC INVERSION OF A LATERALLY INVARIANT MEDIUM: APPLICATION TO REAL DATA¹

Helgesen¹,

Kolb²

1993

Geophysical Prospecting

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“…Full-waveform inversion (FWI) using two-way wave equation obtains a velocity update by crosscorrelation between the state wavefield, which is similar to the source wavefield in RTM, and the adjoint wavefield (Tarantola, 1984;Hindlet and Kolb, 1988;Plessix, 2006). The adjoint wavefield is extrapolated from a data residual, which is often defined as the difference between observed and synthetic data.…”

Section: Introductionmentioning

confidence: 99%

Acoustic wavefield imaging using the energy norm

2016

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Wavefield energy can be measured by the so-called energy norm. We have extended the concept of "norm" to obtain the energy inner product between two related wavefields. Considering an imaging condition as an inner product between the source and receiver wavefields at each spatial location, we have developed a new imaging condition that represents the total reflection energy. Investigating this imaging condition further, we have found that it accounts for wavefield directionality in space time. Based on the directionality discrimination provided by this imaging condition, we have applied it to attenuate backscattering artifacts in reverse time migration (RTM). This imaging condition can be designed not only to attenuate backscattering artifacts, but also to attenuate any selected reflection angle. By exploiting the flexibility of this imaging condition for attenuating certain angles, we have developed a procedure to preserve the type of events that propagate along the same path, i.e., backscattered, diving, and head waves, leading to a suitable application for full-waveforminversion (FWI). This application involves filtering the FWI gradient to preserve the tomographic term (waves propagating in the same path) and attenuate the migration term (reflections) of the gradient. We have developed the energy imaging condition applications for RTM and FWI using numerical experiments in simple (horizontal reflector) and complex models (Sigsbee and Marmousi).

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Inversion of 1‐D acoustic medium from real seismic data

Helgesen

Kolb²

1989

SEG Technical Program Expanded Abstracts 1989

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Inversion of prestack field data: An application to 1‐D acoustic media

Cited by 4 publications

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MULTI‐OFFSET ACOUSTIC INVERSION OF A LATERALLY INVARIANT MEDIUM: APPLICATION TO REAL DATA¹

MULTI‐OFFSET ACOUSTIC INVERSION OF A LATERALLY INVARIANT MEDIUM: APPLICATION TO REAL DATA¹

Acoustic wavefield imaging using the energy norm

Inversion of 1‐D acoustic medium from real seismic data

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Inversion of prestack field data: An application to 1‐D acoustic media

Cited by 4 publications

References 0 publications

MULTI‐OFFSET ACOUSTIC INVERSION OF A LATERALLY INVARIANT MEDIUM: APPLICATION TO REAL DATA1

MULTI‐OFFSET ACOUSTIC INVERSION OF A LATERALLY INVARIANT MEDIUM: APPLICATION TO REAL DATA1

Acoustic wavefield imaging using the energy norm

Inversion of 1‐D acoustic medium from real seismic data

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Product

Resources

About

MULTI‐OFFSET ACOUSTIC INVERSION OF A LATERALLY INVARIANT MEDIUM: APPLICATION TO REAL DATA¹

MULTI‐OFFSET ACOUSTIC INVERSION OF A LATERALLY INVARIANT MEDIUM: APPLICATION TO REAL DATA¹