68th EAGE Conference and Exhibition incorporating SPE EUROPEC 2006

From large-offset PP seismic reflections one can estimate three traveltime parameters: the zero-offset two-way traveltime, the NMO velocity and a heterogeneity coefficient, using the shifted hyperbola approximation or a fractional approximation. From large-offset PS seismic reflections one can estimate two traveltime parameters: the zero-offset two-way traveltime and the NMO velocity.

Full wavefield inversion of seismic data has a less than stering reputation as a process for direct Earth model estimation. One reason for this reputation is the absence of low frequencies in observed seismic data. In this presentation we discuss the theoretial aspects of this issue and provide empirical evidence of its validity. We further discuss this dearth of low frequencies and its relation to inverse scattering based inversion.

In linearized inversion methods, the computational cost is dominated by the generation of the sensitivity matrix and by the least-squares solution of linear systems. The multiple re-weighted least square (MRLS) is more robust than to the Gauss-Newton method and explores the model space in an extensive and effective way, since many models can be generated from the same sensitivity matrix. In the present paper we investigate the use of preconditioners associated to triangular matrices formed by L-bands in order to decrease the computational cost of the MRLS method. The preconditioners are generated from a partial orthogonalization of the sensitivity matrix. The original system of linear equations is modified in order that the coefficient matrix, in the normal equation, has a band of L co-diagonals with null elements. We apply the new approach to the inversion of 2D seismic waveform inversion. Numeric examples illustrate the performance of the MRLS approach and the decrease in the total computational cost as a function of the number L of bands in the preconditioners.

In deep offshore, crustal-scale seismic imaging is classically performed by traveltime tomography applied to wide-angle seismic data recorded by a network of Ocean Bottom Seismometers (OBS). The resulting velocity model is of limited resolution. If the wide-angle experiment is multifold thanks to densely sampled OBSs, this large-scale velocity model can be used as a starting model for full-waveform inversion. Considering the full wavefield recorded over a broad range of apertures is expected to provide a significant resolution improvement in the velocity models.
We applied 2D frequency-domain full-waveform inversion to wide-angle data recorded by 100 OBSs deployed perpendicular to the trench axis of a subduction zone, offshore Japan. The full-waveform modelling/inversion are entirely implemented in the frequency domain. Thirteen frequencies ranging from 3 to 15 Hz were inverted sequentially with a weighted least-square method, the velocity model obtained for each frequency being used to start the inversion of the next one. The resolution of the velocity models inferred from traveltime and full waveform tomographies were estimated to be ~10 km and 500 m respectively at 10 km depth suggesting a resolution improvement by an over order of magnitude. The relevance of the structures was assessed by ray tracing and full-waveform modelling.

The Common-Reflection-Surface stack extracts kinematic wavefield attributes from pre-stack data which can be used for a tomographic inversion scheme to determine smooth velocity models for depth migration. These kinematic wavefield attributes give a second-order approximation of the diffraction traveltimes. Thus, the obtained velocity models can only explain the pre-stack data up to second order. In this paper I present a technique to update these models. The method makes use of residual traveltime information picked in CIG gathers and is, therefore, beyond second order. Migration is performed only for selected depth points and directly to residual time. The picking of residual moveout does not need to follow a specific trend. Moreover, there is no pulse stretch phenomenon in migration to residual time. The inversion algorithm is demonstrated on a synthetic data example.

This paper presents a full wave-equation methodology for velocity model building based on the non-linear inversion of a semblance criterium with respect to the velocity field. A new type of migration, called the modulated-shot migration, is used to obtain the necessary gathers. The semblance of these gathers after spatial averaging is used as the cost function. This methodology is shown to successfully image the Marmousi model and the sub-salt part of the Sigsbee model.

Seismic full waveform inversion based on the acoustic wave equation attempts to find the acoustic parameters of the subsurface from seismic data. Because the least-squares error between observed and modelled data has local minima, a good initial velocity model is
required. We therefore prefer the name nonlinear migration. We compared three gradient-based minimisation methods on a two-dimensional acoustic test problem: the limited-memory BFGS method with or without bounds on the model parameters, and Nesterov's method.

We found that the L-BFGS method without bound constraints performs best on the test problem, followed by Nesterov's method. However, the cost of decreasing the error by a given factor increases dramatically when the error becomes smaller.

Subsalt velocity analysis using prestack wave equation migration scans through perturbed velocity model is an accurate but expensive approach. To reduce turnaround time and computation cost, we investigated an alternative approach for subsalt velocity analysis. In this approach, we separate the prestack focusing step from the poststack modeling step. We first use the current best velocity model to perform one prestack migration to produce a subsalt image. We then use the subsalt image as a reflectivity model to perform upgoing one-way exploding reflector modeling to produce demigrated zero-offset seismic data. Using this demigrated data as input, we perform a scan of poststack wave equation migrations through perturbed subsalt velocity model. We demonstrate the necessity of demigrating only to the base of salt in order to avoid significant image degradation and we show the feasibility of this methodology using the 2D Sigsbee data set.

Our analysis shows that frequencies less than 6-7 Hz, if they are recorded in marine surveys, are often very noisy and of little use. Here we analyze the potential benefits of these lower frequencies to justify our extensive acquisition efforts to record them with less noise.
We find that the recording and use of low frequencies for subsalt imaging offers the following advantages:
1) A sharper wavelet,
2) Ability to produce interpretable images where there were none before,
3) Ability to improve velocities so that higher frequencies can be imaged.
4) Low frequencies penetrate into shadow zones
5) Provide stability for wave equation inversion algorithms

Surface-related multiple elimination (SRME) can predict and attenuate all multiples generated by the air-water interface. Earlier SRME schemes for walkaway VSP (WVSP) data involve a model in order to generate primaries recorded at the air-water surface which are not recorded in a WVSP experiment. In this paper, we generate surface data from the WVSP using interferometry. Using this approach we obtain a data driven SRME scheme for WVSP data. The SRME algorithms developed for marine seismic can be used with minor revisions.