Pascal Podvin

Practical aspects and applications of 2D stereotomography

Stereotomography is a new velocity estimation method. This tomographic approach aims at retrieving subsurface velocities from prestack seismic data. In addition to traveltimes, the slope of locally coherent events are picked simultaneously in common offset, common source, common receiver, and common midpoint gathers. As the picking is realized on locally coherent events, they do not need to be interpreted in terms of reflection on given interfaces, but may represent diffractions or reflections from anywhere in the image. In the high‐frequency approximation, each one of these events corresponds to a ray trajectory in the subsurface. Stereotomography consists of picking and analyzing these events to update both the associated ray paths and velocity model. In this paper, we describe the implementation of two critical features needed to put stereotomography into practice: an automatic picking tool and a robust multiscale iterative inversion technique. Applications to 2D reflection seismic are presented on syn...

Migration velocity analysis from locally coherent events in 2‐D laterally heterogeneous media, Part I: Theoretical aspects

We present a new method based on migration velocity analysis (MVA) to estimate 2‐D velocity models from seismic reflection data with no assumption on reflector geometry or the background velocity field. Classical approaches using picking on common image gathers (CIGs) must consider continuous events over the whole panel. This interpretive step may be difficult—particularly for applications on real data sets. We propose to overcome the limiting factor by considering locally coherent events. A locally coherent event can be defined whenever the imaged reflectivity locally shows lateral coherency at some location in the image cube.In the prestack depth‐migrated volume obtained for an a priori velocity model, locally coherent events are picked automatically, without interpretation, and are characterized by their positions and slopes (tangent to the event). Even a single locally coherent event has information on the unknown velocity model, carried by the value of the slope measured in the CIG. The velocity is e...

3-D preserved amplitude prestack depth migration on a workstation

We present an algorithm based on the ray+Born approximation for 3-D preserved amplitude prestack depth migration (PAPsDM) of seismic reflection data. This ray+Born inversion scheme allows the quantitative recovery of model perturbations. The Green’s functions are estimated by dynamic ray tracing in 3-D heterogeneous smooth velocity fields with a wavefront construction (WFC) method. The PAPsDM algorithm was implemented on a single‐processor Sun Sparc 20 workstation. Special attention was paid to CPU efficiency and memory requirements. We present an application on a 3-D real marine data set (13 Gbytes). About one week of CPU time is needed to obtain a migrated image of 7 × 1 × 1 km.

Migration velocity analysis from locally coherent events in 2‐D laterally heterogeneous media, Part II: Applications on synthetic and real data

We demonstrate a method for estimating 2-D velocity models from synthetic and real seismic reflection data in the framework of migration velocity analysis (MVA). No assumption is required on the reflector geometry or on the unknown background velocity field, provided that the data only contain primary reflections/diffractions. In the prestack depth-migrated volume, locations where the reflectivity exhibits local coherency are automatically picked without interpretation in two panels: common image gathers (CIGs) and common offset gathers (COGs). They are characterized by both their positions and two slopes. The velocity is estimated by minimizing all slopes picked in the CIGs. We test the applicability of the method on a real data set, showing the possibility of an efficient inversion using (1) the migration of selected CIGs and COGs, (2) automatic picking on prior uncorrelated locally coherent events, (3) efficient computation of the gradient of the cost function via paraxial ray tracing from the picked events to the surface, and (4) a gradient-type optimization algorithm for convergence.

3D ray+Born migration/inversion—Part 1: Theory

Prestack ray+Born migration/inversion can be split in two steps : the computation of common image gathers (CIGs) and their weighted stack (the migration stack). The choice of the domain for the CIGs (shot, offset, angle, etc.) has a direct impact on the resolution of the migration stack. This resolution can be studied easily in the frame of ray+Born migration/inversion theory resulting into improved migration/inversion formulas according to the acquisition geometry. This paper is devoted to this analysis in the cases of a simple 2D acquisition and of a 3D swath acquisition, both corresponding to classical data sets from the SEG/EAGE 3D overthrust experiment. We show that the migration formula originally designed for 3D marine acquisition is not adaptable to the 3D swath acquisition. Finally, we propose a new formula for this specific acquisition, which improves the resolution of the final migrated image. The relevance of this new formula is illustrated in the frame of the SEG/EAGE experiment in the companion paper.

3D ray+Born migration/inversion—Part 2: Application to the SEG/EAGE overthrust experiment

The SEG/EAGE overthrust model is a synthetic onshore velocity model that was used to generate several large synthetic seismic data sets using acoustic finite-difference modeling. From this database, several realistic subdata sets were extracted and made available for testing 3D processing methods. For example, classic onshore-type data-acquisition geometries are available such as a swath acquisition, which is characterized by a nonuniform distribution of long offsets with azimuth and midpoints. In this paper, we present an application of 2.5D and 3D ray+Born migration/inversion to several classical data sets from the SEG/EAGE overthrust experiment. The method is formulated as a linearized inversion of the scattered wavefield. The method allows quantitative estimates of short wavelength components of the velocity model. First, we apply a 3D migration/inversion formula formerly developed for marine acquisitions to the swath data set. The migrated sections exhibit significant amplitude artifacts and acquisition footprints, also revealed by the shape of the local spatial resolution filters. From the analysis of these spatial resolution filters, we propose a new formula significantly improving the migrated dip section. We also present 3D migrated results for the strike section and a small 3D target containing a channel. Finally, the applications demonstrate, that the ray+ Born migration formula must be adapted to the acquisition geometry to obtain reliable estimates of the true amplitude of the model perturbations. This adaptation is relatively straightforward in the frame of the ray+Born formalism and can be guided by the analysis of the resolution operator.

Stereotomographic picking in practice

Stereotomography allows estimating velocity macro models from seismic reflection data. Compared to travel time tomography the specificity of the method is that it considers locally coherent events. As a result, Stereotomographic picking is easier and leads to a much denser coverage of the model. Several applications have demonstrated the efficiency but also the principal difficulties of the approach : regularization and picking. For picking, in order to retain the efficiency of the method, we propose a semi-automatic procedure. Starting from an initial automatic picking we propose various strategies for semi-automatic or interactive selections of the stereotomographic picks. We illustrate this procedure with an application to a PZ component OBC line on the Mahogany field.

Testing the Behaviour of Differential Semblance for Velocity Optimization

Background velocity estimation is a critical step for the depth imaging process. Because of constant increase of acquired 3D data volumes, this velocit estimation, cast as an inverse problem, should be automated (no picking).

Migration Based Velocity Analysis In 2D Laterally Heterogeneous Media

We present a new method based on Migration Velocity Analysis (MVA) to estimate 2D velocity models with no assumption on the re ector geometry nor on the background velocity eld. In the prestack depth migrated volume, locally coherent events are automatically picked without interpretation and characterized by their positions and two slopes. The velocity is estimated by optimizing the atness of these events in the Common Image Gathers. We show how to compute the gradient of the cost function via ray tracing. The e ciency of the method is illustrated by inverting the velocity eld on a 2D synthetic data set using a local optimization algorithm. We also show that two di erent kinds of methods, Di erential Semblance Optimization formulated in the migrated domain and Stereotomography or slope tomography in time data space, are equivalent.

3-D Refraction Traveltime Tomography Algorithm Based on Adjoint State Techniques

Classical 3-D refraction traveltime tomography algorithms may suffer from computational limitations due to the large datasets that come from current seismic acquisition surveys. To overcome these issues, we suggest a 3-D refraction tomography algorithm based on adjoint state techniques to derive the gradient of the traveltime misfit function. We use the Eikonal equation for the forward modelling, and iterate with a conjugate gradient method. A 3-D synthetic example with a realistic size acquisition demonstrates the efficiency and the great potential of the adjoint state method for 3-D applications of refraction tomography.