Vetle Vinje

Traveltime and amplitude estimation using wavefront construction

We have developed and implemented a new method for estimation of first and later arrival traveltimes and amplitudes in a general 2D model. The basic idea of this wavefront (WF) construction approach is to use ray tracing to estimate a new WF Erom the old one. The calculation goes along the WFs rather than along the rays.

3-D ray modeling by wavefront construction in open models

A synthesis of two newly developed concepts in 3-D modeling is developed in this paper: (1) The open, (non-complete) seismic model, and (2) the ray tracing based wavefront (WF) construction method. The open model may contain interfaces with holes and other missing parts, which simplifies model building considerably because the input horizon data from standard interpretation and processing packages are often incomplete. A set of volumes is defined in the model. A volume is a logical unit that points to a set of property functions, e.g., P-velocity, S-velocity, and density. The properties are represented either as constants or as B-spline functions of the spatial coordinates (x, y) or (x, y, z). The volumes of the model are assigned to opposing sides of each interface and not to specific spatial areas of the model, which is the case in most (blocky) model representations. The interfaces are given explicitly by triangular grids where the sizes of the triangles are determined locally by the curvature of the interface. We show how modeling by WF construction is both possible and computationally efficient in open models, but only after some modifications to deal with the ambiguity of the model representation. It is not possible to find a unique volume for the spatial positions in an open model. Instead, the volumes (with associated velocities, etc.) are determined from the last interface encountered by each ray in the WF. To find an arrival in a receiver, the volume associated to the receiver has to match the volume of the WF hitting the receiver.

Full waveform inversion: A North Sea OBC case study

Full Waveform Inversion (FWI) aims to obtain superior velocity models by minimizing the difference between observed and modelled seismic waveforms. We apply FWI to a North Sea OBC field data set with wide azimuths and more than 10 km long offsets. We discuss the methodology used and the associated practical issues. Our FWI result has revealed detailed velocity features associated with thin, gas-charged layers and faulting in the shallow sections of the model. We demonstrate that this velocity update has improved the imaging of the deeper structures.

Review of Ray Theory Applications in Modelling and Imaging of Seismic Data

Throughout the last twenty years, 3D seismic ray modelling has developed from a research tool to a more operational tool that has gained growing interest in the petroleum industry. Various areas of application have been established and new ones are under development. Many of these applications require a modelling system with flexible, robust and efficient modelling algorithms in the core. The present paper reviews the basic elements of such a system, based on the ‘open model’ concept and the ‘wavefront construction’ technique. In the latter, Červenýs dynamic ray tracing is an intrinsic part. The modelling system can be used for generating ray attributes and synthetic seismograms for realistic 3D surveys with tens of thousands of shots and receivers. Moreover, some other types of application areas are illustrated: Production of Greens functions for prestack depth migration and hybrid modelling (combined ray and finite-difference modelling), attribute mapping and illumination analysis, both for survey planning and interpretation. Finally, the concepts of ‘isochron rays’ and ‘velocity rays’ related to seismic isochrons have been introduced recently, with very interesting future applications.

Simulated migration amplitude for improving amplitude estimates in seismic illumination studies

Ideally, a seismic data cube should contain amplitudes that are proportional to the reflectivity of the subsurface. However, when working with real data, the seismic amplitudes used for interpretation are highly dependent on other factors such as survey geometry, instrumentation, filtering and muting of prestack data, migration artifacts, focusing/defocusing, wave attenuation in the overburden, and several other factors. When an amplitude variation is encountered in the seismic data, determining which factor is responsible is not easy. In this paper we apply a method based on a combination of 3D seismic ray modeling and simulation of migration that is able to distinguish between some factors contributing to the amplitudes. This will reduce the risk of interpreting “false” anomalies and drilling dry wells.

Towards better amplitude maps by simulated migration

Illumination maps are a useful tool for survey planning and for QC of amplitudes picked on selected target horizons after depth migration. The illumination amplitude maps, which are used most often, are based on a simple summation of ray-theoretical amplitudes within bin cells of the target horizon. Although better than just counting the hits, this approach is still to simple to give amplitudes directly comparable to PSDM, because it neither takes the seismic pulse nor the Fresnel zone into account. Here we improve an approach based on Kirchhoff migration of ray traced data. We use a local paraxial approximation of the true traveltime field on the target horizon around the reflection point to generate amplitude maps where both the source pulse and the Fresnel zone are taken into account. The ray tracing is fully elastic and includes 3D geometrical spreading and reflection/transmission effects. For the synthetic examples, the results are almost equal to results from prestack depth migration (PSDM).

PreStack Depth Migration and illumination maps

Summary Designing a survey is often based on fold and offset distribution under the assumption of a flat subsurface geometry. In real situations, this is hardly the case. Recently, ray tracing has frequently been used to predict the illumination at selected reflectors corresponding to given seismic surveys. Illumination maps are used as an aid to choose the best possible survey when planning a seismic acquisition. In this 2-D synthetic study we compare hit density and illumination amplitude maps from ray tracing with the result from prestack depth migration (PSDM). We show that (i) holes (i.e. non-illuminated zones) in the ray-tracing based illumination maps correspond well with holes in the PSDM images and (ii) illumination amplitude maps only crudely approximate the amplitudes in the PSDM images.

Using Full Waveform Inversion to Update Anisotropy - A North Sea Case Study

Full Waveform Inversion (FWI) aims to obtain high resolution velocity models by minimizing the misfit between observed and modelled data. While FWI algorithms that take into account anisotropy are often used in the industry, it is still common practice to update for vertical velocity only, keeping the anisotropic parameters fixed during the inversion. The main advantage of such an approach is mitigating the different sensitivity of the data to the parameters that characterize the subsurface. Nonetheless, fixing the anisotropic parameters imposes a constraint on the update of the vertical velocity, potentially leading to a sub-optimal solution of the inverse problem. Here we formulate the inverse problem within the Vertical Transverse Isotropy (VTI) model, and present an approach for updating both vertical and horizontal velocities. The necessary theory for the implementation of the algorithm is reviewed and developed within the scope of this work and a practical application to a North Sea field dataset is then presented. Our FWI result reveals velocity and anisotropy details associated with shallow channels and other features in the near surface geology.

SOURCE SIGNATURE ESTIMATION BASED ON RECORDINGS IN DEEP-TOWED STREAMERS BELOW THE SOURCE

Source-over-spread acquisition design is a recent development in marine seismic acquisition, aiming to improve imaging of the shallow subsurface. Contrary to conventional towedstreamer acquisition, source-over-spread acquisition records the direct wave below the source. We propose an inversion algorithm that takes advantage of the recordings of the direct wave in source-over-spread acquired seismic data to estimate notional source signatures for each air gun. The obtained notional source signatures from the inversion can be used to estimate directional far-field signatures, similar to the approach of notional source signatures estimated from measurements in near-field hydrophones. The forward modeling of the algorithm is based upon a physical modeling of the air bubble created by each air gun in the source array. A damped Gauss-Newton approach is used as a local search algorithm to minimize the difference between the recorded direct wave and the modeled direct wave from the forward modeling. The inversion is first carried out for a lowfrequency part of the data, before higher frequencies are included in the inversion. Typical inversion parameters are empirical damping factors for the bubble oscillations and firing time delay for each air gun. Variations in streamer depth are taken into account and a constant sea surface reflection coefficient is also estimated as a by-product of the inversion. The algorithm is tested on shallow and deepwater data sets acquired with CGGs acquisition design called TopSeis. The notional source signatures are used in a designature flow and compared with designature results with notional source signatures from near-field hydrophone measurements. The results indicate that utilizing the direct wave in source-over-spread seismic can provide more accurate estimation of the strongest part of the bubble for deepwater data sets. To improve bubble estimation further, one may add more empirical factors to describe the oscillations of the bubble in the forward operator. It was furthermore observed that for shallow water data sets, subsurface reflections contaminated the bubble train of the direct wave. This affected the stability of the inversion, even when the water bottom reflection was included in the forward modeling.

Simulated migration amplitude: modeling amplitude anomalies of PSDM in a real North Sea case

The Simulation Migration Amplitude is a ray-based, targetoriented Kirchhoff migration of synthetic data around the reflection points using the local paraxial approximation of the two-way traveltime field on the target horizon. Compared to conventional migration of synthetic data, the method is computationally efficient, making it, for example, suitable for survey planning, as the amplitude response of several configurations can be compared in a reasonable amount of time. On a real 3D case provided by PGS, the results of the method have been compared with the results from PSDM. Amplitudes from PSDM and Simulated Migration show clear similarities.