Seismic imaging provides much of our information about the Earth's crustal structure. The principal source of imaging errors derives from simplistic modelled predictions of the complex, scattered wavefields that interact with each subsurface point to be imaged. A new method of wavefield extrapolation based on inverse scattering theory in mathematical physics produces accurate estimates of these subsurface scattered wavefields, while still using relatively little information about the Earth's properties. We use it for the first time to create real target-oriented seismic images of a North Sea field. We synthesise underside illumination from surface reflection data, and use it to reveal subsurface features that are not present in an image from conventional migration of surface data. To reconstruct underside reflections, we rely on the so-called downgoing focusing function, whose coda consists entirely of transmission-born multiple scattering. As such, with the method presented here, we provide the first field data example of reconstructing underside reflections with contributions from transmitted multiples, without the need to first locate or image any reflectors in order to reconstruct multiple scattering effects.

The solution of the inverse scattering problem for the one-dimensional Schrödinger equation is given by the Marchenko equation. Recently, a Marchenko-type equation has been derived for three-dimensional (3D) acoustic wave fields, whose solution has been shown to recover the Green's functions from points within the medium to its exterior, using only single-sided scattered data. Here we extend this approach to 3D vectorial wave fields that satisfy the elastodynamic wave equation and recover Green's functions from points interior to an elastic, solid-state medium from purely external and one-sided measurements. The method is demonstrated in a solid-earth-like model to construct Green's functions using only subsurface sources, from earth-surface force and deformation sources and particle velocity and stress measurements.

Standard seismic processing steps such as velocity analysis and reverse time migration (imaging) usually assume that all reflections are primaries: Multiples represent a source of coherent noise and must be suppressed to avoid imaging artifacts. Many suppression methods are relatively ineffective for internal multiples. We show how to predict and remove internal multiples using Marchenko autofocusing and seismic interferometry. We first show how internal multiples can theoretically be reconstructed in convolutional interferometry by combining purely reflected, up- and downgoing Green’s functions from virtual sources in the subsurface. We then generate the relevant up- and downgoing wavefields at virtual sources along discrete subsurface boundaries using autofocusing. Then, we convolve purely scattered components of up- and downgoing Green’s functions to reconstruct only the internal multiple field, which is adaptively subtracted from the measured data. Crucially, this is all possible without detailed modeled information about the earth’s subsurface. The method only requires surface reflection data and estimates of direct (nonreflected) arrivals between subsurface virtual sources and the acquisition surface. The method is demostrated on a stratified synclinal model and shown to be particularly robust against errors in the reference velocity model used.

Conventional seismic imaging methods rely on the single-scattering Born approximation, requiring the removal of multiply scattered events from reflection data prior to imaging. Additionally, many methods use an acoustic approximation, representing the solid Earth as an acoustic (fluid) medium. We propose imaging methods for (solid) elastic media that use primaries and internal multiples, including their P S and SP conversions, thus obviating the need for internal multiple removal and improving handling of internal conversions. The methods rely on the elastic autofocusing method which creates multi-component elastodynamic Green's functions from virtual sources interior to the medium to receivers placed on the surface. They require only surface seismic reflection data and estimates of the direct waves from virtual sources interior to the medium, both of which are commonly available at the imaging step of seismic processing. We demonstrate our methods on a synthetic model with constant P and S velocities and vertical and horizontal density variations, by producing for the first time P P and SS images from elastic autofocusing which are compared to 1 reference seismic images based on conventional methods. Effects of multiples are greatly attenuated in the images, with fewer spurious reflectors than are observed when using Born imaging.2

Conventional seismic processing aims to create data that contain only primary reflections, whereas real seismic recordings also contain multiples. As such, it is desirable to predict, identify, and attenuate multiples in seismic data. This task is more difficult in elastic (solid) media because mode conversions create families of internal multiples not present in the acoustic case. We have developed a method to predict prestack internal multiples in general elastic media based on the Marchenko method and convolutional interferometry. It can be used to identify multiples directly in prestack data or migrated sections, as well as to attenuate internal multiples by adaptively subtracting them from the original data set. We developed the method on two synthetic data sets, the first composed of horizontal density layers and constant velocities, and the second containing horizontal and vertical density and velocity variations. The full-elastic method is computationally expensive and ideally uses data components that are not usually recorded. We therefore tested an acoustic approximation to the method on the synthetic elastic data from the second model and find that although the spatial resolution of the resulting image is reduced by this approximation, it provides images with relatively fewer artifacts. We conclude that in most cases where cost is a factor and we are willing to sacrifice some resolution, it may be sufficient to apply the acoustic version of this demultiple method.

The objective of prestack depth migration is to position reflectors at their correct subsurface locations. However, migration methods often also generate artifacts along with physical reflectors, which hamper interpretation. These spurious reflectors often appear at different spatial locations in the image depending on which migration method is used. Therefore, we have devised a postimaging filter that combines two imaging conditions to preserve their similarities and to attenuate their differences. The imaging filter is based on combining the two constituent images and their envelopes that were obtained from the complex vertical traces of the images. We have used the method to combine two images resulting from different migration schemes, which produce dissimilar artifacts: a conventional migration method (equivalent to reverse time migration) and a deconvolution-based imaging method. We show how this combination may be exploited to attenuate migration artifacts in a final image. A synthetic model containing a syncline and stochastically generated small-scale heterogeneities in the velocity and density distributions was used for the numerical example. We compared the images in detail at two locations where spurious events arose and also at a true reflector. We found that the combined imaging condition has significantly fewer artifacts than either constituent image individually.

The Marchenko redatuming method estimates surface-tosubsurface Green's functions. It has been employed to diminish the effects of multiples in seismic data. Several such methods rely on an absolute scaling of the data; this is usually considered to be known in synthetic experiments, or is estimated using heuristic methods in real data. Here, we show using real ultrasonic laboratory data that the most common of these methods may be ill suited to the task, and that reliable ways to estimate scaling remains unavailable. Marchenko methods which rely on adaptive subtraction may therefore be more appropriate. We present two adaptive Marchenko methods: one is an extension of a current adaptive method, and the other is an adaptive implementation of a non-adaptive method. Our results show that Marchenko methods improve imaging compared to reverse-time migration, but less so than expected. This reveals that some Marchenko assumptions were violated in our experiment and likely are also in seismic data, showing that laboratory experiments contribute critical information to the development and testing of Marchenko-based methods.

SUMMARYMarchenko redatuming estimates the full response (including internal multiples) from a virtual source inside of an medium, using only reflection measurements at the Earth's surface and a smooth estimate of the velocity model. As such, it forms a new way to obtain full field propagators to form images of target zones in the subsurface by means of Marchenko imaging, without necessarily have to create detailed models of overburden structure.One of the main obstacles to the application of such novel techniques to field datasets is the set of requirements of the reflection response: it should be wideband, acquired with wide aperture, densely sampled arrays of co-located sources and receivers, and should have undergone removal of direct waves, source and receiver ghosts and free-surface multiples. We use a wave-equation approach to jointly redatum, demultiple, and source designature to transform data recorded using ocean-bottom acquisition systems into a suitable proxy of the reflection response required by the Marchenko scheme.We briefly review the Marchenko redatuming scheme, and present the first encouraging field results of 2D target-oriented imaging of an ocean-bottom cable dataset, acquired over the Volve field. We further discuss the 'challenge of convergence' of the Marchenko redatuming scheme for real data.