ALBERT

Description: Methods for wavefield injection are used in, for instance, reverse time extrapolation of shot gathers in reverse time migration. For correct injection of recorded data without any ambiguity of the propagation direction, the wavefield-injection methodology requires pressure and particle velocity data such as multicomponent towed marine or seabed seismic recordings. We discovered that by carefully considering the models (medium parameters and boundary conditions) for injection, wavefield injection of multicomponent data can also be used to solve several long-standing challenges in marine seismic data processing by means of conventional time-space-domain finite-difference propagators. We outlined and demonstrated several of these important applications including up-down separation of wavefields (deghosting), direct-wave removal, source-signature estimation, multiple removal, and imaging using primaries and multiples. Only acoustic models are considered, but the concepts are straightforward to generalize to elastodynamic and electromagnetic models.

Description: We have developed a new and simple method for deghosting of conventional hydrophone streamer data towed at arbitrary variable depths. The method uses a time-space domain finite-difference (FD) solution to the wave equation with pressure field boundary conditions to predict and remove ghosts. Because it operates in the time domain, our method is unaffected by any number of notches in the frequency spectrum of the data and therefore will deghost "through notches." Apart from the acquired hydrophone data, the method relies on the depth profile of the streamer recording the data beneath a sea surface with a known reflection coefficient as well as the propagation velocity in the water above the streamer. The method was applied to simple and more complex synthetic data, which illustrated its ability to deal with complex data and any acquisition geometry.

Description: The finite-difference method is among the most popular methods for modelling seismic wave propagation. Although the method has enjoyed huge success for its ability to produce full wavefield seismograms in complex models, it has one major limitation which is of critical importance for many modelling applications; to naturally output up- and downgoing and P - and S -wave constituents of synthesized seismograms. In this paper, we show how such wavefield constituents can be isolated in finite-difference-computed synthetics in complex models with high numerical precision by means of a simple algorithm. The description focuses on up- and downgoing and P - and S -wave separation of data generated using an isotropic elastic finite-difference modelling method. However, the same principles can also be applied to acoustic, electromagnetic and other wave equations.

Description: A new method for discrete sampling of signals is presented with specific applications to the reconstruction of recorded interfering wavefields from two or more sources excited simultaneously at discrete positions along lines. By utilizing a periodic sequence of source signatures along one of the source lines, the corresponding wavefield becomes separately visible in a part of the spectral domain where it can be isolated, processed and subtracted from the interfering wavefields. As a result, interfering wavefields from multiple sources recorded at a single location can be fully separated from each other. The concept is referred to as signal apparition which we suggest refers to ‘the act of becoming visible’. It may find applications in a wide range of disciplines relying on wave experimentation, such as acoustic, seismic and electromagnetic imaging of the Earth's interior for instance to significantly enhance resolution of subsurface images.

Description: Finite-difference simulations are an important tool for studying elastic and acoustic wave propagation, but remain computationally challenging for elastic waves in three dimensions. Computations for acoustic waves are significantly simpler as they require less memory and operations per grid cell, and more significantly can be performed with coarser grids, both in space and time. In this paper, we present a procedure for correcting acoustic simulations for some of the effects of elasticity, at a cost considerably less than full elastic simulations. Two models are considered: the full elastic model and an equivalent acoustic model with the same P velocity and density. In this paper, although the basic theory is presented for anisotropic elasticity, the specific examples are for an isotropic model. The simulations are performed using the finite-difference method, but the basic method could be applied to other numerical techniques. A simulation in the acoustic model is performed and treated as an approximate solution of the wave propagation in the elastic model. As the acoustic solution is known, the error to the elastic wave equations can be calculated. If extra sources equal to this error were introduced into the elastic model, then the acoustic solution would be an exact solution of the elastic wave equations. Instead, the negative of these sources is introduced into a second acoustic simulation that is used to correct the first acoustic simulation. The corrected acoustic simulation contains some of the effects of elasticity without the full cost of an elastic simulation. It does not contain any shear waves, but amplitudes of reflected P waves are approximately corrected. We expect the corrected acoustic solution to be useful in regions of space and time around a P -wave source, but to deteriorate in some regions, for example, wider angles, and later in time, or after propagation through many interfaces. In this paper, we outline the theory of the correction method, and present results for simulations in a 2-D model with a plane interface. Reflections from a plane interface are simple enough that an analytic analysis is possible, and for plane waves, we give the correction to the acoustic reflection and transmission coefficients. Finally, finite-difference calculations for plane waves are used to confirm the analytic results. Results for wave propagation in more complicated, realistic models will be presented elsewhere.

Description: The source depth influences the frequency band of seismic data. Due to the source ghost effect, it is advantageous to deploy sources deep to enhance the low-frequency content of seismic data. But, for a given source volume, the bubble period decreases with the source depth, thereby degrading the low-frequency content. At the same time, deep sources reduce the seismic bandwidth. Deploying sources at shallower depths has the opposite effects. A shallow source provides improved high-frequency content at the cost of degraded low-frequency content due to the ghosting effect, whereas the bubble period increases with a lesser source depth, thereby slightly improving the low-frequency content. A solution to the challenge of extending the bandwidth on the low- and high-frequency side is to deploy over/under sources, in which sources are towed at two depths. We have developed a mathematical ghost model for over/under point sources fired in sequential and simultaneous modes, and we have found an inverse model, which on common receiver gathers can jointly perform designature and deghosting of the over/under source measurements. We relate the model for simultaneous mode shooting to recent work on general multidepth level array sources, with previous known solutions. Two numerical examples related to over/under sequential shooting develop the main principles and the viability of the method.

Description: Marine seismic data are distorted by ghosts as waves propagating upward reflect downward from the sea surface. Ghosts appear on the source side and the receiver side. However, whereas the receiver-side ghost problem has been studied in detail, and many different solutions have been proposed and implemented commercially, the source-side ghost problem has remained largely unsolved with few satisfactory solutions available. We have developed a new and simple method to remove sea-surface ghosts that is related to the recently introduced concept of signal apparition. As opposed to the temporal/spatial source signature modulation functions used in the original signal apparition theory, our source deghosting method relies on using sources at different depths but not at the same lateral positions. The new method promises to be particularly suitable for 3D applications on sparse or incomplete acquisition geometries.

Description: Many applications in computational geophysics involve the modeling of seismic wave propagation on a set of closely related subsurface models. In such scenarios, it is of interest to recompute the seismic wavefields locally (only in the regions of change), instead of in the full subsurface model. We have developed a method for local acoustic wavefield recomputation that makes it possible to fully immerse a local modeling domain within a larger domain of arbitrary extent and complexity, such that the wave propagation in the full domain is completely accounted for. The method enables wavefield modeling on much smaller local domains, while relying on the up-front generation of a large number of Green’s functions and a wavefield extrapolation step at each time step of the simulation. A Kirchhoff-Helmholtz extrapolation integral is used to predict the interaction of the wavefield leaving the local domain with the exterior domain. The outward propagating wavefield and the wavefield reentering the local domain are applied as a boundary condition along the edges. Thanks to these dynamically calculated boundary conditions, all higher order long-range interactions between the two domains are fully accounted for. We have implemented the method in a conventional finite-difference time-domain scheme and determined that the locally calculated wavefields are equal to wavefields generated on the full domain to within numerical precision. The efficiency of the local modeling algorithm will greatly depend on the nature and size of the problem.

Description: Wavefield injection in finite-difference (FD) grids can be described by the method of multiple point sources. The method teaches how synthetically generated wavefields and wavefield constituents can be reconstructed from surface recordings using a combination of monopole and dipole sources on an injection surface surrounding the model. We show how to properly record surface wavefields and inject point sources in staggered FD grids, in a way that is consistent with the order of spatial accuracy of the FD scheme. The description is general and can be used for schemes of any order. Only one or two surface wavefields are required to reconstruct the original wavefields or wavefield constituents to numerical precision, independent of the order of spatial accuracy of the FD stencil. We have applied the method for the separation of up- and downgoing wavefields and for source wavefield reconstruction for reverse time migration. Our implementation enables accurate source wavefield reconstruction with optimally minimal memory requirements.