A dual-sensor towed streamer records the pressure and vertical component of particle motion associated with the incident wavefield that may be used to separate the wavefield into its upand downgoing parts. This procedure requires information about the water properties (wave-propagation velocity and density) and is robust in the presence of errors in the estimation of these quantities of the magnitude likely to be encountered. In practice, the particle motion data recorded by current towed marine streamers encounter very strong mechanical noise such that, for the lowest frequencies, the wavefield separation must be approximated by deconvolving the ghost function from the pressure data. This procedure requires information about the streamer depth and is robust to small depth errors over the frequency range for which it is required for dual-sensor streamer processing, but it is much more sensitive if applied over the bandwidth necessary to deghost pressure data acquired at a conventional streamer depth. The signal-to-noise ratio can be further enhanced by recombining the up-and downgoing pressure fields at the sea surface, which has the effect of applying a ghostlike filter to noise that is recorded by only one of the two sensors. In practical marine acquisition scenarios, spatial sampling is often insufficient to yield an accurate result, especially in the crossline direction. If each streamer is processed independently assuming that the wavefield propagation is purely inline, significant errors can be introduced. For arrivals with high emergent angles, errors may also be introduced even if the wavefield propagation actually is purely inline due to incorrect treatment of spatially aliased energy. However, these effects are almost entirely confined to very shallow events. They can be mitigated by using independently derived information about the crossline propagation angle and, for data comprising predominantly forward scattered energy, appropriate application of linear moveout.
Migration of primary and multiple reflections leads to enhanced subsurface illumination and to increased image resolution. A joint migration approach using the complete wavefield requires properly imaged primaries and multiples of all orders. In recent works, primaries and multiples have therefore been imaged separately, using the upgoing and downgoing pressure wavefields obtained by decomposing dual-sensor streamer data. The matches between the corresponding depth images are still not found to be sufficiently accurate, so new and more appropriate imaging conditions need to be found. We reviewed the classical imaging approach used in one-way wave-equation migration, with the aim of extending it for simultaneous migration of primaries and all orders of multiples. Based on Rayleigh’s reciprocity theorem and well-known theoretical developments, we derived a new imaging condition described in terms of the upgoing pressure wavefield and a filtered version of the downgoing vertical-velocity wavefield. To evaluate the efficiency of this new imaging approach, primaries and multiples were separately migrated using synthetic and real data examples. These results were compared to those obtained using a conventional imaging condition. We found that the use of the new imaging condition led to a better match between the depth images and spectra of the migrated primaries and migrated multiples.
Several studies have shown the benefits of including multiple reflections together with primaries in the structural imaging of subsurface reflectors. However, to characterize the reflector properties, there is a need to compensate for propagation effects due to multiple scattering and to properly combine the information from primaries and all orders of multiples. From this perspective and based on the wave equation and Rayleigh’s reciprocity theorem, recent works have suggested computing the subsurface image from the Green’s function reflection response (or reflectivity) by inverting a Fredholm integral equation in the frequency-space domain. By following Claerbout’s imaging principle and assuming locally reacting media, the integral equation may be reduced to a trace-by-trace deconvolution imaging condition. For a complex overburden and considering that the structure of the subsurface is angle-dependent, this trace-by-trace deconvolution does not properly solve the Fredholm integral equation. We have inverted for the subsurface reflectivity by solving the matrix version of the Fredholm integral equation at every subsurface level, based on a multidimensional deconvolution of the receiver wavefields with the source wavefields. The total upgoing pressure and the total filtered downgoing vertical velocity were used as receiver and source wavefields, respectively. By selecting appropriate subsets of the inverted reflectivity matrix and by performing an inverse Fourier transform over the frequencies, the process allowed us to obtain wavefields corresponding to virtual sources and receivers located in the subsurface, at a given level. The method has been applied on two synthetic examples showing that the computed reflectivity wavefields are free of propagation effects from the overburden and thus are suited to extract information of the image point location in the angular and spatial domains. To get the computational cost down, our approach is target-oriented; i.e., the reflectivity may only be computed in the area of most interest.
A method that extracts the response of the earth from continuous wavefields on both the source and the receiver side is presented. Seismic data recorded continuously are treated over the entire time length at once. The source(s) can emit signals continuously while moving. The entire source wavefield contributing to each stationary receiver position is derived and used to extract common receiver gathers with the response of the earth. The trace spacing in the resulting gathers can be chosen in processing and corresponding anti-aliasing protection is applied. With the proposed method, no minimum listening time is needed since both the source(s) and the receivers are operating continuously. The emitted sound pressure levels are reduced by spreading the emitted energy out in time. Multiple sources can be operated simultaneously by designing each source such that the correlation between the wavefields emitted from each of them is minimized. In a companion paper (Klüver, T., Hegna, S., and Lima J., 2018, Making the transition from discrete shot records to continuous wavefields -Real data application: Expanded abstract submitted to the EAGE annual meeting) we discuss source design using existing equipment and show application of the proposed method on real data.
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