In conventional seismic surveys, there is a waiting time between sequentially fired shots. This time is determined such that the deepest reflection of interest is recorded before the following source is fired. In a survey with simultaneous or blended sources, the waiting time between the firing of shots is not dependent on the deepest reflection of interest, it is usually much shorter and/or can have random time delays. Thus, the wavefields due to independent sources are overlapped in the records.
The blended data exhibit strong discontinuities in the source direction, in contrast to the coherency expected from seismic measurements. A strategy for deblending could then be to suppress these discontinuities. In this paper, we propose to do this by designing an energy functional that uses a combination of individual functionals that penalize deviations from local plane waves in the reconstructed (deblended) data, as well as a least squares term that penalizes discrepancies between the deblended and the measured data. In this way, we derive a set of coupled nonlinear partial differential equations that we use for the deblending procedure.
In this paper we prove that the recently introduced method of signal apparition optimally separates signals from interfering sources recorded during simultaneous source seismic data acquisition. By utilizing a periodic sequence of source signatures along one source line, that wavefield becomes separately partially visible in the spectral domain where it can be isolated from interfering signals, processed, and subtracted from the original recordings, thereby separating the wavefields from each other. Whereas other methods for simultaneous source separation can recover data in triangle-shaped region in the spectral domain, signal apparition allows for the exact separation of data in a diamond-shaped region that is twice as large thereby enabling superior reconstruction of separated wavefields throughout the entire data bandwidth.
In this paper we prove that the recently introduced method of signal apparition optimally separates signals from interfering sources recorded during simultaneous source seismic data acquisition. By utilizing a periodic sequence of source signatures along one source line, that wavefield becomes separately partially visible in the spectral domain where it can be isolated from interfering signals, processed, and subtracted from the original recordings, thereby separating the wavefields from each other. Whereas other methods for simultaneous source separation can recover data in a triangle-shaped region in the spectral domain, signal apparition allows for the exact separation of data in a diamond-shaped region that is twice as large thereby enabling superior reconstruction of separated wavefields throughout the entire data bandwidth.
Signal apparition offers a fundamentally new perspective on simultaneous source separation. Whereas the method exactly separates the signal from interfering sources in diamond-shaped regions of the f-k space, signal from simultaneous source still overlap outside these regions. We present a method based on using local phase functions and the analytic part of the blended data to reconstruct the separated data throughout the full data bandwidth.
Signal apparition offers a fundamentally new perspective on simultaneous source separation. Whereas the method exactly separates the signal from interfering sources in diamond-shaped regions of the frequency-wavenumber domain, signals from simultaneous sources still overlap outside these regions. We present a method based on using quaternion representations of the blended data that reconstruct the separated data throughout the full data bandwidth by iteratively using reconstructions for lower frequencies to recover the higher frequency content. Presentation Date: Tuesday, September 26, 2017 Start Time: 9:20 AM Location: Exhibit Hall C, E-P Station 2 Presentation Type: EPOSTER
In recent years, it has been recognized that the seismic wave equation solved with a finite-difference method in time causes a predictable and removable error through the use of so-called time-dispersion transforms. These transforms were thought not to apply to visco-elastic media. However, in this paper we demonstrate that the time-dispersion transforms remain applicable when the visco-elastic wave equation is solved with memory variables, as is commonly done. The crucial insight is that both the wave equation and the memory variables are computed with the same time-dispersion error. We show how the time-dispersion transforms can be implemented in, for example, MATLAB, and demonstrate the developed theory on a visco-elastic version of the Marmousi model. Then, the time-dispersion transforms allow computation of the visco-elastic wave equation with large steps in time without significant loss of accuracy, and without having to make any modifications to the model.
Signal apparition is a recent signal processing advance that has numerous applications in seismic data acquisition and processing. In this paper we review the basic principles of signal apparition and discuss applications related to simultaneous source acquisition. We discuss the generalization of the technique to large number of sources and the application in a full 3D configuration enabling large productivity gains and the acquisition of broad band seismic data.
The recently introduced method of ‘signal apparition’ offers a fundamentally different approach to separation of multiple interfering sources, by using a periodic sequence of source signatures along one source line. This leads to exact separation of signals in diamond-shaped regions of the frequency-wavenumber domain which are twice as large compared to those recovered by other methods. In this paper we investigate the method’s sensitivity to the appearance of white noise in the periodic sequence, and show that signal apparition is stable by using a probabilistic model. We also demonstrate the stability by numerical simulations on a finite-difference synthetic data set generated over a complex salt model.
A major focus of research in the seismic industry of the past two decades has been the acquisition and subsequent separation of seismic data using multiple sources fired simultaneously. The recently introduced method of signal apparition provides a new take on the problem by replacing the random time-shifts usually employed to encode the different sources by fully deterministic periodic time-shifts. In this paper, we give a mathematical proof showing that the signal apparition method results in optimally large regions in the frequency–wavenumber space where exact separation of sources is achieved. These regions are diamond shaped and we prove that using any other method of source encoding results in strictly smaller regions of exact separation. The results are valid for arbitrary number of sources. Numerical examples for different number of sources (three, respectively, four sources) demonstrate the exact recovery of these diamond-shaped regions. The implementation of the theoretical proofs in the field is illustrated by the results of a conducted field test.
In the field of exploration geophysics, the method known as "signal apparition" offers a different perspective on how to separate signals acquired from simultaneously fired seismic sources. The method uses a periodic sequence of small time shift variations to encode the different sources, and this choice leads to exact separation of signals in diamond-shaped regions of the frequency-wavenumber domain which are twice as large compared to those recovered by other methods. In this paper we investigate the signal apparition method's sensitivity to perturbations of the periodic time shift sequence. We model (measured or unknown) perturbations in a stochastic fashion and prove that the resulting inverse problem of separating the data is still well-posed, and we demonstrate the stability by numerical simulations on a finite-difference synthetic data set generated over a complex salt model.