The principle of reciprocity says that when a vertical source (a vibrator) and a vertical receiver (a geophone) are interchanged, the same seismogram will be recorded in each case. In a field study conducted by D. Fenati and F. Rocca in 1984, it was found that the reciprocal principle also applies surprisingly well even when the required conditions are technically violated, such as when an isotropic source (dynamite) is used with a vertical receiver (again a geophone).
Beginning in 2007 and continuing into 2015 BP designed, built, and field tested Wolfspar®, a full-scale ultra-low-frequency seismic source optimized for full-waveform inversion. Like airguns or marine vibrators, at low frequencies the Wolfspar source declines in amplitude at about 18 dB / octave. However, Wolfspar differs from airguns in that it can tailor its output precisely to the needs of our preferred algorithm for velocity model building, full-waveform inversion (i.e., it is "FWI friendly"). The source also precisely records its radiated wavefield and this information can be used in the modeling step of the inversion algorithm. Although producing much less power than a large airgun array, this new source is more efficient with the energy it produces. Field-testing the source under tow at 4 knots, recording into ocean-bottom sensors, we achieved an excellent signal-to-noise ratio in the deep water Gulf of Mexico at offsets of over 30 km and at frequencies as low as 1.6 Hz despite the significant ambient noise at these frequencies. We expect that lower frequencies will be possible while under tow, but this has not yet been tested. Presentation Date: Monday, October 17, 2016 Start Time: 1:50:00 PM Location: 163/165 Presentation Type: ORAL
The permanent ocean-bottom array at the Valhall Field in Norway provides an excellent source of passive seismic data to test what might be accomplished with seismic interferometry. The array was installed in 2003 (Kommedal et al., 2004) and data can be recorded for long periods in all weather conditions. The subsurface structure is well known, both from numerous wells and from seismic imaging. During periods without active seismic acquisition at Valhall, there is abundant passive energy in the data over a wide range of fre-quencies.
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Kirchhoff depth migration is a widely used algorithm for imaging seismic data in both two and three dimensions. To perform the summation at the heart of the algorithm, standard Kirchhoff migration requires a traveltime map for each source and receiver. True‐amplitude Kirchhoff migration in 2.5-D υ(x, z) media additionally requires maps of amplitudes, out‐of‐plane spreading factors, and takeoff angles; these quantities are necessary for calculating the true‐amplitude weight term in the summation. The increased input/output (I/O) and computational expense of including the true‐amplitude weight term is often not justified by significant improvement in the final muted and stacked image. For this reason, some authors advocate neglecting the weight term in the Kirchhoff summation entirely for most everyday imaging purposes. We demonstrate that for nearly the same expense as ignoring the weight term, a much better solution is possible. We first approximate the true‐amplitude weight term by the weight term for constant‐velocity media; this eliminates the need for additional source and receiver maps. With one small additional approximation, the weight term can then be moved entirely outside the innermost loop of the summation. The resulting Kirchhoff method produces images that are almost as good as for exact true‐amplitude Kirchhoff migration and at almost the same cost as standard methods that do not attempt to preserve amplitudes.
Mathematically, 21 stiffnesses arranged in a 6 × 6 symmetric matrix completely describe the elastic properties of any homogeneous anisotropic medium, regardless of symmetry system and orientation. However, it can be difficult in practice to characterize an anisotropic medium's properties merely from casual inspection of its (often experimentally measured) stiffness matrix. For characterization purposes, it is better to decompose a measured stiffness matrix into a stiffness matrix for a canonically oriented transversely isotropic (TI) medium (whose properties can be readily understood) plus a generally anisotropic perturbation (representing the medium's deviation from perfect symmetry), followed by a rotation (giving the relationship between the medium's natural coordinate system and the measurement coordinate system). To accomplish this decomposition, we must find the rotated symmetric medium that best approximates a given stiffness matrix. An analytical formula exists for calculating the distance between the elastic properties of two anisotropic media. Starting from this formula, I show how to analytically calculate the TI medium with a [Formula: see text] symmetry axis that is nearest to a given set of 21 stiffness constants. There is no known analytical result if the symmetry axis is not fixed beforehand. I therefore present a simple search algorithm that scans all possible orientations of the nearest TI medium's symmetry axis. The grid is iteratively refined to optimize the solution. The algorithm is simple and robust and works well in practice, but it is not guaranteed to always find the optimal global answer if there are secondary minima that provide almost as good a fit as the optimal one.