Fermionic reductions of the AdS4 x CP3 superstring

We discuss fermionic reductions of type IIA superstrings on AdS4 x CP3 in relation to the conjectured AdS4/CFT3 duality. The superstring theory is described by means of a coset model construction, which is classically integrable. We discuss the global light-cone symmetries of the action and related kappa-symmetry gauge choices, and also present the complete quartic action in covariant form with respect to these. Further, we study integrable (fermionic) reductions, in particular, a reduction yielding a quadratic action of two complex fermions on the string world-sheet. Interestingly, this model appears to be exactly the same as the corresponding integrable reduction found in the AdS5 x S5 case.Comment: 24 pages, v3 as publishe

Propagator and transfer matrices, Marchenko focusing functions and their mutual relations

Many seismic imaging methods use wave field extrapolation operators to redatum sources and receivers from the surface into the subsurface. We discuss wave field extrapolation operators that account for internal multiple reflections, in particular propagator matrices, transfer matrices and Marchenko focusing functions. A propagator matrix is a square matrix that `propagates' a wave-field vector from one depth level to another. It accounts for primaries and multiples and holds for propagating and evanescent waves. A Marchenko focusing function is a wave field that focuses at a designated point in space at zero time. Marchenko focusing functions are useful for retrieving the wave field inside a heterogeneous medium from the reflection response at its surface. By expressing these focusing functions in terms of the propagator matrix, the usual approximations (such as ignoring evanescent waves) are avoided. While a propagator matrix acts on the full wave-field vector, a transfer matrix (according to the definition employed in this paper)`transfers' a decomposed wave-field vector (containing downgoing and upgoing waves) from one depth level to another. It can be expressed in terms of decomposed Marchenko focusing functions. We present propagator matrices, transfer matrices and Marchenko focusing functions in a consistent way and discuss their mutual relations. In the main text we consider the acoustic situation and in the appendices we discuss other wave phenomena. Understanding these mutual connections may lead to new developments of Marchenko theory and its applications in wave field focusing, Green's function retrieval and imaging.Comment: 42 pages, 4 figure

Tripartite entanglement dynamics in a system of strongly driven qubits

We study the dynamics of tripartite entanglement in a system of two strongly driven qubits individually coupled to a dissipative cavity. We aim at explanation of the previously noted entanglement revival between two qubits in this system. We show that the periods of entanglement loss correspond to the strong tripartite entanglement between the qubits and the cavity and the recovery has to do with an inverse process. We demonstrate that the overall process of qubit-qubit entanglement loss is due to the second order coupling to the external continuum which explains the exp[-g^2 t/2+g^2 k t^3/6+\cdot] for of the entanglement loss reported previously.Comment: 9 pages, 5 figure

Minimum-phase property and reconstruction of elastodynamic dereverberation matrix operators

Minimum-phase properties are well-understood for scalar functions where they can be used as physical constraint for phase reconstruction. Existing scalar applications of the latter in geophysics include, for example the reconstruction of transmission from acoustic reflection data, or multiple elimination via the augmented acoustic Marchenko method. We review scalar minimum-phase reconstruction via the conventional Kolmogorov relation, as well as a less-known factorization method. Motivated to solve practice-relevant problems beyond the scalar case, we investigate (1) the properties and (2) the reconstruction of minimum-phase matrix functions. We consider a simple but non-trivial case of 2 × 2 matrix response functions associated with elastodynamic wavefields. Compared to the scalar acoustic case, matrix functions possess additional freedoms. Nonetheless, the minimum-phase property is still defined via a scalar function, that is a matrix possesses a minimum-phase property if its determinant does. We review and modify a matrix factorization method such that it can accurately reconstruct a 2 × 2 minimum-phase matrix function related to the elastodynamic Marchenko method. However, the reconstruction is limited to cases with sufficiently small differences between P- and S-wave traveltimes, which we illustrate with a synthetic example. Moreover, we show that the minimum-phase reconstruction method by factorization shares similarities with the Marchenko method in terms of the algorithm and its limitations. Our results reveal so-far unexplored matrix properties of geophysical responses that open the door towards novel data processing tools. Last but not least, it appears that minimum-phase matrix functions possess additional, still-hidden properties that remain to be exploited, for example for phase reconstruction.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Applied Geophysics and Petrophysic

Data-driven suppression of short-period multiples from laterally varying thin-layered overburden structures

Marchenko multiple elimination methods remove all orders of overburden-generated internal multiples in a data-driven way. In the presence of thin beds, however, these methods have been shown to underperform. This is because the underlying inverse problem requires the information about short-period internal multiple (SPIM) imprint on the inverse transmission to be correctly constrained. This has been addressed in 1.5D media with energy conservation and minimum-phase reconstruction. Extending the applications to two dimensions and, hence, making the step toward field data were believed to be hampered by the need for a multidimensional minimum-phase reconstruction which is (1) not unique and (2) no algorithm has been found to perform this in practice on band-limited data. Here, we address both of these problems with an approach that includes solving the Marchenko equation with a trivial constraint, evaluating the energy conservation condition of its solutions to find the spatially dependent error syndrome, using the 1.5D minimum-phase reconstruction for each shot gather to find the spatially dependent constraint, and finally using that inside another run of the Marchenko equation solver to find a much-improved result. We find that the method works because in 2D media the expression of SPIMs in the inverse transmission coda is approximately 1.5D. We then investigate a class of models and synthetic data sets to verify where the 1.5D approximation starts breaking down. Our analysis indicates that this approach could perform very well in settings with moderate lateral variations, which also is where the (short-period) internal multiples are most difficult to differentiate from primary reflections.ISSN:0016-8033ISSN:1942-215

Towards understanding the impact of the evanescent elastodynamic mode coupling in Marchenko equation-based demultiple methods

Marchenko equation-based methods promise data-driven, true-amplitude internal multiple elimination. The method is exact in 1-D acoustic media, however it needs to be expanded to account for the presence of 2- and 3-D elastodynamic wave-field phenomena, such as compressional (P) to shear (S) mode conversions, total reflections or evanescent waves. Mastering high waveform-fidelity methods such as this, could further advance amplitude vs offset analysis and lead to improved reservoir characterization. This method-expansion may comprise of re-evaluating the underlying assumptions and/or appending the scheme with additional constraints (e.g. minimum phase). To do that, one may need to better understand the construction of the Marchenko equation solutions, the so-called focusing functions, in a mathematically simple and numerically stable fashion. The latter could be a challenge at large angles of incidence where the elastodynamic effects and evanescent waves start playing a dominant role. We demonstrate that the elastodynamic focusing functions are the bridge between the Marchenko equation theory and the transfer matrix formalism. Using the latter, we show how we can try to gain further insights into how time-reversal (correlations) behaves when either of the elastic modes becomes evanescent. We also show how this construction allows us to shed light on into the mathematical properties of elastodynamic inverse transmissions, which takes us a step closer towards understanding the elastodynamic minimum phase reconstruction.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Applied Geophysics and Petrophysic

Internal multiple elimination: Can we trust an acoustic approximation?

Correct handling of strong elastic, internal, multiples remains a challenge for seismic imaging. Methods aimed at eliminating them are currently limited by monotonicity violations, a lack of a-priori knowledge about mode conversions, or unavailability of multi-component sources and receivers for not only particle velocities but also the traction vector. Most of these challenges vanish in acoustic media such that Marchenko-equation-based methods are able in theory to remove multiples exactly (within a certain wavenumber-frequency band). In practice, however, when applied to (elastic) field data, mode conversions are unaccounted for. Aiming to support a recently published marine field data study, we build a representative synthetic model. For this setting, we demonstrate that mode conversions can have a substantial impact on the recovered multiple-free reflection response. Nevertheless, the images are significantly improved by acoustic multiple elimination. Moreover, after migration the imprint of elastic effects is considerably weaker and unlikely to alter the seismic interpretation.Accepted Author ManuscriptApplied Geophysics and PetrophysicsImPhys/Medical Imagin