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  • Physics  (2)
  • 1
    Online Resource
    Online Resource
    AIP Publishing ; 2020
    In:  Journal of Mathematical Physics Vol. 61, No. 7 ( 2020-07-01)
    In: Journal of Mathematical Physics, AIP Publishing, Vol. 61, No. 7 ( 2020-07-01)
    Abstract: Complex-valued functions defined on a finite interval [a, b] generalizing power functions of the type (x−x0)n for n ≥ 0 are studied. These functions called Φ-generalized powers, Φ being a given nonzero complex-valued function on the interval, were considered to construct a general solution representation of the Sturm–Liouville equation in terms of the spectral parameter [V. V. Kravchenko and R. M. Porter, Math. Methods Appl. Sci. 33(4), 459–468 (2010)] . The Φ-generalized powers can be considered as natural basis functions for the one-dimensional supersymmetric quantum mechanics systems taking Φ=ψ02, where the function ψ0(x) is the ground state wave function of one of the supersymmetric scalar Hamiltonians. Several properties are obtained such as Φ-symmetric conjugate and antisymmetry of the Φ-generalized powers, a supersymmetric binomial identity for these functions, a supersymmetric Pythagorean elliptic (hyperbolic) identity involving four Φ-trigonometric (Φ-hyperbolic) functions, as well as a supersymmetric Taylor series expressed in terms of the Φ-derivatives. We show that the first n Φ-generalized powers are a fundamental set of solutions associated with nonconstant coefficient homogeneous linear ordinary differential equations of order n + 1. Finally, we present a general solution representation of the stationary Schrödinger equation in terms of geometric series where the Volterra compositions of the first type are considered.
    Type of Medium: Online Resource
    ISSN: 0022-2488 , 1089-7658
    RVK:
    Language: English
    Publisher: AIP Publishing
    Publication Date: 2020
    detail.hit.zdb_id: 1472481-9
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  • 2
    Online Resource
    Online Resource
    Society of Exploration Geophysicists ; 2023
    In:  GEOPHYSICS Vol. 88, No. 5 ( 2023-09-01), p. R655-R669
    In: GEOPHYSICS, Society of Exploration Geophysicists, Vol. 88, No. 5 ( 2023-09-01), p. R655-R669
    Abstract: Monitoring the change in permafrost conditions and distribution is crucial for forecasting global warming. As seismic velocities increase with ice content, marine seismic surveys can map the top of ice-bearing subsea permafrost on a large scale. However, conventional seismic methods cannot fully map internal velocity variations linked to changes in ice content because the removal of guided waves and multiples is challenging for reflection processing. Nevertheless, these arrivals carry information about velocity variations with depth. We investigate if a joint analysis of various wave arrivals could provide information about velocity variations within permafrost and accurately estimate the permafrost thickness. Through a sensitivity analysis, we estimate the feasibility of using different wave arrivals, such as reflections, refractions, multiples, and guided waves, to better characterize permafrost conditions. We find that guided waves are sensitive to velocity variations within permafrost and can detect the depth of the permafrost’s base under certain geologic conditions. Then, we combine the analysis of all seismic arrivals to derive a subsurface permafrost model for a seismic line collected in the Beaufort Sea. The joint analysis reveals the transitions in depth between ice-bonded and partially ice-bonded permafrost and offers a crude estimate of permafrost thickness.
    Type of Medium: Online Resource
    ISSN: 0016-8033 , 1942-2156
    RVK:
    Language: English
    Publisher: Society of Exploration Geophysicists
    Publication Date: 2023
    detail.hit.zdb_id: 2033021-2
    detail.hit.zdb_id: 2184-2
    SSG: 16,13
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