1,173 research outputs found
Tackling Different Velocity Borne Challenges of the Elastodynamic Marchenko Method
No full textThe elastodynamic Marchenko method removes overburden interactions obscuring the target information. This method either relies on separability of the so-called focusing and Green's functions or requires an accurate initial estimate of the focusing and Green's function overlap. Hitherto, F1- and G-+ have been assumed separable, whereas F1+ and (G-)* share an unavoidable overlap, which has been considered understood but hard to predict without knowing the model. However, velocity differences between P- and S-waves cause so far unexplored fundamental challenges for elastodynamic Marchenko autofocusing. These challenges are analysed for horizontally-layered media. First, the F1-/G-+ separability assumption can be violated depending on the medium, the redatuming depth and the angle of incidence. Second, the initial estimate of the said unavoidable overlap can be even more complicated than originally thought, including some of the internal multiples. We propose a strategy where we trade-off this sophisticated initial estimate with a trivial one at the cost of a more restrictive F1-/G-+ separability assumption, or at the cost of introducing an overlap between F1- and G-+ instead. The proposed method finds the desired solutions convolved by an unknown matrix which we can hope to remove by exploiting energy conservation and minimum-phase properties of the focusing functions.Accepted author manuscriptApplied Geophysics and PetrophysicsQN/Theoretical PhysicsImPhys/Acoustical Wavefield Imagin
Towards understanding the impact of the evanescent elastodynamic mode coupling in Marchenko equation-based demultiple methods
No full textMarchenko 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
Iphidozercon altaicus Gwiazdowicz & Marchenko 2012, sp. n.
No full textIphidozercon altaicus sp. n. (Figs 1–4) <p>Description. Female (N = 3). Dorsum (Fig. 1). Dorsal shield oval, length 375–380 µm, width 230–250 µm distinct foveate sculpture throughout. 18 pairs of setae on podonotal part of shield and 14 pairs of setae on opisthonotal part of shield. All setae fine, smooth and pointed, length of 25–30 µm, except j1 (10 µm, inserted ventrally), and two antero-lateral setae s1, s2 (15 µm).</p> <p>Venter (Fig. 2) Tritosternum with trapezoidal base (25 µm) and finely pilose laciniae (35 µm). Sternal shield rectangular, 70 × 55 µm, setae st1–st3 smooth and pointed, length 10 µm. Metasternal setae st4 (10 µm) on soft membrane. Genital shield small and narrow (55 µm), spatulate posteriorly. Genital setae st5 (15 µm) outside the shield. Anal shield relatively large 60 µm long, 70 µm wide with para-anal setae (15 µm) and post-anal seta (20 µm). Narrow cribrum below post-anal seta. Sternal, genital and anal shields are unornamented. Peritremes ending anteriorly to coxae I, stigmata at level of coxae IV. Peritremal shields wide, with weak posterior lineate ornamentation. Opisthogastric integument behind coxae IV with one pair of oval metapodal plates, a pair of smaller plates near posterior ends of peritrematal shields. Opisthogastric setae JV1–JV5, ZV1–ZV2 15 µm long, others (R2–R4) approximately 20 µm.</p> <p>Gnathosoma. Hypostome with robust horn-like corniculi and four pairs of setae. Anterior seta h1 longest (30 µm), internal seta h3 (20 µm), palp coxal seta h4 (25 µm) shorter, external seta h2 (10 µm) shortest. Seven transverse rows of hypostomal denticles present, numbers of denticles per row (anterior to posterior) 12, 15, 17, 15, 17, 16, 13 (Fig. 3a). Chelicera typical of genus, fixed digit with three teeth, movable digit with two teeth (Fig. 3b), other details of chelicerae not visible in available specimens. Epistome with central prong longest, lateral prongs shorter, with denticulate outer margins (Fig. 3c).</p> <p>Legs and palps. Lengths of legs: I – 230 µm, II – 200 µm, III – 180 µm, IV – 210 µm. Setation of genua I–II–III–IV: 12–10–7–7 (Fig. 4a); tibiae 12–9–7–7 (Fig. 4b). Tarsus II to IV each with the dorsoproximal setae ad2 and pd2 short and straight (Fig 4c). Palp apotele 2-tined.</p> <p> Material examined: Holotype: Female. Russia, North-East of Altai Mountains, Teletskoe lake region, environs of Obogo village, in litter of <i>Betula pubescens – Populus tremula</i> forest, (51°30’48’’ N, 87°18’7’’ E, 900 m a.s.l.), 6 August 2007, leg. I.I. MARCHENKO. Paratypes: 2 females, North-East of Altai Mountains, Teletskoe lake region, environs of Obogo village, in litter of <i>Abies sibirica – Pinus sibirica</i> forest, (51°30’48’’N, 87°18’7’’E, 900 m a.s.l.), 6 August 2007, leg. I. I. MARCHENKO.</p> <p>Etymology. The name of this species reflects the fact that it was collected in the Altai Mountains.</p> <p> Differential diagnosis. <i>Iphidozercon altaicus</i> sp. n. is similar to <i>Iphidozercon foveatus</i> GWIAZDOWICZ et HALLIDAY, 2008. Both species have foveate sculpture on the dorsal shield and similar lengths of dorsal setae. The length of peritreme and the shape of genital shield is similar in both species. Nevertheless, many differences have been detected, such as shapes of the peritremal and anal shields. In <i>I. foveatus</i> the anal shield is narrow, while in <i>I. altaicus</i> it is wider than long. In <i>I. foveatus</i> the peritremal shield is wide, with tiny denticles on the internal side and in <i>I. altaicus</i> the shield is narrower and without denticles. In <i>I. foveatus</i> five pairs of smaller platelets bearing pores are located on the ventral side, in <i>I. altaicus</i> there are no such platelets. In <i>I. foveatus</i> the epistome has a central elongated prong ending in three denticles, but in <i>I. altaicus</i> the prong ends in spikes. In <i>I. foveatus</i> the movable digit has three teeth, but in <i>I. altaicus</i> it has two teeth.</p>Published as part of <i>Gwiazdowicz, D. J. & Marchenko, I. I., 2012, Two New Species Of Iphidozercon (Acari: Ascidae) With A Key To Females, pp. 41-52 in Acta Zoologica Academiae Scientiarum Hungaricae 58 (1)</i> on pages 42-44, DOI: <a href="http://zenodo.org/record/5732065">10.5281/zenodo.5732065</a>
Inverse scattering for optical couplers. Exact solution of Marchenko equations
No full textAn exact solution of Marchenko equations for rational scattering data of arbitrary order is developed, with reference to the case of two coupled waves propagating in a lossless (optical) waveguide. Some numerical examples are presented for the synthesis of coupling structures having a prescribed frequency response
Rate of convergence in probability to the Marchenko-Pastur law
No full textGötze F, Tikhomirov A. Rate of convergence in probability to the Marchenko-Pastur law. BERNOULLI. 2004;10(3):503-548.It is shown that the Kolmogorov distance between the spectral distribution function of a random covariance (1/p)XXT, where X is an nxp matrix with independent entries and the distribution function of the Marchenko-Pastur law is of order O(n(-1/2)) in probability. The bound is explicit and requires that the twelfth moment of the entries of the matrix is uniformly bounded and that p/n is separated from 1
Inverse scattering designs of dispersion-engineered single-mode planar waveguides
No full textWe use an inverse-scattering (IS) approach to design single-mode waveguides with controlled linear and higher-order dispersion. The technique is based on a numerical solution to the Gelfand-Levitan-Marchenko integral equation, for the inversion of rational reflection coefficients with arbitrarily large number of leaky poles. We show that common features of dispersion-engineered waveguides such as trenches, rings and oscillations in the refractive index profile come naturally from the IS algorithm without any a priori assumptions. Increasing the leaky-pole number increases the dispersion map granularity and allows design of waveguides with identical low order and differing higher order dispersion coefficients
Energy-independent complex single -waves potential from Marchenko equation
No full textWe extend our previous results of solving the inverse problem of quantum
scattering theory (Marchenko theory, fixed- inversion). In particular, we
apply an isosceles triangular-pulse function set for the Marchenko equation
input kernel expansion in a separable form. The separable form allows a
reduction of the Marchenko equation to a system of linear equations for the
output kernel expansion coefficients. We show that in the general case of a
single partial wave, a linear expression of the input kernel is obtained in
terms of the Fourier series coefficients of functions in the
finite range of the momentum [ is the scattering
matrix, is the angular orbital momentum, ]. Thus, we show
that the partial --matrix on the finite interval determines a potential
function with -step accuracy. The calculated partial potentials describe a
partial --matrix with the required accuracy. The partial --matrix is
unitary below the threshold of inelasticity and non--unitary (absorptive) above
the threshold. We developed a procedure and applied it to partial-wave analysis
(PWA) data of elastic scattering up to 3 GeV. We show that
energy-independent complex partial potentials describe these data for single
-waves.Comment: 7 pages, 6 figures. arXiv admin note: text overlap with
arXiv:2112.1434
Marchenko imaging for 2D and 3D complex structures—with field applications to sub-salt and sub-basalt imaging
No full textIncludes bibliographical references.2019 Fall.Seismic imaging is a geophysical technique that uses elastic waves to form images of geologic formations in the subsurface. Seismic imaging has become the most reliable diagnostic tool for modern hydrocarbon exploration and production. Conventional imaging methods, however, rely on the single-scattering assumption, which requires the recorded seismic data to not include multiples—waves that are reflected more than once in the subsurface before reaching the receivers. While the surface related multiples can be effectively suppressed with the Surface Related Multiples Elimination (SRME) method, the elimination of the internal multiples—multiples that are not surface related—remains challenging with current seismic processing techniques. The traditional workflow to mitigate the artifacts associated with internal multiples involves 1) predicting internal multiples, and 2) subtracting them from the acquired seismic data. This workflow requires accurate horizons of the multiple generators and a labor-intensive adaptive subtraction, which is usually performed in a least-squares sense and may damage primary events when primaries and multiples interfere. The Marchenko framework used in this dissertation is based on inverse problems in quantum physics. This framework consists of two steps. The first step is Marchenko redatuming, which allows one to use surface seismic reflection data to retrieve seismic responses (Green’s functions) between arbitrary points in the subsurface to the acquisition surface. The second step is Marchenko imaging, which utilizes the Green’s functions retrieved by Marchenko redatuming for imaging. These two steps provide a solution for resolving the issues associated with internal multiples and producing multiple-free images, without requiring horizons of multiple generators or performing adaptive subtraction. For my PhD research, I develop and investigate the 2D and 3D Marchenko framework for field data deployment and application. I elucidate the specific requirements for the two inputs of the Marchenko method: the seismic reflection data acquired on the earth surface and a background velocity model for estimating first arrivals from subsurface locations to the surface. To make the standard surface seismic data (which can be sparsely sampled in practice) useful for Marchenko redatuming, I consider forward interpolation methods to convert sparse surface data to densely and uniformly sampled data that corresponds to an equal number of co-located sources and receivers at the acquisition surface. I show that the background velocity model does not need to be known in great detail since the first-arriving wave needed by the Marchenko method is mostly determined by its travel time. A smooth velocity model is sufficiently accurate for such estimations. I demonstrate that the combination of Marchenko redatuming and imaging is robust with respect to erroneous velocity models. I extend the Marchenko redatuming algorithm to 3D seismic data by reformulating the Marchenko-type equations in 3D Cartesian coordinate system and develop an efficient 3D numerical implementation, in which I resolve the associated computational optimization and memory issues. Despite the idealized assumptions and the specific requirements for the input data within the Marchenko framework, I obtained two successful field data applications of the Marchenko method for imaging complex subsurface areas and propose a practical and effective workflow for processing streamer field data. With a Gulf of Mexico field dataset, I show that discontinuities along true reflectors—resulting from the destructive interference between primaries and the internal multiples due to salt layers—is resolved by the Marchenko method, which produces a clean and continuous sub-salt image. With an offshore Brazil dataset, I show that the artificial or nonphysical interfaces—resulting from the internal multiples that are generated by volcanic intrusion layers in the overburden—are adequately eliminated by performing Marchenko imaging
Local Marchenko-Pastur Law for Sparse Rectangular Random Matrices
No full textGötze F, Timushev DA, Tikhomirov AN. Local Marchenko-Pastur Law for Sparse Rectangular Random Matrices. Doklady Mathematics. 2021;104(3):332-335.We consider sparse sample covariance matrices with sparsity probability with p(n) >= c(0) log((aleph) over bar) n/n with aleph > 0. Assuming that the distribution of matrix elements has a finite absolute moment of order 4 + delta, delta > 0, it is shown that the distance between the Stieltjes transforms of the empirical spectral distribution function and the Marchenko-Pastur law is of order n(1/(nv) + 1/(np(n))), where v is the distance to the real axis in the complex plane
Marchenko inversion of gpr data for a 1d dissipative medium
No full textRadar data collected on two sides of a horizontally dissipative layered medium are required to invert for the medium parameters. The two-sided reflection and transmission responses are reduced to two single-sided reflection responses. One is the measured dissipative medium response, and the other is the reflection response of the corresponding effectual medium, which has negative dissipation. Marchenko-type equations are solved using these two reflection responses. The obtained focusing functions in the dissipative and effectual media are used to invert for the permittivity and the permeability under the assumption of weak dissipation in reflection. Once these parameters are known, the travel times are used to estimate the layer thicknesses. Finally, the focusing functions are used to estimate the conductivity in each layer. The method does not require any model information and runs as a fully automated process. A numerical example shows that the method works well for a horizontally dissipative layered medium. Statistical analysis for several noise models shows that the method is robust at least up to 40 dB additive and multiplicative white noise.</p
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