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Write the z-transform of wavelet Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") Design a three-term inverse filter and apply it to the original. Hint: The z-transform of the wavelet can be written as a product of two doublets, (1, - 1/2) and (1, 1/2). Consider wavelet A in Exercise 2-2. Note that ε 0 already is assigned in Exercise 2-2.
- Information Technology > Knowledge Management (0.76)
- Information Technology > Communications > Collaboration (0.76)
An ellipse is the locus of points for which the sum of the distances from the two foci is constant. A satellite follows an elliptical path about a body at one focus. If a semimajor axis, b semiminor axis, eccentricity Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.")
- Information Technology > Knowledge Management (0.76)
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All material in this report, with accompanying figures, is property of SEG Advanced Modeling Corporation (SEAM). License to use the data and models can be obtained through SEAM. This document contains contributions from many different individuals and has been reviewed for accuracy. Reported errors will be fixed on a timely basis. The SEAM Carbonate model is the petroleum industry's first field-scale, digital model of a carbonate reservoir to be openly available.
- Geology > Rock Type > Sedimentary Rock (1.00)
- Geology > Geological Subdiscipline > Geomechanics (1.00)
At this point, we introduce an important relation that is familiar to us from elementary calculus -- Euler's equation: For negative Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") Here, Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") The two versions of Euler's equation above give the following expressions for the cosine and the sine: We now introduce the continuous time variable t, and we let Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") The function Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") The angular frequency is Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.")
Physics-based Data-informed Prediction of Vertical, Catenary, and Stepped Riser Vortex-induced Vibrations
Mentzelopoulos, Andreas P. (Massachusetts Institute of Technology, Cambridge, Massachusetts) | Ferrandis, José del Águila (Massachusetts Institute of Technology, Cambridge, Massachusetts) | Rudy, Samuel (Massachusetts Institute of Technology, Cambridge, Massachusetts) | Sapsis, Themistoklis (Massachusetts Institute of Technology, Cambridge, Massachusetts) | Triantafyllou, Michael S. (Massachusetts Institute of Technology, Cambridge, Massachusetts) | Fan, Dixia (Westlake University, Hangzhou, Zhejiang)
_ Semi-empirical models serve as current state-of-the-art prediction technologies for vortex-induced vibrations (VIV). Accurate prediction of the flexible body’s structural response relies heavily on the accuracy of the acquired hydrodynamic coefficient database. The construction of systematic databases from rigid cylinder forced vibration experiments not only requires an extensive amount of time and resources but also is a virtually impossible task, given the wide multidimensional space the databases span. In this work, we improve the flexible cylinder VIV prediction by machine learning the hydrodynamic databases using measurements along the structure; such a methodology has been proven effective for vertical flexible risers in uniform and sheared flows using vibration amplitude and frequency data. This work demonstrates the effectiveness of the framework on flexible vertical risers in a stepped current and flexible catenary risers (with the catenary plane parallel or at an oblique angle with respect to the incoming flow). Moreover, the framework is applied to stepped (two-diameter) risers undergoing dual-frequency vibrations. Last, but not least, the framework is extended to using only sparse strain sensing. The predicted VIV responses using the learned hydrodynamic coefficient databases are compared with experimental observations.
- North America > United States > California (0.46)
- North America > United States > Massachusetts > Middlesex County > Cambridge (0.28)
Wraparound is the effect of finite data length in time and space on a migration algorithm implemented in the Fourier transform domain. A migration algorithm implemented in the time-space domain does not suffer from wraparound effect. But a migration algorithm implemented in the frequency-space domain suffers from wraparound along the time axis. Similarly, a migration algorithm implemented in the frequency-wavenumber domain suffers from wraparound effects both along the time and space axes. Figure 4.5-22 shows a zero-offset section that contains a diffraction hyperbola and its migration using frequency-wavenumber migration based on the phase-shift method.
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Our next task is to use the eikonal equation to find the wavefronts. The eikonal equation tells us that the wavefronts are orthogonal to the raypaths. We will use this orthogonal property to construct a wavefront (Figure 14). To this end, it is advantageous to make a one-to-one relationship between raypaths and wavefronts. For each point on the (x,y) plane, a raypath exists whose tangent at that point is horizontal.
- Information Technology > Knowledge Management (0.40)
- Information Technology > Communications > Collaboration (0.40)
Figure 9.2-9 shows the semblance curves derived from coherency inversion at CMP location 75. The CMP gather itself is shown in Figure 9.2-7a. Note that the sharpness of the peak in the semblance curve, hence the velocity resolution, depends upon the depth of the layer boundary and the magnitude of the layer velocity. Also, recall from Figure 9.1-12 that the velocity resolution also depends on the effective cable length. The sampling interval for the velocity axis in the semblance curves should be chosen by taking into consideration the velocity resolution that can be achieved.
- Geophysics > Seismic Surveying > Seismic Processing (0.87)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling (0.32)
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When there are dipping interfaces, the upcoming-wave profile needs to be migrated; that is, the energy must be mapped to the actual subsurface reflection points. This is true even for zero-offset VSP data. A ray-tracing procedure for reflector mapping is illustrated in Figure 11.4-4. Note that reflection points D, E, and F have different lateral displacements OA, OB, and OC, respectively, from borehole Oz (Figure 11.4-4a). However, upcoming wave energy from all three reflection points is recorded on the same VSP trace at the receiver location R. The reflection times RG, RH, and RK (Figure 11.4-4b) are associated with raypaths SDR, SER, and SFR, respectively.
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Often used in complex trace analysis (q.v.). The ambiguity in sign of the expressions results, in part, from the preferred notation for the Fourier transform and the common practices of numerical implementation. Named for David Hilbert (1862–1943), German mathematician. There are varied notations and varied sign conventions depending on choices that may be made, but this has no effect on the usage of the Hilbert transform, as long as consistency is maintained. The function f {\displaystyle f} is analytic meaning that the derivative of f ( z) {\displaystyle f(z)} with respect to z {\displaystyle z} exists (and similarly the derivative with respect to w {\displaystyle w} of f ( w) {\displaystyle f(w)} exists) for some region bounded by the closed curve C {\displaystyle C} called the contour of integration.
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