A simple design procedure for depth extrapolation operators that compensate for absorption and dispersion

Geophysics ◽  
2007 ◽  
Vol 72 (2) ◽  
pp. S105-S112 ◽  
Author(s):  
Rune Mittet

I compensate for the effects of absorption and dispersion in deriving the space-frequency domain depth extrapolation operators by starting from the ones without such compensation. The procedure is simple and requires only trivial cosine transforms applied to the original noncompensating operators. I show that compensating operators enhance resolution as a function of depth when applied in prestack depth migration.

2010 ◽  
Vol 2010 (1) ◽  
pp. 1-4
Author(s):  
Yi Xie ◽  
Kefeng Xin ◽  
James Sun ◽  
Carl Notfors ◽  
Ajoy Kumar Biswal ◽  
...  

Geophysics ◽  
1995 ◽  
Vol 60 (5) ◽  
pp. 1485-1494 ◽  
Author(s):  
Rune Mittet ◽  
Roger Sollie ◽  
Ketil Hokstad

In prestack depth migration using explicit extrapolators, the attenuation and dispersion of the seismic wave has been neglected so far. We present a method for accommodating absorption and dispersion effects in depth migration schemes. Extrapolation operators that compensate for absorption and dispersion are designed using an optimization algorithm. The design criterion is that the wavenumber response of the operator should equal the true extrapolator. Both phase velocity and absorption macro models are used in the wavefield extrapolation. In a model with medium to high absorption, the images obtained are superior to those obtained using extrapolators without compensation for absorption.


Author(s):  
G. Fusco ◽  
M. Russo

This paper proposes a simple design procedure to solve the problem of controlling generator transient stability following large disturbances in power systems. A state-feedback excitation controller and power system stabilizer are designed to guarantee robustness against uncertainty in the system parameters. These controllers ensure satisfactory swing damping and quick decay of the voltage regulation error over a wide range of operating conditions. The controller performance is evaluated in a case study in which a three-phase short-circuit fault near the generator terminals in a four-bus power system is simulated.


Geophysics ◽  
1997 ◽  
Vol 62 (4) ◽  
pp. 1226-1237 ◽  
Author(s):  
Irina Apostoiu‐Marin ◽  
Andreas Ehinger

Prestack depth migration can be used in the velocity model estimation process if one succeeds in interpreting depth events obtained with erroneous velocity models. The interpretational difficulty arises from the fact that migration with erroneous velocity does not yield the geologically correct reflector geometries and that individual migrated images suffer from poor signal‐to‐noise ratio. Moreover, migrated events may be of considerable complexity and thus hard to identify. In this paper, we examine the influence of wrong velocity models on the output of prestack depth migration in the case of straight reflector and point diffractor data in homogeneous media. To avoid obscuring migration results by artifacts (“smiles”), we use a geometrical technique for modeling and migration yielding a point‐to‐point map from time‐domain data to depth‐domain data. We discover that strong deformation of migrated events may occur even in situations of simple structures and small velocity errors. From a kinematical point of view, we compare the results of common‐shot and common‐offset migration. and we find that common‐offset migration with erroneous velocity models yields less severe image distortion than common‐shot migration. However, for any kind of migration, it is important to use the entire cube of migrated data to consistently interpret in the prestack depth‐migrated domain.


2021 ◽  
Author(s):  
Olaf Hellwig ◽  
Stefan Buske

<p>The polymetallic, hydrothermal deposit of the Freiberg mining district in the southeastern part of Germany is characterised by ore veins that are framed by Proterozoic orthogneiss. The ore veins consist mainly of quarz, sulfides, carbonates, barite and flourite, which are associated with silver, lead and tin. Today the Freiberg University of Mining and Technology is operating the shafts Reiche Zeche and Alte Elisabeth for research and teaching purposes with altogether 14 km of accessible underground galleries. The mine together with the most prominent geological structures of the central mining district are included in a 3D digital model, which is used in this study to study seismic acquisition geometries that can help to image the shallow as well as the deeper parts of the ore-bearing veins. These veins with dip angles between 40° and 85° are represented by triangulated surfaces in the digital geological model. In order to import these surfaces into our seismic finite-difference simulation code, they have to be converted into bodies with a certain thickness and specific elastic properties in a first step. In a second step, these bodies with their properties have to be discretized on a hexahedral finite-difference grid with dimensions of 1000 m by 1000 m in the horizontal direction and 500 m in the vertical direction. Sources and receiver lines are placed on the surface along roads near the mine. A Ricker wavelet with a central frequency of 50 Hz is used as the source signature at all excitation points. Beside the surface receivers, additional receivers are situated in accessible galleries of the mine at three different depth levels of 100 m, 150 m and 220 m below the surface. Since previous mining activities followed primarily the ore veins, there are only few pilot-headings that cut through longer gneiss sections. Only these positions surrounded by gneiss are suitable for imaging the ore veins. Based on this geometry, a synthetic seismic data set is generated with our explicit finite-difference time-stepping scheme, which solves the acoustic wave equation with second order accurate finite-difference operators in space and time. The scheme is parallelised using a decomposition of the spatial finite-difference grid into subdomains and Message Passing Interface for the exchange of the wavefields between neighbouring subdomains. The resulting synthetic seismic shot gathers are used as input for Kirchhoff prestack depth migration as well as Fresnel volume migration in order to image the ore veins. Only a top mute to remove the direct waves and a time-dependent gain to correct the amplitude decay due to the geometrical spreading are applied to the data before the migration. The combination of surface and in-mine acquisition helps to improve the image of the deeper parts of the dipping ore veins. Considering the limitations for placing receivers in the mine, Fresnel volume migration as a focusing version of Kirchhoff prestack depth migration helps to avoid migration artefacts caused by this sparse and limited acquisition geometry.</p>


2006 ◽  
Author(s):  
Scott MacKay ◽  
Héctor Ramírez Jiménez ◽  
Jorge San Martín Romero ◽  
Mark Morford

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