Limitations on the determination of interval velocity from reflection seismic data

1990 ◽  
Author(s):  
C. J. Sicking ◽  
T. K. Kan
Keyword(s):  
Seismic Data ◽  
Interval Velocity ◽  
Reflection Seismic

Generalized form of the Dix equation for the calculation of interval velocities and layer thicknesses

Geophysics ◽  
1989 ◽  
Vol 54 (5) ◽  
pp. 659-661 ◽  
Author(s):  
Ali A. Nowroozi
Keyword(s):  
Root Mean Square ◽  
Seismic Data ◽  
Approximate Equation ◽  
Mean Square ◽  
Interval Velocity ◽  
Reflection Seismic ◽  
Interval Velocities ◽  
Horizontal Layers

Over three decades ago, Dix (1955) derived an approximate equation for the determination of interval velocity from observed reflection seismic data. Assuming a stack of m horizontal layers, with interval velocities [Formula: see text], layer thicknesses [Formula: see text], j = 1, m, and near‐vertical raypaths, Dix (1955) showed that [Formula: see text]where [Formula: see text] and [Formula: see text] are the two‐way vertical times and [Formula: see text] and [Formula: see text] are the root‐mean‐square (rms) velocities to interfaces j + 1 and j, respectively.

Seismic attributes — A historical perspective

Geophysics ◽  
2005 ◽  
Vol 70 (5) ◽  
pp. 3SO-28SO ◽  
Author(s):  
Satinder Chopra ◽  
Kurt J. Marfurt
Keyword(s):  
Seismic Data ◽  
Quantitative Measure ◽  
Seismic Attributes ◽  
Seismic Attribute ◽  
Black And White ◽  
Interval Velocity ◽  
Reflection Seismic ◽  
Color Displays ◽  
Attribute Analysis ◽  
Other Information

A seismic attribute is a quantitative measure of a seismic characteristic of interest. Analysis of attributes has been integral to reflection seismic interpretation since the 1930s when geophysicists started to pick traveltimes to coherent reflections on seismic field records. There are now more than 50 distinct seismic attributes calculated from seismic data and applied to the interpretation of geologic structure, stratigraphy, and rock/pore fluid properties. The evolution of seismic attributes is closely linked to advances in computer technology. As examples, the advent of digital recording in the 1960s produced improved measurements of seismic amplitude and pointed out the correlation between hydrocarbon pore fluids and strong amplitudes (“bright spots”). The introduction of color printers in the early 1970s allowed color displays of reflection strength, frequency, phase, and interval velocity to be overlain routinely on black-and-white seismic records. Interpretation workstations in the 1980s provided interpreters with the ability to interact quickly with data to change scales and colors and to easily integrate seismic traces with other information such as well logs. Today, very powerful computer workstations capable of integrating large volumes of diverse data and calculating numerous seismic attributes are a routine tool used by seismic interpreters seeking geologic and reservoir engineering information from seismic data. In this review paper celebrating the 75th anniversary of the Society of Exploration Geophysicists, we reconstruct the key historical events that have lead to modern seismic attribute analysis.

The migration of common midpoint slant stacks

Geophysics ◽  
1984 ◽  
Vol 49 (3) ◽  
pp. 237-249 ◽  
Author(s):  
Richard Ottolini ◽  
Jon F. Claerbout
Keyword(s):  
Seismic Data ◽  
Lateral Velocity ◽  
Velocity Inversion ◽  
Interval Velocity ◽  
Reflection Seismic ◽  
Straightforward Method ◽  
Velocity Surface ◽  
Velocity Variations ◽  
Migration Equation ◽  
Ray Parameter

Reflection seismic data can be imaged by migrating common midpoint slant stacks. The basic method is to assemble slant stack sections from the slant stack of each common midpoint gather at the same ray parameter. Earlier investigators have described migration methods for slant stacked shot profiles or common receiver gathers instead of common midpoint gathers. However, common midpoint slant stacks enjoy the practical advantages of midpoint coordinates. In addition, the migration equation makes no approximation for steep dips, wide offsets, or vertical velocity variations. A theoretical disadvantage is that there is no exact treatment of lateral velocity variations. Slant stack migration is a method of “migration before stack.” It solves the dip selectivity problem of conventional stacking, particularly when horizontal reflectors intersect steep dipping reflectors. The correct handling of all dips also improves lateral resolution in the image. Slant stack migration provides a straightforward method of measuring interval velocity after migration has improved the seismic data. The kinematics (traveltime treatment) of slant stack migration is also accurate for postcritical reflections and refractions. These events transform into a p-τ surface with the additional dimension of midpoint. The slant stack migration equation converts the p-τ surface into a depth‐midpoint velocity surface. As with migration in general, the effects of dip are automatically accounted for during velocity inversion.

THE DETERMINATION OF DIGITAL WIENER FILTERS BY MEANS OF GRADIENT METHODS

Geophysics ◽  
1973 ◽  
Vol 38 (2) ◽  
pp. 310-326 ◽  
Author(s):  
R. J. Wang ◽  
S. Treitel
Keyword(s):  
Seismic Data ◽  
High Speed ◽  
Gradient Methods ◽  
Wiener Filter ◽  
Gradient Algorithm ◽  
Rapid Convergence ◽  
True Solution ◽  
Peripheral Device ◽  
Wiener Filters

The normal equations for the discrete Wiener filter are conventionally solved with Levinson’s algorithm. The resultant solutions are exact except for numerical roundoff. In many instances, approximate rather than exact solutions satisfy seismologists’ requirements. The so‐called “gradient” or “steepest descent” iteration techniques can be used to produce approximate filters at computing speeds significantly higher than those achievable with Levinson’s method. Moreover, gradient schemes are well suited for implementation on a digital computer provided with a floating‐point array processor (i.e., a high‐speed peripheral device designed to carry out a specific set of multiply‐and‐add operations). Levinson’s method (1947) cannot be programmed efficiently for such special‐purpose hardware, and this consideration renders the use of gradient schemes even more attractive. It is, of course, advisable to utilize a gradient algorithm which generally provides rapid convergence to the true solution. The “conjugate‐gradient” method of Hestenes (1956) is one of a family of algorithms having this property. Experimental calculations performed with real seismic data indicate that adequate filter approximations are obtainable at a fraction of the computer cost required for use of Levinson’s algorithm.

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