A platform for data mapping in scalar models of data acquisition

Jaramillo, Herman

doi:10.1190/1.1820221

Cited by 8 publications

(9 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Tygel et al . (1998 ), Jaramillo (1998) and Jaramillo and Bleistein (1998, 1999) carried out this process in the space–time domain, while a space–frequency domain derivation, partially described by Bleistein and Jaramillo (1998), is presented here. An advantage of space–time methods is that the time‐domain integral produces a delta function that essentially reduces the dimension of the space‐domain integration.…”

Section: Introductionmentioning

confidence: 99%

“…The principle survives in the mapping of traveltimes from input to output con®guration under a stationarity condition that forces the isochrons to be tangential at a potential image point. Tygel et al (1998), Jaramillo (1998) and Jaramillo andBleistein (1998, 1999) carried out this process in the space±time domain, while a space±frequency domain derivation, partially described by Bleistein and Jaramillo (1998), is presented here. An advantage of space±time methods is that the time-domain integral produces a delta function that essentially reduces the dimension of the space-domain integration.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A platform for Kirchhoff data mapping in scalar models of data acquisition

Bleistein

Jaramillo

2000

Geophysical Prospecting

View full text Add to dashboard Cite

Kirchhoff data mapping (KDM) is a procedure for transforming data from a given input source/receiver configuration and background earth model to data corresponding to a different output source/receiver configuration and background model. The generalization of NMO/DMO, datuming and offset continuation are three examples of KDM applications. This paper describes a ‘platform’ for KDM for scalar wavefields. The word, platform, indicates that no calculations are carried out in this paper that would adapt the derived formula to any one of a list of KDMs that are presented in the text. Platform formulae are presented in 3D and in 2.5D. For the latter, the validity of the platform equation is verified — within the constraints of high‐frequency asymptotics — by applying it to a Kirchhoff approximate representation of the upward scattered data from a single reflector and for an arbitrary source/receiver configuration. The KDM formalism is shown to map this Kirchhoff model data in the input source/receiver configuration to Kirchhoff data in the output source/receiver configuration, with one exception. The method does not map the reflection coefficient. Thus, we verify that, asymptotically, the ray theoretical geometrical spreading effects due to propagation and reflection (including reflector curvature) are mapped by this formalism, consistent with the input and output modelling parameters, while the input reflection coefficient is preserved. In this sense, this is a ‘true‐amplitude’ formalism. As with earlier Kirchhoff inversion, a slight modification of the kernel of KDM provides alternative integral operators for estimating the specular reflection angle, both in the input configuration and in the output configuration, thereby providing a basis for amplitude‐versus‐angle analysis of the data.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A platform for Kirchhoff data mapping in scalar models of data acquisition

Bleistein

Jaramillo

2000

Geophysical Prospecting

View full text Add to dashboard Cite

show abstract

“…For example, Biondi et al (1998) compute the operator that maps general input data to single-azimuth output data; Black et al (1993), Liner (1991), and Bleistein (1990) compute the DMO operator; and more general continuation is given in Bleistein et al (1999), Bleistein and Jaramillo (2000), Fomel and Bleistein (2001), Stolt (2002), andFomel (2003).…”

Section: Continuationmentioning

confidence: 99%

“…[In a constant-velocity model, our continuation operator can be thought of as a solution to the partial differential equation used by Goldin (1994) and Goldin and Fomel (1995).] This approach has been developed in the absence of caustics (e.g., constant-velocity and constant-velocity-gradient media) by Bleistein and Jaramillo (2000), Canning and Gardner (1996), and Stolt (2002). Other related approaches can be found in Hubral et al (1996), Santos et al (1997), and Tygel et al (1998).…”

Section: Introductionmentioning

confidence: 99%

The applicability of dip moveout/azimuth moveout in the presence of caustics

2005

View full text Add to dashboard Cite

Reflection seismic data continuation is the computation of data at source and receiver locations that differ from those in the original data, using whatever data are available. We develop a general theory of data continuation in the presence of caustics and illustrate it with three examples: dip moveout (DMO), azimuth moveout (AMO), and offset continuation. This theory does not require knowledge of the reflector positions. We construct the output data set from the input through the composition of three operators: an imaging operator, a modeling operator, and a restriction operator. This results in a single operator that maps directly from the input data to the desired output data. We use the calculus of Fourier integral operators to develop this theory in the presence of caustics. For both DMO and AMO, we compute impulse responses in a constant-velocity model and in a more complicated model in which caustics arise. This analysis reveals errors that can be introduced by assuming, for example, a model with a constant vertical velocity gradient when the true model is laterally heterogeneous. Data continuation uses as input a subset (common offset, common angle) of the available data, which may introduce artifacts in the continued data. One could suppress these artifacts by stacking over a neighborhood of input data (using a small range of offsets or angles, for example). We test data continuation on synthetic data from a model known to generate imaging artifacts. We show that stacking over input scattering angles suppresses artifacts in the continued data.

show abstract

“…2,3,4,5,6,7,8,9,19] and the Neumann series methods [Refs. Popular methods include downward continuation [Refs.…”

mentioning

confidence: 99%

Application of Helix Filters to Pattern-Based Multiple Suppression

2000

View full text Add to dashboard Cite

Modern approaches to multiple suppression begin by producing corrupted estimates of recorded multiple energy. Popular methods include downward continuation [Refs. 2,3,4,5,6,7,8,9,19] and the Neumann series methods [Refs. 13,17,18]. Errors in the downward continuation model contribute to incorrect arrival times. Inaccuracies in the backpropagation algorithm result in poor amplitudes and phases. While the arrival times from a Neumann series approach are exact, wavefield phase and character are not. The limitations inherent in these estimation processes are generally overcome either through pattern capturing, or energy minimization techniques that seek to optimally remove the multiple energy from the recorded wavefield. In the pattern approach, the idea [Refs. 15,16] is to use the recorded data and the estimated noise to characterize the primary and multiple patterns separately. Separating the signal from the noise is then accomplished by statistical techniques. The problem was originally formulated in the frequency domain. A significant advantage of this approach is that the prediction error filters that capture the various patterns are one-dimensional and easy to compute. The helix filter [10] offers a new and robust approach to these methods with the same advantage. Because they convert multi-dimensional filters to one-dimensional equivalents, helix filters provide the same advantages in space-time that frequency domain filters provide in f-x. This paper reviews the helix concepts and shows that they provide an effective approach to pattern-based multiple suppression. Helix FiltersHelix filters [10] are a deceptively easy concept to master. Figure 1 explains the entire process. In this case a two-dimensional filter shown in (a) is wrapped around a coil (b) and then unwound (c) on a one-dimensional data vector (d). The result, within helix boundary constraints, is a two-dimensional convolution of a two-dimensional filter with a two-dimensional data set.Traditionally, we think of one-dimensional objects as vectors, and multi-dimensional objects as either rows or columns of vectors. In the memory of most modern computers, the FORTRAN programming language stores multi-dimensional arrays as fixed length columns in contiguous memory locations. Treating this memory block as a one-dimensional array produces a super data vector. Storing a similar array of filter coefficients produces a one-dimensional filter operator that can be convolved in one-dimension. The resulting array is exactly equivalent to the result of a twodimensional convolution. Fig. 1-Winding a two-dimensional filer onto a helix. (a) Twodimensional filter. (b) Two-dimensional filter as a helix. (c) A helix about to be unwound. (d) Helix unwound on a one-dimensional impulse.

show abstract

A platform for data mapping in scalar models of data acquisition

Cited by 8 publications

References 1 publication

A platform for Kirchhoff data mapping in scalar models of data acquisition

A platform for Kirchhoff data mapping in scalar models of data acquisition

The applicability of dip moveout/azimuth moveout in the presence of caustics

Application of Helix Filters to Pattern-Based Multiple Suppression

Contact Info

Product

Resources

About