scholarly journals The critical reflection theorem

1985 ◽  
Author(s):  
J. T. Fokkema ◽  
A. Ziolkowski
Keyword(s):  
Critical Reflection ◽  
Reflection Theorem

scholarly journals The critical reflection theorem

Geophysics ◽  
1987 ◽  
Vol 52 (7) ◽  
pp. 965-972 ◽  
Author(s):  
Jacob T. Fokkema ◽  
Anton Ziolkowski
Keyword(s):  
Plane Wave ◽  
Half Space ◽  
Critical Reflection ◽  
Lower Layer ◽  
Plane Waves ◽  
Source Spectrum ◽  
Demarcation Criterion ◽  
The Earth ◽  
Reflection Theorem ◽  
Uppermost Layer

In predictive deconvolution of seismic data, it is assumed that the response of the earth is white. Any nonwhite components are presumed to be caused by the source wavelet or by unwanted multiples. We show that this whiteness assumption is invalid at precritical incidence. We consider plane waves incident on a layered acoustic half‐space. At exactly critical incidence at any interface in the half‐space, the lower layer acts similar to a rigid plate. The response of the half‐space is then all‐pass, or white. This result we call the critical reflection theorem. The response is also white if the waves are postcritically incident on the lower half‐space. In normal data processing these postcritical components are removed by muting. Thus the whiteness assumption is normally applied to exactly that part of the data where it is invalid. The demarcation between precritical and postcritical incidence can be exploited for the purposes of deconvolution, provided the data can be decomposed into plane waves. To develop this application, we consider the response of a point source in the uppermost layer of the layered half‐space, with a free surface above. The response is simply a superposition of the plane‐wave responses already studied, with complications introduced by the source and receiver ghosts and by multiples in the upper layer. At postcritical incidence the earth response is white for all plane‐wave components; the source spectrum may be estimated from the postcritical plane‐wave components after removing the effects of ghosts and multiples in the upper layer. If the source signature is already known, the demarcation criterion can be used to separate intrinsic absorption effects from attenuation effects caused by scattering.

On: “The critical reflection theorem” by J. T. Fokkema and A. Ziolkowski (GEOPHYSICS, 52, 965–972, July 1987).

Geophysics ◽  
1988 ◽  
Vol 53 (11) ◽  
pp. 1490-1491
Author(s):  
Andrew Walden ◽  
Roy White
Keyword(s):  
Critical Reflection ◽  
The Earth ◽  
Reflection Theorem

In this paper, Fokkema and Ziolkowski consider precritical and postcritical incidence and resulting implications for the reflection response of the earth. The ideas are interesting and thought provoking, but their inferences with regard to the whiteness assumption in standard deconvolution are misleading. We will endeavor to show why.

Beauty, Critical Reflection, and Justice

2011 ◽  
Vol 34 (1-2) ◽  
pp. 130-152 ◽  
Author(s):  
Gordon Rixon
Keyword(s):  
Critical Reflection

It’s Deeper Than That!: Restorative Justice and the Challenge of Racial Reflexivity in White-led Schools

2021 ◽  
pp. 004208592199841
Author(s):  
Arthur Romano ◽  
Rochelle Arms Almengor
Keyword(s):  
Black Women ◽  
Critical Race Theory ◽  
Restorative Justice ◽  
Case Studies ◽  
Students Of Color ◽  
White Privilege ◽  
Critical Reflection ◽  
White Led ◽  
Race Theory ◽  
Systemic Racism

This paper uses critical race theory to analyze several case studies focused on the experiences of two restorative justice coordinators (RJCs), both Black women and how they understood and responded to perceived racial injustices in urban schools with white leadership. These schools were attempting to address unequal disciplinary practices toward students of color through restorative justice and the RJCs adapted their approaches to addressing racialized dynamics while also developing school-wide networks to foster broader critical reflection on race. They navigated the risks of challenging white privilege and systemic racism both of which at times limited their attempts at influencing change.

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