Direct non-linear inversion of multi-parameter 1D elastic media using the inv...Arthur Weglein
In this paper, we present the first non-linear direct target identification method and algorithm
for 1D elastic media (P velocity, shear velocity and density vary in depth) from the inverse
scattering series. Direct non-linear means that we provide explicit formulas that: (1) input data
and directly output changes in material properties, without the use or need for any indirect procedures
such as model matching, searching, optimization or other assumed aligned objectives or
proxies, and (2) the algorithms recognize and directly invert the intrinsic non-linear relationship
between changes in material properties and changes in the concomitant wave-field. The results
clearly demonstrate that, in order to achieve full elastic inversion, all four components of data
(ˆD PP , ˆDPS, ˆD SP and ˆDSS) are needed. The method assumes that only data and reference
medium properties are input, and terms in the inverse series for moving mislocated reflectors
resulting from the linear inverse term, are separated from amplitude correction terms. Although
in principle this direct inversion approach requires all four components of elastic data, synthetic
tests indicate that a consistent value-added result may be achieved given only ˆDPP measurements,
as long as the ˆD PP were used to approximately synthesize the ˆD PS, ˆDSP and ˆD SS
components. We can reasonably infer that further value would derive from actually measuring
ˆD
PP , ˆDPS, ˆDSP and ˆD SS as the method requires. For the case that all four components of
data are available, we give one consistent method to solve for all of the second terms (the first
terms beyond linear). The method’s nonlinearity and directness provides this unambiguous data
requirement message, and that unique clarity, and the explicit non-linear formulas casts doubts
and reasonable concerns for indirect methods, in general, and their assumed aligned goals, e.g.,
using model matching objectives, that would never recognize the fundamental inadequacy from
a basic physics point of view of using only PP data to perform elastic inversion. There are important
conceptual and practical implications for the link between data acquisition and target
identification goals and objectives.
Direct non-linear inversion of multi-parameter 1D elastic media using the inv...Arthur Weglein
In this paper, we present the first non-linear direct target identification method and algorithm
for 1D elastic media (P velocity, shear velocity and density vary in depth) from the inverse
scattering series. Direct non-linear means that we provide explicit formulas that: (1) input data
and directly output changes in material properties, without the use or need for any indirect procedures
such as model matching, searching, optimization or other assumed aligned objectives or
proxies, and (2) the algorithms recognize and directly invert the intrinsic non-linear relationship
between changes in material properties and changes in the concomitant wave-field. The results
clearly demonstrate that, in order to achieve full elastic inversion, all four components of data
(ˆD PP , ˆDPS, ˆD SP and ˆDSS) are needed. The method assumes that only data and reference
medium properties are input, and terms in the inverse series for moving mislocated reflectors
resulting from the linear inverse term, are separated from amplitude correction terms. Although
in principle this direct inversion approach requires all four components of elastic data, synthetic
tests indicate that a consistent value-added result may be achieved given only ˆDPP measurements,
as long as the ˆD PP were used to approximately synthesize the ˆD PS, ˆDSP and ˆD SS
components. We can reasonably infer that further value would derive from actually measuring
ˆD
PP , ˆDPS, ˆDSP and ˆD SS as the method requires. For the case that all four components of
data are available, we give one consistent method to solve for all of the second terms (the first
terms beyond linear). The method’s nonlinearity and directness provides this unambiguous data
requirement message, and that unique clarity, and the explicit non-linear formulas casts doubts
and reasonable concerns for indirect methods, in general, and their assumed aligned goals, e.g.,
using model matching objectives, that would never recognize the fundamental inadequacy from
a basic physics point of view of using only PP data to perform elastic inversion. There are important
conceptual and practical implications for the link between data acquisition and target
identification goals and objectives.
Esta pesquisa analisa a constituição das ações sistêmicas de preservação do patrimônio
cultural no Brasil, abordando a busca pela implantação de um sistema de preservação, constituído por órgãos das instâncias federal, estadual e municipal, e usando o processo de preservação em Cáceres como estudo de caso.
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