Virtual reflector representation theorem (acoustic medium)

Virtual reflector representation theorem (acoustic medium).

The virtual reflector method simulates new seismic signals by processing traces recorded by a plurality of sources and receivers. The approach is based on the crossconvolution of the recorded signals and makes it possible to obtain the Green's function of virtual reflected signals as if in the position of the receivers (or sources) there were a reflector, even if said reflector is not present. ...

Improving limited-view photoacoustic tomography with an acoustic reflector.

The versatility and real-time imaging capability of commercial linear array transducers make them widely used in clinical ultrasound and photoacoustic imaging. However, they often suffer from limited detection view. For instance, acoustic waves traveling at a grazing angle to the transducer surface are difficult to detect. In this letter, we propose a simple and easy approach to ameliorate this...

Experimental verification of the acoustic computer model using triangle reflector

Objective of this study was experimental verification of the acoustic computer model, which enables calculation of the signals reflected by triangles arbitrally oriented in space. Verification of the computer model was carried out comparing the C-scan images of triangle reflectors, obtained experimentally and by simulation in the case when ultrasonic beam is reflected by triangle reflectors, re...

Representation Theorem for Stacks

In this paper i is a natural number and x is a set. Let A be a set and let s1, s2 be finite sequences of elements of A. Then s1s2 is an element of A∗. Let A be a set, let i be a natural number, and let s be a finite sequence of elements of A. Then s i is an element of A∗. The following two propositions are true: (1) ∅ i = ∅. (2) Let D be a non empty set and s be a finite sequence of elements of...

The Riesz representation theorem