Build array - Revision history

Mao: /* Visualization of Array Reponse */

2008-10-31T20:25:44Z

Visualization of Array Reponse

2008-10-31T20:24:44Z

Visualization of Array Reponse

2008-10-31T20:23:56Z

Visualization of Array Reponse

2008-10-30T17:16:54Z

Visualization of Array Reponse

2008-10-30T17:16:09Z

Visualization of Array Reponse

2008-10-30T17:12:51Z

Visualization of Array Reponse

2008-10-30T17:12:21Z

Visualization of Array Reponse

2008-10-30T17:10:16Z

Visualization of Array Reponse

2008-10-30T16:46:15Z

Visualization of Array Reponse

2008-10-30T16:34:54Z

New page: == Visualization of Array Reponse ==

New page

== Visualization of Array Reponse ==

@@ Line 9: / Line 9: @@
 \| \frac{1}{N} \sum_{i=1}^{N} \exp(-j\vec{r}_i(\vec{k}-\vec{k}_0)) \|</math>
-Here, <math><\vec{r}_i</math> is the position vector of sensor i in
+Here, <math>\vec{r}_i</math> is the position vector of sensor i in
 a cartesian coordinate system, <math>j</math> the imaginary unit and
 <math>\vec{k}_0</math> the ''true'' wavenumber vector of a single
@@ Line 25: / Line 25: @@
 size of the grid should allow to determine the position of
 grating lobes or strong secondary side lobes in the 2D surface.

@@ Line 9: / Line 9: @@
 \| \frac{1}{N} \sum_{i=1}^{N} \exp(-j\vec{r}_i(\vec{k}-\vec{k}_0)) \|</math>
-Here, <math><\vec{r}_i/math> is the position vector of sensor i in
+Here, <math><\vec{r}_i</math> is the position vector of sensor i in
 a cartesian coordinate system, <math>j</math> the imaginary unit and
 <math>\vec{k}_0</math> the ''true'' wavenumber vector of a single
@@ Line 15: / Line 15: @@
 As most seismological array applications are restricted to the
 deployment of sensors on the earth's surface, the above equation
-is evaluated in the horizontal plane, i.e. <math><\vec{r}_i = (r_{ix}, r_{iy})</math>
+is evaluated in the horizontal plane, i.e. <math>\vec{r}_i = (r_{ix}, r_{iy})</math>
 and <math>\vec{k} = (k_x, k_y)</math> (horizontal wavenumber vector).

@@ Line 1: / Line 1: @@
 == Visualization of Array Reponse ==
-build_array ia a graphical interface for simple visualization
+'''build_array''' ia a graphical interface for simple visualization
 of the array response function for a specific array geometry.
 The array reponse function is computed on a regular cartesian grid
-in the wavenumber domain <math>(k_x, k_y)</math> by computing:
+in the wavenumber domain <math>\vec{k}</math> by evaluating:
 <math>AR(\vec{k}-\vec{k}_0) =
 \| \frac{1}{N} \sum_{i=1}^{N} \exp(-j\vec{r}_i(\vec{k}-\vec{k}_0)) \|</math>
-though the computation of the array reponse function is simple in principle,
+Here, <math><\vec{r}_i/math> is the position vector of sensor i in
-there exists the particular problem of being computationally efficient
+a cartesian coordinate system, <math>j</math> the imaginary unit and
-on one hand, i.e. small number of grid points, and not to miss small details
+<math>\vec{k}_0</math> the ''true'' wavenumber vector of a single
-of the peaked surface on the other hand, i.e. sufficiently high wavenumber resolution
+plane wave.
-<math>(\delta k_x, \delta k_y)</math>.
+As most seismological array applications are restricted to the

@@ Line 6: / Line 6: @@
 in the wavenumber domain <math>(k_x, k_y)</math> by computing:
-<math>AR(\vec{k}-\vec{k}_0) = \sum_{i=1}^{N} \exp(-j\vec{r}_i(\vec{k}-\vec{k}_0))</math>
+<math>AR(\vec{k}-\vec{k}_0) =
 though the computation of the array reponse function is simple in principle,

@@ Line 6: / Line 6: @@
 in the wavenumber domain <math>(k_x, k_y)</math> by computing:
-<math>AR(k_x,k_y) = \sum_{i=1}^{N} \exp(-i(k_x r_{ix}+k_y r_{iy}))</math>
+<math>AR(\vec{k}-\vec{k}_0) = \sum_{i=1}^{N} \exp(-j\vec{r}_i(\vec{k}-\vec{k}_0))</math>
 though the computation of the array reponse function is simple in principle,

← Older revision		Revision as of 16:46, 30 October 2008
Line 1:		Line 1:
		+	== Visualization of Array Reponse ==

−	~~== Visualization~~ of ~~Array Reponse ==~~	+	build_array ia a graphical interface for simple visualization
		+	of the array response function for a specific array geometry.
		+	The array reponse function is computed on a regular cartesian grid
		+	in the wavenumber domain (k_x, k_y) by computing:
		+	<math>Insert formula here</math>
		+
		+	though the computation of the array reponse function is simple in principle,
		+	there exists the particular problem of being computationally efficient
		+	on one hand, i.e. small number of grid points, and not to miss small details
		+	of the peaked surface on the other hand, i.e. sufficiently high wavenumber resolution
		+	<math>(\delta k_x, \delta k_y)</math>.