Sensitivity integral

We determine the integrated sensitivity of the data to the parameter as the ratio... 

One can see that the integrated sensitivity depends on the parameter k. In other words, the sensitivity of the data to the different parameters varies, because the contributions of the different parameters to the observation are also variable. 

Definition 17 The diagonal matrix with the diagonal elements equal to Sk = Pd /6mk is called an integrated sensitivity matrix ... 

In other words, it is formed by the norms of the columns of the matrix A. The basic idea of introducing a weighting matrix, W , for the model parameters is as follows. We identify this matrix as the diagonal integrated sensitivity matrix... 

Note, however, that in the case of the approximate solution, the weighting matrix for the model parameters should be selected as the square root of the integrated sensitivity matrix ... 

Formula ( i.94) sliows that the new matrix of the integrated sensitivity S is a unit matrix ... 

The integrated sensitivity, in accordance with the definition (3.75), is calculated bv the formula... 

Formula (7.20) should be treated as the integrated sensitivity of the gravity data to the local density anomaly located at the depth z in the lower half-plane (z < 0). We can see that the sensitivity is inversely proportional to the square root of the depth of the density anomaly. 

The integrated sensitivity, S (r"), of the data, collected over some observation line b over a frequency interval fl, in accordance with the definition (3.75), is equal to... 

Therefore, the integrated sensitivity of the electric field to the local perturbation of the conductivity in point r" is equal to... 

In a similar way, we can find the differential and integrated sensitivities for magnetic field ... 

The weighting operators We and Wn for electric and magnetic forward operators are linear operators of the multiplication of conductivity Act by the functions We (r) and Wu (r) equal to the square root of the integrated sensitivity (see formula (3.78) in Chapter 3) ... 

Formula (10.30) should be treated as the integrated sensitivity of the anomalous electric field to the local conductivity anomaly located at a point with the radius vector r. Similarly, we can find the integrated sensitivity of the anomalous magnetic field to the local conductivity anomaly, using formula (9.60) ... 

In accordance with definition (3.75), the integrated sensitivities for an electromagnetic field, are calculated by formulae (9.34) and (9.36). 

Similarly, we can find the integrated sensitivity of the scattered vector wave-field to the local slowness anomaly, using formula (14.88) ... 

Detection wavelength (VIS, UV, or fluorimetric detection) Reference wavelength Detection wavelength bandwidth Reference wavelength bandwidth Integration sensitivity Peak detection ... 

FIGURE 4. Limiting continuum sensitivity for HXT. Detection threshold is 5a in lOS. XMM and INTEGRAL sensitivities are also shown... 

The added mass should be evenly distributed over the electrode. The integral sensitivity determined can only be used for the calculation if this is the case because the maximum sensitivity at the center of the crystal decreases to zero at the edges of the electrode. The differential sensitivity (c/ = 5ff5m) is proportional to the sqitare of the vibration amplitude, and the amphtude distribution can be described by Gaussian-type or Bessel-type functions. The integral mass sensitivity can be computed from the differential sensitivity function ... 

Expressions for nonuniform mass distributions have been derived for different cases and can be found in [152]. It should also be mentioned that if the surface film is uneven but the distribution of the mass is uniformly nonuniform, i.e., the thinner and thicker regions of the film are distributed more or less regularly, the application of the integral sensitivity does not usually cause substantial error. 

Figure 4. Integrated sensitivity field depending on bladder volume and electrode position. 

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