By using ( matlab ) please ..

I. The gravity field g(x) over a 2-D horizontal circular cylinder, its Hilbert transform (HT) h(x) and their analytic signal amplitude AA(x) are given by the following equations. 8(x)Az h(x) AA(x) = Vg(x)' t z Ax x2 + z2 + h(x) [h(x) can be computed as the hilbert transform of g(x) using Matlab command hilbert(g(x)] where A aR2 Go, R being the radius of the cylinder, G. the Universal gravitational constant and the density contrast. Z- is the depth to the centre of the cylinder. Compute g(x), hx) and AA(x) at x-100 to 100 at an interval of 5 units assuming z 3 units, R -1, G 1 and p-I. Also, compute only g(x) for various depths namely z-5,7.5 & 10 and plot all the anomalies of g(x) at different depths 3.5.7.5&10 to understand the changes in shape of the plots. Draw neat sketches for g(x), h) and AA0 a). Very the depth to target by half width method. b). Explain how do you locate the cylinder in the subsurface from AA(x) and also calculate the values of z and R based on the mathematical method discussed in the class. Plot g(x), hx) and AA(x) all in one graph, identify the maximum of AA(x) which is the origin. Then note the point of intersection of g(x) and h(x) which is the real root of both these equations.Find its value from the graph and discuss c). Obtain the horizontal derivative of g03) at least for one set of same model parameters. Compare this horizontal derivative with the numerical differentiation of g(x). Further, compute the vertical derivative using the relation. Edx)--HT-_-Edx) (d). Evaluate the depth to the centre of cylinder by the method of Fourier spectral analysis. Hint: Let yy fi( gravity anamaly)&amag-abs(yy) Then, plot frequency vs spectrum ( amag spectrum). Take the slope of the resulting Straight line which yields the depth as discussed in lecture