By J.K. Costain, C. Coruh

The cloth during this quantity presents the fundamental conception essential to comprehend the foundations in the back of imaging the subsurface of the Earth utilizing mirrored image and refraction seismology. For mirrored image seismology, the top product is a "record part" from a suite of "wiggly lines" which are recorded within the box from which information regarding the houses of subsurface constitution and rock will be derived. For the main half, the rules of imaging are a similar whatever the intensity to the objective; an identical mathematical history is critical for concentrating on a shallow water desk as for investigating the bottom of the earth's continental "crust" at a intensity of 30-50 km.

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**Example text**

The conventional approach of introducing orthogonality, which results in integral expressions for the coefficients. Examples are provided to show that either approach gives the same result. r—l) f[2] = o o + 2 o i cos ( 2rr—2 ) + 2a2 cos ( 2TT — 2 I + 2b! sin ( 2TT—2 | + 262 sin ( 2rr—2| V m J V 7 " / V m I V m J /[3] = o 0 + 2aicos ( 2TT—3 ) + 2a2 cos ( 2TT—3 ) + 26i sin ( 27r— 3 ) + 262 sin ( 2it— 3 ) /[4] = a0 + 2o! 14) 56 CHAPTER 3. FOURIER TRANSFORMS This is a system of five equations in the five unknowns a,Q, ai, a-z, b\, and &2Thus, the determination of the unknown Fourier coefficients an and bn, is nothing more than the solution of m simultaneous linear equations in m unknowns.

Some electronic noise is always present, so the dynamic range will generally be 10-20 dB less than the theoretical value. 000002 volts (2 /JV) accurately then the dynamic range of the system is 201og -(ao4o2)= 1 2 0 d b so signals with an amplitude difference of 1 million can be measured accurately at the same time. Of course the geophones or hydrophones must have a true dynamic range at least equal to this for faithful reproduction. SUBROUTINE FT As a nostalgic note, the following Fortran subroutine FT from Enders Robinson's Multichannel Time Series Analysis With Digital Computer Programs [148] properly used (and easily translated for Mathematica) can approximate quite 48 CHAPTER 3.

10), because of the symmetry in the frequency domain, we need to deal only with positive frequencies. By definition, w = dd/dt. The angle 8 is measured from the x—axis. If 0 increases with time away from the a;—axis toward the positive imaginary i—axis, then d8 > 0. Positive values of frequency u simply mean that the phasor rotates counterclockwise. Negative values of frequency mean that the phasor rotates counterclockwise. 10) by the factor of "2" that multiplies each summation. As noted above, if the timedomain signal f(t) is pure real, then the amplitudes of sine waves of negative frequency —n/T are of opposite sign to sine waves of positive frequency +n/T.