Basic Theory in Reflection Seismology, Volume 1: (Handbook by J.K. Costain, C. Coruh

By J.K. Costain, C. Coruh

The fabric during this quantity presents the elemental thought essential to comprehend the rules at 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 set of "wiggly lines" which are recorded within the box from which information regarding the homes of subsurface constitution and rock will be derived. For the main half, the rules of imaging are an analogous whatever the intensity to the objective; a similar mathematical history is critical for focusing 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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Additional resources for Basic Theory in Reflection Seismology, Volume 1: (Handbook of Geophysical Exploration: Seismic Exploration)

Example text

No matter what the signal processing application, however, Fourier transforms play an important role. We view seismograms in the time domain, and examine Fourier coefficients in the frequency domain. The mathematics of Fourier transformation is used to get from one domain to the other and back. Thus, data in time domain J Fourier transformation "1 \ -4=^ / data in frequency domain Wherever the symbol <*=> appears in this volume it means the data on each side are a Fourier transform pair. 1: Rayleigh waves obscure the reflections from crystalline basement on a typical "wiggly trace" display of a seismogram.

Analysis i N—l Synthesis N-1 F[k]e+i2w^n F[k] = — J2 f[n]e~i2 f[n = Yl ^ n=0 f[n] is discrete, periodic, and can be complex. fc=0 F[k] is discrete, periodic, and can be complex. 2. SIGNAL NOMENCLATURE 47 cause it is easier to read. In addition, although seismic data are digital data, continuous integrals are often substituted for discrete summations because they are easier to write. Furthermore, digital signals are commonly derived from continuous ones. In addition, a "Fourier transform" really applies only to continuous signals in both the time and frequency domains but we will relax this definition and use it interchangeably with the term "discrete Fourier transform" (DFT), one of the work horses of geophysical data processing.

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. FOURIER TRANSFORMS well all of the above Fourier transformations for either complex or real transforms, including other members of the Fourier family such as Hilbert transforms.

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