By J.K. Costain, C. Coruh
The fabric during this quantity offers the elemental thought essential to comprehend the foundations at the back of imaging the subsurface of the Earth utilizing mirrored image and refraction seismology. For mirrored image seismology, the tip product is a "record part" from a suite of "wiggly strains" which are recorded within the box from which information regarding the houses of subsurface constitution and rock should be derived. For the main half, the rules of imaging are a similar whatever the intensity to the objective; an analogous mathematical historical past 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.
Read or Download Basic Theory in Reflection Seismology, Volume 1: (Handbook of Geophysical Exploration: Seismic Exploration) PDF
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Extra resources for Basic Theory in Reflection Seismology, Volume 1: (Handbook of Geophysical Exploration: Seismic Exploration)
Example text
Frequency is discrete, time is continuous. More commonly referred to as a Discrete Fourier Series (DFS) or simply a Fourier Series. 3. Discrete-Time Fourier Transform (DTFT). Time is discrete, frequency is continuous. 4. Discrete Fourier Transform (DFT). Both time and frequency are discrete. The introduction of the "fast Fourier transform" (FFT) version of the CHAPTER 3. 1: Notation for the Fourier transform (FT) Analysis Synthesis /•+OO F{y) = I f(t)e~i2*vtdt f(t) = / J — oo FHe+i2"'^ J — oo /(£) is continuous, aperiodic, and can be complex oo < t < oo F(i^) is complex, continuous, and aperiodic OO < V < OO oo < t < oo OO < V < 00 DFT has revolutionized geophysics and other fields that deal with large data sets.
1. The target to be imaged is a reflection from crystalline basement, which arrives at the receivers most distant from the energy source at a two-way traveltime of about 220 ms. The continuity of the reflection is interrupted by Rayleigh surface wave noise, and the reflection cannot be traced across the seismogram. The noise is lower in frequency content. If we can determine which frequencies are associated with the surface waves and which are associated with the reflection signal, then we might be able to attenuate the amplitudes of those frequencies that are associated with the surface wave noise.
2 Determination of the Fourier coefficients The coefficients an and bn are called Fourier, or Euler coefficients. volume we determine the coefficients by using two general methods: In this 1. Determine the coefficients by solving a set of simultaneous linear equations, and 2. 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!