227 7. Seismic inversion and characterization applied to geothermal energy source, which, after its path, can be deformed (phase, energy) and some frequencies can be absorbed. Limited by its bandwidth, the result of the convolution acts as a frequency filter. If the reflection coefficients are defined more precisely, the convolution models the interferences; thus, in this case, there are series of reflection coefficients for which the synthetic has the same response (Figure 7.4). This is called a resolution problem. Figure 7.4 Convolution and model of the interferences. In the industry, several considerations are commonly accepted: • Resolution: A contrast is “resolved” when it represents a change of half a period of the signal. The signal has the “time” to reach the expected amplitude value. • Detection: A contrast is “detected” when it represents a change of one-eighth of a period of the signal. The signal retains the dynamics without reaching the expected amplitude value. The response is sufficient to interpret a contrast, however, it is insufficient to deduce a quantitative property. T s f T s f Z m v f Z resolution ection resolution e ( ) = ( ) = ( ) = 1 2 1 8 4 det det ction m v f ( ) = 16 where f represents the dominant or maximum frequency of the signal contained in the wavelet (in Hz), and v the instantaneous velocity of the medium traversed (in m/s). The convolution theory is, and the definition of the wavelet, is the main reason why seismic inversion must be performed in two-way time domain.
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