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Figure 1 – (a) The “complex” trace composed of the original measured trace, d(t), (the real part, in red) and its Hilbert transform, dH(t) , (the imaginary part, in blue) extracted from the survey shown in figures 2 and 3. The envelope and its reverse are plotted in orange. Note how it “envelopes” the real and the imaginary trace (and indeed any phase-rotated version of the trace). (b) The complex trace plotted parametrically against time on a complex plot. Each time sample can also be represented in polar coordinates as a magnitude and phase, with phase being measured counterclockwise from the real axis. (c) The wrapped phase computed as φ=ATAN2[dH(t),d(t)]. The definition of the arctangent gives rise to discontinuities at ±1800. (d) The unwrapped phase, retaining only discontinuities associated with waveform interference (geology and crossing noise).
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Figure 1 – (a) The “complex” trace composed of the original measured trace, d(t), (the real part, in red) and its Hilbert transform, dH(t) , (the imaginary part, in blue) extracted from the survey shown in figures 2 and 3. The envelope and its reverse are plotted in orange. Note how it “envelopes” the real and the imaginary trace (and indeed any phase-rotated version of the trace). (b) The complex trace plotted parametrically against time on a complex plot. Each time sample can also be represented in polar coordinates as a magnitude and phase, with phase being measured counterclockwise from the real axis. (c) The wrapped phase computed as φ=ATAN2[dH(t),d(t)]. The definition of the arctangent gives rise to discontinuities at ±1800. (d) The unwrapped phase, retaining only discontinuities associated with waveform interference (geology and crossing noise).