Destructive and constructive interference for a wedge

**Problems in Exploration Seismology and their Solutions**
Series	Geophysical References Series
Title	Problems in Exploration Seismology and their Solutions
Author	Lloyd P. Geldart and Robert E. Sheriff
Chapter	6
Pages	181 - 220
DOI	http://dx.doi.org/10.1190/1.9781560801733
ISBN	ISBN 9781560801153
Store	SEG Online Store

Problem 6.17

Figures 6.17a show three reflections, where the second and third reflections are from the top and bottom of wedges that converge to the right. Explain why waves in Figure 6.17a(i) interfere destructively and in Figure 6.17a(ii) constructively when the wedge thickness is ${\frac {1}{4}}\lambda$ .

Solution

In Figure 6.17a(i) both reflections from the wedge have the same polarity. As the reflectors converge, at a thickness of ${\frac {1}{4}}\lambda$ (2-way distance ${\frac {1}{4}}\lambda$ ) one half-cycle of the wavelet reflected from the base interferes destructively with the next half-cycle from the top. In Figure 6.17a(ii), where a phase reversal occurs on reflection at one surface but not at the other surface, the reflections from the top and base of the wedge interfere constructively at ${\frac {1}{4}}\lambda$ thickness (before they undergo destructive interference as they converge further). Note that timing the peaks or troughs does not give the correct traveltimes to the respective interfaces where the thickness is $<{\frac {1}{4}}\lambda$ (about 8 ms in Figure 6.17a).

Figure 6.17a. Reflections where the second and third reflectors converge; zero-phase wavelet.

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