Difference between revisions of "Traveltime curves for various events"

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  | isbn    = ISBN 9781560801153
 
  | isbn    = ISBN 9781560801153
 
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== Problem ==
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== Problem 6.14 ==
 
Draw arrival-time curves for the five events in Figure 6.14a.
 
Draw arrival-time curves for the five events in Figure 6.14a.
  
[[file:Ch06_fig6-14a.png|thumb|{{figure number|6.14a.}} Events involving a mesa.]]
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[[file:Ch06_fig6-14a.png|thumb|center|{{figure number|6.14a.}} Events involving a mesa.]]
  
[[file:Ch06_fig6-14b.png|thumb|{{figure number|6.14b.}} Arrival times of events. (i) Geometry; (ii) traveltimes.]]
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[[file:Ch06_fig6-14b.png|thumb|center|{{figure number|6.14b.}} Arrival times of events. (i) Geometry; (ii) traveltimes.]]
  
 
=== Solution ===
 
=== Solution ===

Latest revision as of 15:24, 8 November 2019

Problem 6.14

Draw arrival-time curves for the five events in Figure 6.14a.

Figure 6.14a.  Events involving a mesa.
Figure 6.14b.  Arrival times of events. (i) Geometry; (ii) traveltimes.

Solution

We have for the depth to the mesa, 1900 m; height of mesa, 900 m. The traveltime curves were obtained graphically. We let Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle R} stand for receiver locations.

For the reflected diffraction from Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle S_{1}} (diffracted at A), the virtual source (see problem 4.1) for the event is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle I_{1}} in Figure 6.14b(i) (note that traveltime increases upward), so that

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} t=(S_{1} A+I_{1} R)/V_{1} =(2.20+I_{1} R)/2.00. \end{align} }

For the reflection from Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle S_{2}} , we use the virtual source Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle I_{2}} . We will also have a diffraction from the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle S_{2}} source (paths not shown).

For the reflected refraction from Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle S_{3}} (reflected at C), we find two traveltimes and then draw a straight line through them.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} \hbox {At}\ S_3, t=2(2.20/2.00+2.20/3.64)=2.80 \hbox {s}.\\ \hbox {At}\ S_{4}, t=2(2.20/2.00)+1.10/3.64=2.50 \hbox {s}. \end{align} }

For the diffraction at Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle C} from Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle S_{4}} ,

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} t=(S_{4} C+CR)/2.00=(2.20+CR)/2.00. \end{align} }

For the diffracted reflection from Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle S_{5}} (diffracted at C), we use the image point of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle S_{5}} (not shown) so that

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} t=(I_{5} C+CR)/2.00, \end{align} }

which gives the same curve as for the diffraction from Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle S_{4}} except that it is displaced towards increased time by the difference in traveltimes for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle S_{4}C} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle I_{5}C} .

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