# forensicSeismology.frink

```// Solution to the "Forensic Seismology" geocache: // // http://www.geocaching.com/seek/cache_details.aspx?guid=68083e90-f516-46de-a2c9-55709818a7ed // Import the sun.frink file which contains great circle calculations // and definitions for many of the functions below. use navigation.frink // Coordinates of seismic stations lata = DMS[39,30.840] North longa = DMS[104,44.109] West latb = DMS[39, 31.710] North longb = DMS[104, 47.901] West latc = DMS[39, 27.302] North longc = DMS[104, 46.119] West // Find the distances between seismic stations [dab, bab] = earthDistanceAndBearing[lata, longa, latb, longb] [dbc, bbc] = earthDistanceAndBearing[latb, longb, latc, longc] dca = earthDistance[latc, longc, lata, longa] println["dab: \$dab"] println["dbc: \$dbc"] println["dca: \$dca"] // Find bearings between seismic stations. println["Bearing from a to b: " + (bab->DM)] bac = earthBearing[lata, longa, latc, longc] println["Bearing from a to c: " + (bac->DM)] println["Bearing from b to c: " + (bbc->DM)] // Times of arrival ta1 = .1673 s tb1 = .2890 s tc1 = .5507 s ta2 = .4240 s tb2 = .6065 s tc2 = .9990 s // Velocities of waves v1 = 6.0 km/s v2 = 4.0 km/s // This function was one I derived for finding the distance between // the meteorite and the seismic station, given times of arrival for // the P-waves and S-waves and their velocities. d[t1, t2, v1=v1, v2=v2] := -((t1-t2) v1 v2)/(v1-v2) // Find distances to seismic stations from the meteorite. // I call the meteorite "point D"  dad = d[ta1, ta2] dbd = d[tb1, tb2] dcd = d[tc1, tc2] println["dad: \$dad"] println["dbd: \$dbd"] println["dcd: \$dcd"] // Cosine rule for triangles... find the angle DAB between the meteor, // point A and point B. adab = arccos[(dad^2 + dab^2 - dbd^2)/(2 dad dab)] println["Angle DAB: " + (adab -> DM)] // You can either add or subtract this angle to the angle bab (the bearing // from point a to point b.)  I tried both ways, and only subtracting gave a // self-consistent solution when all points were considered. bad = bab - adab println["Bearing from A to D: " + (bad -> DM)] // Use calculation to find the resultant lat/long of the meteorite given // the initial point (that of seismic station a), the distance, and the // bearing of the meteorite. [latd, longd] = resultantLatLong[lata, longa, dad, bad] println["D is at lat:  " + (latd->DM)] println["D is at long: " + (longd->DM)] // Reverse calculations.  These distances and bearings should match the // ones calculated above. println["\nVerifying:"] [dad, bad] = earthDistanceAndBearing[lata, longa, latd, longd] println["Bearing from A to D: " + (bad -> DM)] println["Distance from A to D: " + dad] [dbd, bbd] = earthDistanceAndBearing[latb, longb, latd, longd] println["Bearing from B to D: " + (bbd -> DM)] println["Distance from B to D: " + dbd] [dcd, bcd] = earthDistanceAndBearing[latc, longc, latd, longd] println["Bearing from C to D: " + (bcd -> DM)] println["Distance from C to D: " + dcd] // Karen's solutions (assuming UTM zone 13, easting 519926, northing 4372660) latk = DMS[39,30.199999] North longk = DMS[104,46.093333] West [diffDist, diffBearing] = earthDistanceAndBearing[latd, longd, latk, longk] println["Difference in solutions is " + (diffDist->"ft")] println["Bearing from Alan's solutions to Karen's: " + (diffBearing->DM)] ```

This is a program written in the programming language Frink.
For more information, view the Frink Documentation or see More Sample Frink Programs.

Alan Eliasen was born 18350 days, 1 hours, 34 minutes ago.