On the determination of source–receiver distances using a new equidistant latitude

Summary. In teleseismic and crustal seismic studies, source–receiver distances are commonly expressed in degrees rather than kilometres. The earlier use of geographic latitudes in determining a meridional distance led to variations in the number of kilometres per degree of up to 1.0 per cent (1.1 km deg ‐1 ) and discrepancies up to 64.2 km in epicentral distance at Δ= 90°. The present standard practice of using geocentric latitudes reduces this maximum variation by a factor of 3 to 0.34 per cent (0.37 km deg ‐1 ) and maximum discrepancies to 21.4 km at Δ= 90°. A third, arbitrarily defined latitude is here proposed which reduces this maximum variation by a further factor of 800 to 0.00042 per cent (0.00047 km deg ‐1 ) and reduces the maximum discrepancy by a further factor of 1600 to 0.0135 km (or 13.5 m) at Δ= 45° (zero at Δ= 90°). This equidistant latitude will be useful in certain geophysical applications where a consistent proportionality between angular distances, Δ, and arc lengths, u , is of prime importance. This could be the case at a high‐latitude station observing many events, or for a single high‐latitude event observed at many stations; in whichever case all source–receiver paths are close to meridional. An additional correction is presented which removes distance discrepancies between meridional and nonmeridional (in the worst case, equatorial) paths; this latter correction being equivalent to the conventional path‐length correction for Earth‐encircling urface waves (namely in the single‐station method). Some areas of application, where the improved accuracy attainable by using equidistant latitudes might be significant, are suggested. In the determination of surface‐wave velocities by the two‐station method, the use of geocentric latitudes introduces relative errors of ∼ 10 ‐3 , Such errors could be significant with high‐accuracy data; and for very long‐period surface waves (τ? 200s) errors of this same order of magnitude are removed by the period dependent apparent‐path‐length correction. Combining this correction with equidistant latitudes would reduce relative errors to ∼ 10 ‐5 or 10 ‐6 . In determining epicentral distances for local earthquakes (say Δ < 5°) the use of geocentric latitudes leads to a maximum discrepancy of 0.16 km within a single locality around 45° latitude, although the discrepancies among all geocentric 5° paths on the Earth can reach 1.9 km. By Richter's rectangular coordinate method, maximum discrepancies are of the same order as the geocentric ones within a single locality; moreover they remain at this level for any two such paths (Δ < 5°) on the Earth. With equidistant latitude, however, the maximum discrepancies are 4 × 10 ‐4 km for a single locality around 22½° or 67½° latitude and 2 × 10 ‐3 km for the whole Earth.