How to calculate zonal statistics of buffer zone with minimum distortion

I want to create 50km buffers around a large set of polylines that have a global extent. My objective is to calculate average raster values within each buffer zone.

The matter of confusion: I want to use an equidistant projection to minimize the buffer distortion introduced by the global extent of my data, but ultimately I wish to use an equal area projection to calculate zonal statistics of the buffer zones.

How do I reconcile these two types of distortion? I cannot find a related question that explicitly addresses distortion when calculating zonal statistics of buffer zones.

• It's a tough problem. Note, though, that an equidistant projection will likely create severe buffer distortions. Unless your polylines all emanate from a common point and move directly away from it, it would be unwise to select any equidistant projection for this work--and even then you would have to use variable-width buffers to compensate for the distortion. – whuber Sep 16 '15 at 17:31
• Thank you for clarifying that an equidistant projection would itself create severe buffer distortions. Unfortunately my polylines do no emanate from a common point. I'm curious how you might proceed then given the situation? My 50km buffer is (somewhat) flexible, so perhaps I could reduce the distance of the buffer and simply use an equal area projection? – acd Sep 16 '15 at 17:52
• I wish it were that simple! Unfortunately, metric distortions are always relative, so if (say) a 50 km buffer were distorted by 25%, a 5m buffer would also be distorted by 25% (at least approximately). No projection will be suitable for the entire globe. There are at least three solution strategies in such cases. (1) Use a patchwork of projections across the globe, doing the calculation for each buffer using the best projection for its location; (2) compute buffers using spherical (or ellipsoidal) geometry; or (3) compute them using 3D Cartesian (earth-centered) coordinates. – whuber Sep 16 '15 at 20:31