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Using ArcGIS 10.4.1 I have aircraft flight line data in vector format, with attributes for altitude, speed and rate of climb. From those attributes, I have estimated a relative loudness for each arc segment, stored in a new attribute field.

Now I need to estimate that loudness on the ground. I do not need to calculate an exact decibel level; rather a simple, relative intensity will suffice. I will assume that the sound decays over distance following the inverse square law, independent of frequency. I envision using raster analysis, where the output cell values derive from the arc segment loudness, decreasing in distance from the flight lines.

While there are various surface interpolation tools available (IDW, Kriging, etc), they all rely on a point input, whereas my input data is linear. Is there an analysis approach that considers a linear source?

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"Topo To Raster" interpolation allows you to use points or lines as it is designed to be used for landscapes (i.e. spotheights and contour lines). It's in the same Interpolation toolbox.

Otherwise, if that method doesn't perform the right kind of interpolation for you, you could convert your lines to points to use the other methods.

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