A 理解 and 了解 comparison
Chinese verbs are usually made up according to this formula:
modificator + modificated or modificator + a verb to modify. 
So when I seen that 理解 and 了解 ending with the same charecter (解), this usually means that there is a slight modification of a verb 解(to divide) is in play. 

So let's find the roots of the word:


  理　(11)　リ　 As per 里# (long strip) + 玉 jewel → veins or streaks in a
  piece of jade → logic; reason (← lines/threads of a reasoning
  process ← vein; streak) → principle; natural science.


So here we already see the connotation which 理 brings: lines/patterns of reasoning. Now add this to 解 and you have "to understand解(split/crack) by reasoning理".

Now about 了 which is 瞭 simplified:


  瞭　(17)　リョウ　 As per 尞# as described in 僚 (circular continuum) + 目 eye →
  observe from a high place, enjoying a clear panoramic view → *clear-sighted; clarity.


Now you add everything up and you have: "to understand 解 clearly or by observation (not by reasoning理)"