Here is a picture of my river birch. Here is a link that might be useful:

yyou have a tree that is going to be significantly retarded in food production.. ergo vigor is going to be limited to the 1/4 inch strip .... it might take a decade to return to vigor .... you MIGHT be better off... cutting the whole thing off ... just below the danmage ... and letting it resprout some vigorous new shoots.. and then pick the best one or two and let them grow like rockets.. since there is no damage to the root zone ... wouldnt be surprised if you dont get one to go 6 to 8 feet by fall ... as compared to the one struggling for the next 5 years.. barely alive.. mending the trunk .... give it a go .. something new to watch and learn about ... its an experiment either way .... which do you prefer to learn about .... i will bet a buck [no pun intended] that you will have more trunk damage to watch heal ... so i vote for truncating [god.. another pun] the damaged trunk .. and watching it grow like a weed .... ken

I love that first one. How lucky for you to live by a lake.

I kinda like how the graining in the center panel flows like the granite (bottom pic). Yes... I love the stone as I"m a fan of "flowy" granites.