If there ist a difference in apparent density between sedimentparticles (which kind of sediment?) and ash-particels (which kind of ashes) then you can try to separate them similar as heavy minerals with an adjusted liquid.....?!?!?

best regards

Andreas

Thank you pleas explore more your recommended method more. Or introduce some paper, Thank you very much.

Dear Zeinab,

maybe the following links will help. In my opinion the ashes are lightweight aggregates and therefore you should use a heavy liquid like 1,2-Dibromethan with a density of 2,056g/cm3  - most minerals like quartz, calcite, feldspars, etc. have a higher density und you can separate them from the lightweight fraction by flotation. 

Search the internet  with the keywords: "heavy liquids for mineral separation"

An other technology of course is the centrifugal separation......

best regards Andreas

http://archives.datapages.com/data/sepm/journals/v01-32/data/003/003001/0030.htm

https://dl.sciencesocieties.org/publications/sssaj/abstracts/51/5/SS0510051390

http://en.wikipedia.org/wiki/Heavy_liquid

http://epsc.wustl.edu/geochronology/wirfley.htm

By the water

DEar Mayyas

Please detailed its more? I want to weight the sediment only. with out ash materials.

Thank you

Dear Zeinab:

you must first sift your sediment, to separate particles by Phi degrees . Ashes , are retained in the generally Phi = 4 ( coarse silt ) . Then you separate by density with dense liquids , as explained colleagues.

If you do, you'll have more details on that fraction and on the other ... and have a lot more data on your sign!