Through reading, I found lots of equations to calculate the anomaly of Ce, Eu and others. Different researcher uses different equations to evaluate the REE anomaly of the same sample media
I encountered the same problem just recently concerning the Eu-anomaly. I think, the one provided by Shields and Stille (2001) is missing a "divided by" and should instead be: Eu-anom = EuN / (SmN + GdN)0.5. A calculation I find more appropriate, given the square root in that equation is: Eu-anom.= EuN / (SmN * GdN)0.5.
Lawrence and Kamber (2006) suggested to use this equation: Eu-anom = EuN / (SmN2 * TbN)1/3.
However, which one is best to use really depends on the nature of your sediments and their REE patterns. If either Sm, Gd or Tb seem enriched/depleted in respect to the overall pattern apply the equation that is not using the respective element. I.e. in a sediment that exhibits a "hat-shaped"-pattern, where Tb is relatively debleted in respect to Gd and Dy.
Also, you usually only use the anomaly for comparison within your own set of data, so you could also think of an equation that you feel is reasonable. Just make sure you use it consistently and if you compare it to other (peoples) data that you re-calculate the anomalies using your or the same equation.
Quick remark regarding the Ce-anomaly, be sure La is not enriched when you use the above mentioned calculations. I think Shields and Stille (2001) also refer to this.
Hope my answer is not too late and might still be helpful.
From my concerned, in tropical or mostly in Australasia-Pacific regional in marginal area the best normalization Ce and Eu for sediment is PAAS and biota is using to Chondrite. However my idea when deal with river compartments the best equation for Ce anomaly conducted through formula by Stein Jacobson from Harvard University and for Eu anomaly try searching formula that had been used by de Baar in his Phd thesis on Marine Geochemistry of REE (1983). And again i hardly inclined to you to introduced the first normalized REE standard specially in biota seen to hitherto no body concern on biota or the best could i say it has been over look by among REE scientists.
I would do 2 things, first a spider plot of REE normalised to NASC or PAAS (a shale standard) to see how enriched they are in relation to a "normal' shale. Secondly, in order to further quantify the anomaly i would calculate Ce*norm by comparing the Ce with the elements (La and Nd) Ce anom.=Ce/Ce*=3CeN/(2LaN+NdN) (N= normalised data.)
Good control as to your mineralogy should be of further help as many Ce enrichments may be related to detritus or phosphate, checking for other REE enrichments may help to identify this. See Shields & Stille (2001) and MacLeod and Irving (1996) for more.
I encountered the same problem just recently concerning the Eu-anomaly. I think, the one provided by Shields and Stille (2001) is missing a "divided by" and should instead be: Eu-anom = EuN / (SmN + GdN)0.5. A calculation I find more appropriate, given the square root in that equation is: Eu-anom.= EuN / (SmN * GdN)0.5.
Lawrence and Kamber (2006) suggested to use this equation: Eu-anom = EuN / (SmN2 * TbN)1/3.
However, which one is best to use really depends on the nature of your sediments and their REE patterns. If either Sm, Gd or Tb seem enriched/depleted in respect to the overall pattern apply the equation that is not using the respective element. I.e. in a sediment that exhibits a "hat-shaped"-pattern, where Tb is relatively debleted in respect to Gd and Dy.
Also, you usually only use the anomaly for comparison within your own set of data, so you could also think of an equation that you feel is reasonable. Just make sure you use it consistently and if you compare it to other (peoples) data that you re-calculate the anomalies using your or the same equation.
Quick remark regarding the Ce-anomaly, be sure La is not enriched when you use the above mentioned calculations. I think Shields and Stille (2001) also refer to this.
Hope my answer is not too late and might still be helpful.
Different formula will give different answers and different opinions. Use any formula and reference it. I use that of Taylor and Mclennan,1985. Very simple; Eu/Eu*= 2x Eu*/ (Sm +Gd)N.
However, recent formula may be used.eg that by Lawrence and Kamber (2006).
The most classic method to quantify Ce anomaly is Ce/Ce*, where
Ce* = (La(n) *Pr(n))^0.5 (the subscript indicates chondrite normalization). However, La and Pr are very low in abundance and frequently below the limit of detection. Therefore, this method often incurs criticism where used, since it is susceptible to contamination by small LREE-enriched melt/ mineral inclusions that are common in zircon (Bindeman et al. 2014). Loader et al. (2017) modified the traditional method and proposed an alternative formulation for Ce* :
Ce*= Nd (n)^2/Sm (n)
Loader MA, Wilkinson JJ, Armstrong RN (2017) The effect of titanite crystallisation on Eu and Ce anomalies in zircon and its implications for the assessment of porphyry cu deposit fertility. Earth Planet Sci Lett 472:107–119