Why do carbonates, oxides, and pure metals precipitate before metal sulfides?
Why Do Carbonates, Oxides, and Pure Metals Precipitate Before Metal Sulfides?


They don't. I cannot get to the particular paper you read, but I can provide both a logical and a quantitative argument that the metal sulfides precipitate first. The thermodynamics of this situation do not involve reduction potentials so much as simple solubilities. Metal sulfides are much less soluble in water than metal carbonates. 

From your description, I imagine a system like the following image. There are two strata of sedimentation: an upper layer of metal oxides and a lower layer of metal sulfides. 



There are three reasonable explanations why the sulfides are on the bottom.


The sulfides did not precipitate from the water; they were always there. The carbonates and oxides deposited on top of them.
The carbonates and oxides were deposited first, and the sulfides were deposited second, settling through the carbonates and oxides to form a deeper layer.
The sulfides were deposited first, and the carbonates and oxides were deposited second.


Explanation 1 is very reasonable, but counterproductive. We will ignore it.

Explanation 2 is the one supposed by the OP in the question, and perhaps it was also provided in the paper. Let us examine this idea a little. In order for this to happen, the metal sulfides would have to be denser than the metal carbonates and oxides to settle through. All it takes the counterexample of iron to see that this is not always the case. Iron (II) sulfide is denser than iron (II) carbonate but less dense than iron (II) oxide. 
 - Iron (II) oxide, $\ce{FeO}$, 5.745 g/mL
 - Iron (II) carbonate, $\ce{FeCO3}$, 3.961 g/mL
 - Iron (II) sulfide, $\ce{FeS}$, 4.84 g/mL

Additionally, if the sulfides were settling through, the layers would not be so well stratified - the boundary between them would be indistinct.




  Metal sulfides are much less soluble in water than metal carbonates. 


That leaves with Explanation 3, which is the correct one. Metal sulfides are almost universally less soluble that metal carbonates. We'll get to where the oxides come from later. Both metal carbonates and metal sulfides are nearly insoluble in water, so the minute amounts present are hard to quantify in the "grams of solute per liter of solution" kind of way. The saturated solution may only have few parts per billion of the compound. Instead, we talk in terms of the solubility equilibrium, in particular, the solubility product (constant), $k_{sp}$, the equilibrium constant associated with the combination dissolution and dissociation.

We can determine the concentration from the $k_{sp}$. Consider barium carbonate $k_{sp}=5.1\times10^{-9} \text{ M}^3$. The solubility equilibrium is:

$$\ce{BaCO3(s) &lt;=&gt;Ba^{2+}(aq) + CO3^{2-}(aq)}$$

And the equilibrium constant is (the concentration of solid barium hydroxide is constant and is thus part of $k_{sp}=k_{obs}$.
$$k_{sp} = [\ce{Ba^{2+}}][\ce{CO3^{2-}}]=5.1 \times 10^{-9} \text{ M}^3$$

Since $[\ce{CO3^{2-}}]=[\ce{Ba^{2+}}]$ (mass balance):
$$[\ce{Ba^{2+}}][\ce{CO3^{2-}}]=[\ce{Ba^{2+}}]^2$$
$$[\ce{Ba^{2+}}]^2=5.1\times 10^{-9} \text{ M}^3$$
$$[\ce{Ba^{2+}}]= 7.14\times 10^{-5} \text{ M}=&gt;0.0141 \text{ grams per liter}$$

Now, let's look at carbonates and sulfides. All $k_{sp}$ came from here.

Cadmium:


Carbonate $\ce{CdCO3}$, $k_{sp}=5.2\times 10^{-12} \text{ M}^2$, $[\ce{Cd^{2+}}]=2.28\times 10^{-6} \text{ M}$
Sulfide $\ce{CdS}$, $k_{sp}=8\times 10^{-27} \text{ M}^2$, $[\ce{Cd^{2+}}]=8.94\times 10^{-14} \text{ M}$


Cadmium sulfide is less soluble than cadmium carbonate by a factor $10^8$ (100 million). The same behavior exists for cobalt, copper, iron, lead, manganese, nickel, silver, and zinc (all metals for which data for both the carbonate and sulfide are listed).


  Why might this paper suppose that the sulfides are deposited second when the sulfides are much less soluble than the carbonates?


The authors of the paper probably did not know that (and perhaps few others did either). That paper was published in 1901. Svante Arrhenius presented his thesis on the behavior of salts in water in 1884. It was not well thought of initially. He received a Nobel Prize for the work in 1903 (after the paper was published), but there is little reason to believe the authors (mining engineers) would have been taught controversial and cutting edge physical chemistry in whatever minimal introductory chemistry courses they had taken (if any). I may mention recent Nobel work in chemistry in my intro courses, but I certainly don't teach recent Nobel work in chemistry in into courses. 


  Where do the metal oxides come from?


Metal oxides form either by decomposition of the carbonates or by oxidation of pure metals (which probably occur from the decomposition of the sulfides):

Decomposition of sulfides:

$$\ce{FeS(s) &lt;=&gt; Fe(s) + S(S)}$$

Oxidation of metal:

$$\ce{6Fe(s) + 3O2(aq) -&gt; 3Fe2O3(s)}$$
$$\ce{2Fe(s) + 3H2O(l) -&gt; Fe2O3(s) + 3H2} \text{ (acid is helpful here)}$$

Decomposition of the carbonate. Since the carbon dioxide would be carried away by the water, this equilibrium is continually pushed toward the oxide.
$$\ce{FeCO3(s) &lt;=&gt; FeO(s) + CO2(aq)}$$