Preheat oven to 350°F degrees.
To slice the citrus: Prepare the citrus by trimming off each end. Stand the citrus upright on one of its cut ends and cut away the pith with a sharp knife, following the contours of each citrus. Slice the fruit crosswise into ¼ - inch thick rounds.
Melt the butter, brown sugar, white sugar and water until all the sugar is dissolved.
Pour this sugar mixture into the bottom of the cake pan, and then line the bottom with the cut citrus fruits. Set aside.
In the bowl of a food processor (or a mixer if you have one), beat the butter and sugars together until light and fluffy. Add in the eggs, citrus juice & zest of your choice, and vanilla extract. Slowly add the flour, baking powder, baking soda, and salt, beating until it’s combined (stopping to scrape sides down so that all the batter gets mixed) then add the yogurt and keep beating until it’s all combined.
Pour the batter over the prepared citrus slices, spreading it evenly to the edges.
Bake for 40 minutes, then allow to cool slightly before inverting onto a serving tray.