In the bowl of a stand mixer or in a large mixing bowl using a handheld electric mixer, beat the butter and sugar until fluffy. Beat in the eggs, vanilla and yogurt in that order.
In a separate bowl, whisk together the flour, baking soda, baking powder and salt.
Slowly beat the dry ingredients into the wet ingredients. Fold in the blackberries.
Coat a 9x13 baking pan with nonstick cooking spray. Pour the cake batter into the pan.
Make the crumb topping: Melt the butter in a microwave safe bowl. Using a fork, stir in the flour, sugars and salt.
Sprinkle the crumb mixture in an even layer over the cake batter. Bake 55 minutes, or until a toothpick inserted in the center of the cake comes out clean.