"seriously depends" is a perfectly correct and usable phrase in written English.
It is used when one needs to emphasize that there is a great deal of dependence on something. For example: "How long it will take to get the project completed seriously depends on how much time and effort we can put in."
But the last one may be even more seriously depends on chemical composition distribution [24].
In addition, the processing time of the graph-based method seriously depends on the number of pixels in the image.
Actually, the DOF of the InIm system not only depends on the the facet braiding in the display process, but also seriously depends on the pickup process.
Actually, the value of α seriously depends on the gray difference between the objects and the background in the dark regions.
However, the efficiency of those methods seriously depends on the factorization techniques of matrix at each iteration, often exploiting the sparsity in for a large-scale quadratic programming.
Propylene epoxidation over the complex catalyst seriously depended on the pressure and the temperature, favoring high pressure and low temperature for improved conversion and yields, respectively.
Uncertainty of rainfall is a major factor affecting the rice yield in India, Bangladesh, and Myanmar with flash flood affecting the plant stand seriously depending on duration of submergence stress which is considered as the third most important constraint to high yield in India, particularly is in the eastern Indian States (Sarkar et al. [2006]; Sarkar et al. [2009a]).
Therefore, someone who attends a three-hour dinner party and drinks a martini before dinner, two glasses of wine with dinner, and an Irish coffee with dessert is impaired at evening's end, perhaps rather seriously depending on how large the martini and how strong the Irish coffee.
All those approached seriously depended on the completeness of the prior knowledge transmitted to the system, at the beginning of the data analysis process.
The statistical shape model and probabilistic atlases seriously depend on the shape and intensity distribution of objects in training dataset, so that they suffer from large variations of shape and intensity.
Whether those criticisms are taken seriously apparently depends on how close to the front line you are standing.
