"profoundly analyze" is correct and usable in written English.
You can use it when you are trying to express the idea of examining something deeply and in great detail. For example: "We must profoundly analyze this data to better understand the problems facing our organization."
In order to develop new insights into the rational drug design, conformational changes were profoundly analyzed and discussed.
It profoundly analyzed the security standard of supply for urban power networks, and established quantitative indicators of load groups based on different fault conditions.
Numerical simulation and field measurement being taken into consideration, Shaft effect has been profoundly analyzed on this study based on construction ventilation of Guantian tunnel, the optimization of fan arrangement near cross passage and the bottom of shaft.
The influences of the surface morphology and the basic physical and chemical properties of the fabric substrates on the PCFs as well as the related structural colors were thoroughly investigated by means of optical microscope, field emission scanning electron microscope (FESEM) and UV Vis spectrometer, and the related mechanisms were profoundly analyzed.
Although profoundly analyzed with respect to fungal biotrophy 11 and gall-causing pathogens, 12 the potential connection of cytokinins to plant immune pathways such as the SA JA/Et backbone of immunity 6 was still not known until recently.
More profoundly, he attempted to analyze the fundamental ideas animating the movement and, fastening on the Revolutionary concepts of "the rights of man" and popular sovereignty, emphasized the dangers of democracy in the abstract and the mere rule of numbers when unrestrained and unguided by the responsible leadership of a hereditary aristocracy.
For further research, it would be interesting to analyze some aspects more profoundly, e.g. the effects of strong symbols like the burning water tap on discourses about technologies.
In the second step, main actors were identified in the articles and analyzed more profoundly by examining their own publications, e.g. press releases, homepages etc.
Castelnuovo et al. [10] analyze the connection of "imitation" and "natural writing" with intelligence, originality, anxiety, compulsiveness, sexuality, and temperament and conclude that handwriting highly reflects writer's personality and "natural writing" does more profoundly than "imitation".
