Brian Wilcox. 'Evening at Back River'
"Prayer" in this writing includes a broad variety from spoken prayer to meditative silence. Moreover, prayer constitutes a posture of heart, which I often call prayerfulness, and found in theistic and nontheistic paths. Prayerfulness has more to do with receptivity, openness, and humbleness than saying or doing prayers. A Buddhist might sit in silence looking at a wall, as some Zen Buddhists do, and be in prayer; a Christian could be saying prayers, not praying prayers, for the praying of prayers entails a prayerful heart-posture.
In my upbringing, we would speak of one "in prayer." For example, "Don't disturb her now; she's in prayer." Being in prayer is akin to this prayerfulness, for one is in prayer, whether praying or not. I will speak of this more below, a heart-posture I have elsewhere called, as have others, "Pure Prayer."
As to "depth," this refers to varied aspects of being that are more subtle than the realm of body-mind. The Chinese, reflected in such writings as that of Chuang-Tzu (b. ca. 369 BCE), speak of three realms of soul, or the living being. A quick look at these might help; here, I follow Chuang Tzu: The Tao of Perfect Happiness, translated and annotated by Livia Kohn.
1) material soul: "our instinctual side and is responsible for survival and sensory satisfaction."
2) spirit soul: "the artistic and intellectual dimension of people and guides us to be altruistic and culturally active."
3) spirit: "the pure potency of aliveness and connects us to the divine."
As I use "depth," it refers to the realm of "spirit." Depth does, however, enhance the spirit soul and material soul realms. Yet, spirit is the one realm that cannot be enhanced, for spirit is complete: the fulness that fills up all else, the life that makes possible all living things.
When a youth, I was a teenage preacher. A church near my home invited me to give the Gospel message at its Sunday worship. After the meeting, I stood at the exit to speak and shake hands with congregants, as was the custom. A woman looked at me and said, "I can remember when you could walk into this church and feel the Spirit so strongly; it's not that way now." She indicated this depth, which in her faith would be called "Holy Spirit," so subtle it is impossible to define, while its absence can feel palpable. This woman, I could see, missed this strong sense of Presence in her church community.