I see. However whether "pervading" or "sending" it is just to produce a feeling of "unboundedness", a feeling of "not being limited in one's own sphere".
Actually everything is much more complicated than that.
Such "pervading" does not mean that you produce a feeling of unboundedness - but that is real unboundedness - like in a superhuman jhana state.
Brahmavihara means "Brahma" and "Vihara (dwelling place)". Let's take MN 120 and see how does "Brahma Dwell":
Again, bhikshus, a monk is accomplished in faith, moral virtue, spiritual learning, charity,
and wisdom. He hears that Brahma of five thousand (pañca,sahasso brahma) is long-lived, beautiful,
enjoying great happiness. Bhikshus, Brahma of five thousand dwells resolved on pervading a worldsystem
of five thousand worlds, and he dwells resolved on pervading the beings that have arisen there.
Just as a man with good sight might take five myrobalans in his hand and review it, so Brahma of five
thousand dwells resolved on pervading a world-system of five thousand worlds, and he dwells resolved
on pervading the beings that have arisen there.
Okey, now we take Commentaries on Majjhima:
“Pervading,” pharitva. Comy explains that there are 5 kinds of pervasion (pharana): pervasion of mind, ie
knowing the minds of beings throughout a thousand world-systems; pervasion of the kasina, ie extending the kasina
meditation image throughout a thousand world-systems; pervasion of the divine eye, ie seeing a thousand worldsystems
through clairvoyance; pervasion of light, ie radiating light throughout a thousand world-systems; and pervasion
of the body, ie extending one’s body aura throughout a thousand world-systems. (MA 4:148)
So you see - this "metta pervasion into 1,2,3,4th direction, everywhere and above" - doesn't simply mean that you make some fantasies about that. But this is real state of enlarged jhanic mind. That is why after death such practice will lead you to Rupa-Loka (1st jhana state, world of Brahma).
Then, let's take MN 127 - here we see explanation between jhanic mind and brahmavihara mind
"What, householder, is the immeasurable deliverance of
mind? (brahmavihara) Here a bhikkhu abides pervading one quarter with a
mind imbued with loving-kindness, likewise the second, likewise
the third, likewise the fourth; so above, below, around, and
everywhere, and to all as to himself, he abides pervading the allencompassing
world with a mind imbued with loving-kindness,
abundant, exalted, immeasurable, without hostility and without
ill will. He abides pervading one quarter with a mind imbued
with compassion...He abides pervading one quarter with a
mind imbued with appreciative joy...He abides pervading one
quarter with a mind imbued with equanimity.. .abundant, exalted,
immeasurable, without hostility and without ill will. This is
called the immeasurable deliverance of mind.
8. "And what, householder, is the exalted deliverance of
mind? (jhana) Here a bhikkhu abides resolved upon an area the size of
the root of one tree, pervading it as exalted: this is called the
exalted deliverance of mind. Here a bhikkhu abides resolved
upon an area the size of the roots of two or three trees, pervading
it as exalted: this too is called the exalted deliverance of
mind. Here a bhikkhu abides resolved upon an area the size of
one village, pervading it as exalted... ..an area the size of
two or three villages...an area the size of one major kingdom...
an area the size of two or three major kingdoms...an area the
size of the earth bounded by the ocean, pervading it as exalted:
this too is called the exalted deliverance of mind. It is in this
way, householder, that it can be understood how these states are
different in meaning and different in name.
And here we see, that this practice of "pervading" leads to rebirth in 2nd Rupa-Loka (Abhassara Devas):
"What do you think, friend Kaccana? When one bhikkhu
abides resolved upon an area the size of the roots of two or three
trees, pervading it as exalted, and another bhikkhu abides
resolved upon an area the size of one village, pervading it as
exalted...an area the size of one village and an area the size of
two or three villages...an area the size of two or three villages
[150] and an area the size of one major kingdom...an area the
size of one major kingdom and an area the size of two or three
major kingdoms...an area the size of two or three major kingdoms
and an area the size of the earth bounded by the ocean,
pervading it as exalted - which of these two types of mental
development is more exalted?" - "The second, venerable sir."
"This is the cause and reason, friend Kaccana, why among
those deities that have reappeared in a single order of gods,
some are deities of Limited Radiance, some deities of Immeasurable
Radiance."
Now, lets take standard definition of Metta practice:
Here a bhikkhu abides pervading one quarter with a
mind imbued with loving-kindness, likewise the second, likewise
the third, likewise the fourth; so above, below, around, and
everywhere, and to all as to himself, he abides pervading the allencompassing
world with a mind imbued with loving-kindness,
abundant, exalted, immeasurable, without hostility and without
ill will.
Okey. And now in Digha Nikaya there is an interesting passage telling about Divine Ear practice (this is DN 6 Mahali sutta).
And there it is said, that at first you "abide pervading one quarter" - and when this is done, you can hear different far sounds and even divine ones
This shows that "pervading one quarter" is not just "imagination about 1 quarter", but some real superhuman psychic seeing.