As far as i know, the torah shebichsav never refers to the splitting of the sea as a 'kriah', i.e. a ripping. The torah says things like ויבקעו המים (Shemos 14:21) which means that the sea split. In torah she'b'al peh, it is always referred to as קריעת ים סוף.
Why did chazal choose to change from.the way the torah refers to that which occurred and why such an odd choice off word? Ripping seems to make little to no sense in this context.
Rabbeinu Bachya says that the water opened up like a zipper. The further they walked the more it opened up. That is similar to kriah which is tearing. One must say that two things happened. First there was a small cut or chop in the water to cause a small split which is bekiah and then the water gradually opened up more and more which is kriah.
Ok. Here's a chidush. The Mechilta has many drashos based upon all the various terminologies used for or applied to this particular miracle in Tanach.
מכילתא על שמות יד-פסוק טז
ואתה הרם את מטך עשרה נסים נעשו לישראל על הים. נבקע הים ונעשה כמין כיפה שנ' נקבת במטיו ראש פרזיו יסערו להפיצני (חבקוק ג) נחלק לשנים עשר גזרים שנ' ונטה את ידך על הים ובקעהו נעשה הים יבשה שנ' ובני ישראל הלכו ביבשה נעשה כמין טיט שנ' דרכת בים סוסיך חומר מים רבים (שם) נעשה פירורין פירורין שנ' אתה פוררת בעזך ים (תהלים עד) נעשה סלעים סלעים שנאמר שברת ראשי תנינים על המים נעשה גזרים גזרים שנ' לגוזר ים סוף לגזרים (שם קלו) נעשה ערימות שנ' וברוח אפיך נערמו מים נעשו כמו נד שנ' נצבו כמו נד נוזלים הוציא להם זיכרי מים מתוקים מתוך מלוחים שנ' ויוצא נוזלים מסלע ויורד כנהרות מים (שם עח) הקפיא להם את הים משני חלקים ונעשה כמין בולוס של זכוכית שנ' קפאו תהומות בלב ים.
So for instance nivka was used to expound that there was a dome of water overhead. Gozer was used to expound that there were many paths cut through not just one big one.
So perhaps we can suggest that chazzal wanted to use a term that was never used in Tanach in order to refer to the miracle in a general sense. If they would refer to it as the miracle of Bekias Yam Suf, one might mistakenly assume they were only referring to the dome miracle. If they referred to it as Gizeiras Yam Suf, one might mistakenly assume they were only referring to many paths aspect of the miracle. So a new name was invented to refer to the entirety of the miracle all together.
1) The Sefer Midrash Chidush (by R' Eliezer Nachman Puah,) writes that Hashem commanded Moshe to split the sea with the term Bekiah, as explained above, this denotes one division. However, as the various Midrashim bring the sea adamantly refused. Until "Hayam ra'ah vayanos” - “The sea saw (Hashem coming) and fled.” However, Hashem was not pleased and punished the sea by tearing it to (twelve) pieces, - "Legozer yam suf Iigzarim”. Therefore, although it is written in the Torah that the sea was split "Vayibaku”, Chazal are mechadesh to us that what actually took place in the end was keriah.
2) An answer (partially brought by the Likutei Yehuda) in the name of the Chidushei Harim. He explained that the term Keriah is used to denote two things: a) When two separate things have been made into one and then are separated. E.g. when one tears a garment which is (separate threads joined together) in mourning this is called "keriah". b) The term Keriah implies the possibility of the two now separate things being rejoined afterward. Again, with the example of the garment, in olden times it was customary to sew it back together after the appropriate time, (known as Me'acha).
Bekiah, however, refers to only one thing - Something that was one piece to begin with for example a tree or piece of wood. When divided it is called Bekiah - e.g. Bereishit 22, 3 "Vayevaka Atzeh Olah”- “And he (Avraham) cleaved the wood for the burnt-offering.”) When creating the sea, Hashem made its existence conditional upon it splitting when the Jews left Egypt.
Therefore, in reality the sea was made from two parts held together as one until that time, it only had the appearance of being one. Therefore, the correct term is for the split should be keriah, because the sea was joined back together afterward to kill the Egyptians.
Hashem called it bekiah. Bekiah refers to splitting only, because when Hashem instructed Moshe regarding the sea, he did not want to use the word keriah which would hint to the destruction that He had to bring upon His creatures when He would later reunite the sea.
The Midrash in this Mishnah alludes to a struggle between Moshe and B'nai Yisra'el regarding crossing Yam Suf (Sea of Reeds). Moshe would command them to enter the sea, and after each request, B'nai Yisra'el would demand another miracle prior to their obeying his request. One of them says
אמר להם משה: קומו, עברו! אמרו לא נעבור עד שנעשה לפנינו גזרים גזרים. נטל משה את המטה והכה על הים ונעשה לפניהם גזרים גזרים, שנאמר: (תהלים קלו) "לגוזר ים סוף לגזרים".
Loose translation:
Moses told them, "Arise and cross the sea" They (B'nai Yisrael) said, "We won't cross until the sea is made into many "shreds" (pieces)" (Hebrew גזרים). Moshe raised his rod and hit it on the sea and it became many shreds, as it says in Tehillim (Psalms) 136:
"For tearing Yam Suf into shreds".
