Terrain Sculpting

This is a trope where the topology of an area of ground is altered by the conscious effort of some person or group.

This can happen on almost any scale, depending on the way it's made. A molehill isn't very impressive, though making one at the snap of a finger is pretty cool. As cities grow, the ground on which they're built is altered greatly, but because of all the buildings on top we are seldom really aware of how great the change is. Meanwhile, causing a mountain (explicitly volcanic or not) to rear out of a plain is just awesome, no matter how difficult or time-consuming it is.

The uses are manifold. First and foremost is tactics. Controlling the existence of passages, obstacles, and high ground for allies and enemies alike yields a supreme advantage in battle. It can also be helpful to prevent natural disasters, improve land arability, or facilitate transportation (by extending a river, say). It can be done to separate peoples or forces that shouldn't be so close together, or simply as a sign of one's power, to lord it over, literally, those less mighty.

The power to do this may be specific to a person, because of some elemental power over earth. But on the larger scales they're more likely to be a Physical God. Alternately, this will be done with the aid of some kind of Applied Phlebotinum, in which case anyone with access to the technology can do it.

But it can also be done in a more mundane way, with dynamite, earthmovers, and patience. This method is less evocative, but the end results are just as impressive. When thinking about an earthworks project (canals, dams, field-tilling, etc) for this trope, consider the magnificence of the creation or the end result.

For alteration of a whole planet's ecology, see Terraforming. For the manipulation of terrain for human settlements, see Terra Deforming. For defacement of monuments, see Rushmore Refacement. For defacement of the moon, see Deface of the Moon. A common small-scale form of this in real-life is an Artificial Riverbank.

Examples of Terrain Sculpting include:

Anime and Manga

Because Tengen Toppa Gurren Lagann centers around drills, this naturally crops up. Mostly toward the end of the first arc, where Team Gurren, for example, traps the enemy battleship Dai-Gunzen in a huge pit. The resulting battle causes the nearby volcanos to (predictably) explode.
In Cowboy Bebop, the MPU, a spy satellite gone sentient, uses Kill Sats to re-carve the Nazca lines into the face of the now ruined earth. And, at Ed's suggestion, a giant smiley face.

Literature

As it is a creation myth, this is seen in The Silmarillion. In the beginning of the world, the Valar tried to shape it according to divine plan, while Melkor came along and undid their work. The end result was that the world was very gradually formed.
Similarly in The Lord of the Rings, the Ents divert a river in order to flood Orthanc. Once this is done, they put it back again.
Happens in the backstory of The Belgariad and is expounded upon in Belgarath The Sorcerer. The evil god Torak, after stealing the all-powerful Orb of Aldur, is faced with a war against all the other gods and their followers. To protect himself and his people, he uses the Orb to crack the entire continent in two, turning a pangaea into two distinct landmasses and causing lots of geological fallout and mayhem. The price of this action is that the Orb turns on him, burning away his hand and eye.
Similarly, in The Tamuli in order to curtail a Troll invasion, the Bhelliom decides to curb bloodshed by creating a humongous escarpment to separate them. The trolls quickly find ways around this.
Also in the backstory of The Wheel of Time. During the Breaking of the World, all male Aes Sedai went mad and caused total upheaval, creating mountain ranges, dredging seas and creating new ones on top of existing countries. It's suggested that the shape of all the world's landmasses has been radically changed.
The Hitchhiker's Guide to the Galaxy features the Magratheans, a race of planet builders whose jobs naturally include this. Slartibartfast, for instance, once won an award for his work on the fjords in Norway.

Live-action TV

In the new Doctor Who, Rose and the Ninth Doctor travel to the year Five Billion to see the Earth be engulfed by the sun. When Rose questions why Earth's continents haven't shifted, the Doctor explains that the continents did shift, but were simply moved back to maintain "classic" Earth.

Mythology

This is common in creation myths and attributed to a creator god or, often a group working in tandem. The typical ways of creating the earth involve piling up dirt until it lies above the ocean (which is presumed to have always existed), and sculpting it out of primordial matter.
According to an American Tall Tale, Paul Bunyan dug the Grand Canyon by dragging his axe behind him, created Mount Hood by piling rocks on top of his campfire to put it out and formed the Great Lakes so his companion Babe the Blue Ox could have a watering hole.

Tabletop RPG

Dungeons & Dragons
- Supplement Deities and Demigods Cyclopedia. The Celtic pantheon section mentioned a deity named Dunatis who could instantaneously raise a mountain peak from a flat plain or flatten a giant mountain into a prairie.
- Supplement Netheril, Empire of Magic. Spells available to Netherese spellcasters included Mavin's Create Volcano and Proctiv's Move Mountain.
- Adventure OA6 Ronin Challenge. A story tells of the creation of the world by the Celestial Emperor, during which he raised mountains, bored holes that would become lakes, flattened the earth into plains and dug out the path of mighty rivers. His subordinate deities the Nine Immortals were each assigned to carve out a valley.

Video Games

This was one of Peter Molyneux's favorite aspects of the game that would become Populous and as such is an important part of all the games. In Populous: The Beginning, there are no less than four spells based around the manipulation of terrain.
Pretty much the whole point of From Dust. The player carries around large amounts of dirt, lava or water in order to gradually create bridges or barriers against environmental hazards.
The SimCity games allow the player to modify the terrain as befits the needs of a growing city. However, doing so as a mayor is expensive (unless you cheat). Fortunately, each game since 2000 has had a mode wherein a player could sculpt the terrain for free before founding a city there. The controls have become increasingly precise and lifelike, and support for terrain imports became available, so as to recreate real-world locations. In 4, you can also make craters before or during city play by dropping meteors or summoning volcanos.
In Spore's space stage, there are numerous tools to modify the shape of any planet you care to visit. However, these are entirely cosmetic and have no tactical or political effects. Also, colonies automatically flatten an area around them when placed.
In Minecraft, you can pretty much change everything you can immediately see, from creating a mountain, destroying it, then building it again.
Wetrix (Nintendo64 puzzle game) has the premise of you creating hills and valleys from an initially flat piece of land in order to create ponds and lakes.
Pilot Wings 64 featured the Little States map, which had the famous "Mount Mario-More" landmark. It had an Easter Egg feature: while flying the gyro plane, you could fire a rocket at Mario's face and a direct hit would change it from Mario to his evil twin, Wario.
Master of Magic has Change Terrain spell and Create Volcano. The latter is mostly used offensively in that a Volcano tile is useless (except producing a bit of Mana that probably won't cover the casting cost before it reverts), but it also reverts to Mountain (randomly or by Change Terrain) or into Hill by Gaia's Blessing. Aside of different terrain granting different bonuses and maximum population, Forest and Mountain or Hill tiles are prerequisites for certain buildings.
In De Blob, as part of a World-Healing Wave, the most powerful Transformation Engines can severely alter the nearby terrain to get Blob to the next area or just celebrate the completion of the level.
The Terraformer tool from Subnautica allowed this before it was Dummied Out. (But not completely; the correct ~~cheat~~ developer code will add it to your inventory.)

Western Animation

An episode of The Magic School Bus had Ms. Frizzle and the class attempt to carve a statue of their town's founder out of stone without using their bare hands. When the statue breaks away from its place, they make a mad chase after it down the mountain. Since the episode focused mainly on erosion, it turned out that they already made a statue of their founder out of stone while chasing after the statue they had been making, by shifting the water flow through different directions of the mountain that formed the face of their founder.

Real Life

Land reclamation has been used to create or extend landmasses into water for various reasons (usually to alleviate overpopulation). A famous example is the Zuiderzee Works in the Netherlands, undertaken to fight the continuous sinking of that country. The resulting island is now, by a certain metric, the largest manmade thing in the world.
- Other major terrain shaping feats include the creation of the Palm Islands and World Islands off the coast of Dubai.
- There is also the Hong Kong International Airport, which was a tiny island expanded until it was big enough to support the airport it was built for.
- That Other Wiki has a list of artificial islands here.
- A number of organizations and companies are now seriously looking into the feasibility of building an actual 2000 meter high mountain in the Netherlands.
The Panama and Suez canals. At 77 and 164 kilometers long, respectively, each has effectively made a continent disappear as far as ships are concerned, making worldwide shipping considerably faster.
Following the latest Tsunami that rocked Japan and much of the Pacific rim, the Japanese Government is planning to build massive, artificial hills some 20+ meters high just off the beach to stand as wave-breaks.
U.S.A. used a mountain—Mount Rushmore—as a monument, further changes of which made a separate trope.