Animated Terrain in Unity using height maps, Perlin Noise and Terrains as seen here - https://www.youtube.com/watch?v=V2zzUbfcnQU

TerrainScript.cs

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class TerrainScript : MonoBehaviour
{

    Terrain terrain;

    public int depth = 20;
    public int width = 256;
    public int height = 256;

    public float scale = 8f;

    public float offsetX;
    public float offsetY;

    public float terrainXSpeed = 1.42f;

    private void Start() {
        offsetX = Random.Range(0f, 9999f);
        offsetY = Random.Range(0f, 9999f);
    }

    void Update()
    {
        terrain = GetComponent<Terrain>();
        terrain.terrainData = GenerateTerrain(terrain.terrainData);

        offsetX += Time.deltaTime * terrainXSpeed;
    }


    TerrainData GenerateTerrain(TerrainData terrainData) {
        terrainData.heightmapResolution = width + 1;

        terrainData.size = new Vector3(width, depth, height);

        terrainData.SetHeights(0, 0, GenerateHeights());

        return terrainData;
    }

    float[,] GenerateHeights() {
        float[,] heights = new float[width, height];

        for (int x = 0; x < width; x++) {
            for (int y = 0; y < height; y++) {
                heights[x, y] = CalucalteHeight(x, y);
            }
        }

        return heights;
    }

    float CalucalteHeight(int x, int y) {
        float xCoord = (float) x / width * scale + offsetX;
        float yCoord = (float) y / height * scale + offsetY;

        return Mathf.PerlinNoise(xCoord, yCoord);
    }

}