Image copyright KCNA Image caption North Korea's official news agency distributed this photo, purportedly of the missile launch

US President Donald Trump said "we'll see" when asked if he was going to attack North Korea after the secretive state claimed to have successfully tested a hydrogen bomb. So what could military action against Kim Jong-un's regime actually look like?

Pyongyang has defied UN sanctions and international pressure to develop nuclear weapons and test missiles that could potentially reach the US.

South Korea, Japan, China and Russia are among those to voice strong criticism against the country's nuclear tests.

And when North Korea fired a missile over Japan's Hokkaido region, sending residents running for cover, President Trump said "all options are on the table".

But while the US has unrivalled military strength, the range of options it actually has against the hermit country are limited.

Option 1: 'Enhanced containment'

This is the least risky but arguably least effective option available since it would simply build on deployments that have long been in place and have had little success in deterring North Korea's ballistic missile and nuclear programme.

The US could move additional ground forces into South Korea, including ground-based missile defences, such as the controversial Thaad system, heavy artillery and armoured vehicles, to demonstrate its willingness to use force to back up its demands.

However, South Korea temporarily halted the current Thaad deployment and is strongly against any increases in US ground forces, because of concerns about provoking the North.

Indeed, North Korea would almost certainly interpret such moves as a prelude to a ground invasion, given its reactions to annual joint exercises between the US and South Korean militaries.

China and Russia would no doubt strenuously object too, and both have the power to make life difficult for the US in other areas such as Eastern Europe and the South and East China Seas.

The US Navy could increase its presence around Korea, sending more cruisers and destroyers able to shoot down ballistic missiles and, possibly, deploying a second carrier strike group.

Alongside the naval options, the US Air Force could bolster its forward-based airpower, with more attack fighter squadrons, support tankers, surveillance aircraft and heavy bombers at bases in Guam, South Korea and Japan.

However, the US Navy and US Air Force are both extremely heavily tasked around the world and are feeling the strain of well over a decade of continuous high-intensity deployments in support of operations, including those in Iraq and Afghanistan.

More importantly, perhaps, time is on North Korea's side, since an enhanced US military presence would not itself force a halt to its rapidly maturing nuclear weapons programme and ballistic missile testing.

And any statement of intent to shoot down North Korean ballistic missiles that travel outside the country's airspace would itself require a major increase in US Navy presence around the peninsula.

North Korea has a large ballistic missile arsenal, and US interceptor missiles are extremely expensive and available in limited quantities aboard each ship.

It would, therefore, be possible for the North to overwhelm and deplete the US Navy's stocks, leaving them vulnerable and forced to return to port.

Such a policy would therefore represent an extremely expensive and probably unsustainable challenge to North Korea, as well as a dangerous escalation towards direct military conflict.

Option 2: Surgical strikes

The US Air Force and US Navy possess the most advanced surgical strike capabilities on Earth.

Using volleys of precision Tomahawk missiles fired from submarines off the North Korean coastline and attacks by B-2 stealth bombers against key North Korean nuclear sites and ballistic missile facilities may seem like an attractive proposition, at first glance.

It is undoubtedly the case that heavy damage could be inflicted on high-value targets, with deeply buried and hardened underground facilities vulnerable to the 30,000lb Massive Ordnance Penetrator bomb.

The immediate danger to US aircraft would depend on many factors, including the amount of warning North Korea received, the number of strikes flown and the contribution of non-stealth aircraft within range of its defences.

However, the state of North Korea's air defence network is very hard to determine since it is a mix of Soviet/Russian, Chinese and home-grown surface-to-air missile and radar systems acquired over 50 years.

The defences are among the densest on Earth, but they have been modified and upgraded to an unknown degree and their readiness is difficult to assess.

If the US lost aircraft to enemy fire or accidents, it would then face the nightmare scenario of having to try to rescue its aircrew, or abandon them to a very public fate.

Image copyright Reuters Image caption A missile launch across a Japanese island caused big concern in August

Far more significant, however, is the fact that even successful strikes on nuclear and missile sites, command centres and even the leadership itself, would not stop North Korea retaliating.

The People's Army would still have the ability to inflict almost inevitably devastating damage in immediate retaliation against South Korea - a key US ally.

It consists of more than a million regular soldiers and, by some estimates, more than six million reserves and paramilitary troops.

A huge number of conventional and rocket artillery pieces, mostly dug in near the demilitarised zone, include hundreds that are within range of parts of the South Korean capital city Seoul, which is home to around 10 million people.

Even the US military would take days to fully eliminate just these artillery batteries, which would be able to fire tens of thousands of shells and rockets during that time.

The catastrophic damage that these batteries would inflict on a crowded modern city, as well as the South Korean military forces, is why the South Korean government is opposed to any pre-emptive military action against North Korea.

Even without a usable nuclear weapon and without actively invading South Korea, the Kim regime could inflict devastating damage and probably end the US-South Korean alliance as we know it.

Option 3: Full-scale invasion

Given the sheer size of the People's Army, the power of its artillery, its dense air defences and South Korea's reluctance to support any US military action, this option is extremely far-fetched.

Any attempt to actually invade North Korea would require months of visible US military build-up, full-scale South Korean participation and a way to guarantee the neutralisation of North Korea's mysterious nuclear capabilities.

It would also cost hundreds of thousands of lives on both sides.

North Korea's missile programme:

North Korea has been working on its missile programme for decades, with weapons based on the Soviet-developed Scud

It has conducted short- and medium-range tests on many occasions, sometimes to mark domestic events or at times of regional tension

In recent months the pace of testing has increased; experts say North Korea appears to be making significant advances towards its goal of building a reliable long-range, nuclear-capable weapon

In July, North Korea launched two missiles that it said were Inter-Continental Ballistic Missiles (ICBMs) capable of hitting the US; experts believe they put parts of the US in range

There is no consensus on how close North Korea is to miniaturising a nuclear warhead to put on a missile

Have North Korea's missile tests paid off?

In addition to heavy artillery bombardments, the People's Army has long trained for large-scale commando infiltration into South Korea, using low, slow-flying biplanes which are hard to detect on radar, small boats and midget submarines.

These would add to the chaos and loss of life in the event of any large-scale conflict, and ensure that the comparatively fewer, albeit much higher-technology US and South Korean forces would be stretched painfully thin.

The last time the US and its allies advanced into North Korea, during the Korean War in 1950, China entered the war on the side of the North to prevent the establishment of a unified Western-aligned Korea on its land border.

Such a development is still something that China is not prepared to contemplate - the main reason it has propped up the Kim regime for so long.

Finally, even if somehow these huge problems could be overcome, a successful invasion of North Korea led by the US would leave it responsible for rebuilding a shattered country.

North Korea has existed in an unparalleled state of psychological manipulation, chronic economic hardship and isolation for over 60 years.

The monumental task of reintegrating East Germany after the Cold War pales in comparison.

The reality is that none of the military options available to the US for dealing with North Korea come without high costs and significant risks - considerations that it will have to weigh up against uncertain and problematic potential outcomes.

About this piece

This analysis piece was commissioned by the BBC from an expert working for an outside organisation.

Justin Bronk is a Research Fellow specialising in combat airpower and technology at The Royal United Services Institute (RUSI). Follow him @Justin_Br0nk.

RUSI describes itself as an independent think tank engaged in defence and security research.

Edited by Duncan Walker