* Saudis seen keen to avoid deeper military involvement
* Action reflects acute worry about instability in Yemen
* Saudi forces needed on border until fence complete
* Yemenis despair of early end to war in north
By Alistair Lyon, Special Correspondent
BEIRUT, Nov 6 (Reuters) - Saudi Arabia, deeply worried by instability in Yemen, has hit back hard at Yemeni insurgents who breached the kingdom’s border, but will try to avoid getting sucked deeper into the conflict in its chaotic neighbour.
The world’s biggest oil exporter has rarely, if ever, taken unilateral military action beyond its borders in recent decades, preferring to wield regional influence via wealth and diplomacy.
Saudi warplanes and artillery were reported in action for a third day on Friday in the border area of Jabal Dukhan, which means "mountain of smoke", in efforts to dislodge Yemeni rebels accused of infiltrating across the undemarcated frontier.
The official Saudi Press Agency said operations would go on until Saudi territory was "cleansed of any hostile element".
The Yemeni government has denied reports by the Zaydi Shi’ite guerrillas, known as Houthis after their leader’s clan, that Saudi air strikes had hit targets inside Yemen.
In the last few weeks the Houthis have accused Saudi Arabia of allowing Yemeni forces to use its territory as a back base to launch attacks against them and have threatened to respond.
Mustafa Alani, a security analyst at the Dubai-based Gulf Research Center, said the move into Jabal Dukhan by the Houthis, who already control two border crossings, was a Saudi "red line", but he ruled out any Saudi intervention inside Yemen.
"Definitely the intention is not to go physically and interfere in the civil war in Yemen," he said.
The Saudis still remember the bitter civil war in Yemen after the overthrow of the Zaydi Imam in 1962. At the time they backed the royalists against their regional foe Egypt, whose troops came to the aid of the fledgling republic and got bogged down.
Ginny Hill, a British-based author on Yemen, said the Saudi action appeared to be a show of strength to tell Yemen, the Houthis and the region that the border is not a "soft flank".
She said it reflected Saudi anxiety, shared by other Arab states and the West, about Yemen’s confluence of crises.
"Its trajectory is deeply concerning, not only because of the fighting in the north, but also the economic crisis, the southern separatist movement, the perception that the government may not be able to maintain control and because of al Qaeda."
The Yemeni and Saudi branches of al Qaeda merged earlier this year into a single transnational group which has used the same border area to infiltrate militants into the kingdom.
The Saudi government is building a high-tech fence along the 1,500-km (930-mile) border, a transit route for smugglers, drug traffickers and economic migrants, but it is far from ready.
"Saudi Arabia will have to deploy an important military contingent along the border until it completes building the fence," said an Arab diplomat in Riyadh.
He said the Saudis might intend their air raids as a swift and effective operation, but risked continued exposure to Houthi border attacks or even a drawn-out guerrilla war.
This might raise tensions among Saudi Arabia’s Shi’ite minority concentrated in its oil-rich Eastern Province, he said, suggesting that Riyadh may adopt a zero-tolerance policy towards dissent among the Shi’ites, or minority Ismailis in the south.
Other than that, the border conflict is unlikely to have any impact on distant Saudi oil installations, analysts agreed.
Even Saudis acknowledge privately that the border fence cannot assure security. "It won’t stop people from infiltrating Saudi territory, only vehicles," a government source said.
"There is going to be a spillover from the unrest in Yemen to Saudi Arabia and the recent developments suggest that Houthis will opt for hit-and-run operations, a war of attrition which may lead to operations inside Saudi territory," he added.
The source, who asked not to be named, said Saudi policy for the moment was one of containment, with the scale of military deployment suggesting a medium- to long-term commitment.
Saudi Arabia is already Yemen’s biggest aid donor, but its financial support may not be enough to brake the impoverished country’s slide towards dangerous ungovernability.
"Saudi Arabia has been aiding the Yemeni government in its fight against the Houthis, but it has remained officially at a distance," said David Bender of the Eurasia Group consultancy.
"Yemen’s problems are myriad. Unless the Saudis really want to commit massive financial and military resources, which they don’t, they can’t hope to improve Yemen’s negative trajectory."
Many Yemenis already despair of government promises of a swift end to the Houthi war, with some blaming profiteering and rivalry among the country’s political-military elite.
"The Saudis are clearly irritated and perhaps feel they are being taken for a ride," said Abdul-Ghani al-Iryani, an independent Yemeni political analyst. "Maybe that finally pushed them to take action to deny Sanaa the excuse that it does not have enough firepower to quell the rebellion."
(Additional reporting by Souhail Karam in Riyadh, editing by Peter Millership)