The rover would have to have had the luck to land in an area of such methane seeps. "Would have" is a modal past tense. "to have" is a different verb (like "to have a car") and is linked to the object "the luck" "had" is an auxiliary verb past tense. The sentence can be simplified as The rover would have had to land in an area of such methane seeps. If you omit "had" the sentence changes to future tense which is wrong because the rover has already landed. The following is the same sentence but written differently. The rover would have had to land in an area of such methane seeps. The rover did not have such luck. Hope this helps.

Each of the three forms of “have” has a different meaning. Would: indicates an unreal condition Have: indicates past tense (actually the base form of "to have" as part of the modal perfect with “would”) Had: This is the main verb (in past participle form), meaning “to possess”. For further information, you can look up “perfect infinitive”, “modal perfect”, and 3rd conditional (i.e. the past unreal / contrary-to-fact conditional). You may also want to read my mini-article: Grammar boost: Conditionals cheat sheet PART 1 https://www.italki.com/discussion/164505

would have to have had -- this is expressing an unreal/non-existent condition. An unreal hypothetical. For example, "In order to buy that Ferrari sports car, she would have to have won the lottery". She did not buy that car and she did not win the lottery. would have to - is like "must". "In order to buy that Ferrari sports car, she would have to win the lottery." This is something that also did not happen, but it is not unreal. It sounds more possible rather than an unreal hypothetical. In the given sentence: "For either to be the explanation of the seasonality observed by Curiosity, the rover would have to have had the luck to land in an area of such methane seeps." It sounds like it is a very unlikely situation that the rover landed in an area of methane seeps. Therefore, those explanations are quite remote to be true. And thus something else must be the cause of the observed phenomenon.

The Economist is usually a hard read for non-English speakers because the sentences the employ are usually more complex than a normal publication. With that said, I congratulate you for reading such a challenging publication. For this sentence: "For either to be the explanation of the seasonality observed by Curiosity, the rover would have to have had the luck to land in an area of such methane seeps." "The rover would have to have" denotes a condition for the rover in order to have "the explanation of the seasonality." That means that in order for explain for the seasons observed by the rover, the rover needed to land on a methane-rich area of Mars to get a sample understanding of the seasons. It is not uncommon in English to use infinitive + perfect tense especially if a condition is specified in the sentence. The general rule for infinitives is to modify a verb, which it does in the sentence (have to have). You can also split infinitives either as a literary license or to underscore a point (have to really have). Another, but simpler, example of this: Because Mother needs to make dinner for 10 guests, she would have to have spent at least 8 hours in the kitchen preparing the food. To cook for ten guests, the condition of the sentence is for her to spend at least 8 hours in the kitchen to make sure the food goes well.