Some of what you describe, just moving to a rural area, hearing it in the spring and sounding like a 4 stroke starting makes me think that you're hearing grouse drumming.TL,DR: I have experienced something similar, but different, and have come to suspect an underground natural gas pipeline as the culprit.
My wife and I moved to rural property two years ago. For two spring seasons now, I have been hearing rhythmic bass noises in the early morning, sometimes extending throughout the day. The closest noise comparison to what I hear is the sound of a small four-stroke motor trying to start for about one second, then stopping. Like when you are camping and someone starts up their quad on the other side of a hill, where you can just hear/feel the bass elements of the noise, with all the high-end starter/mechanical noise stripped away. The noise is more detectable by feel than my actual ears, and is quiet enough where any background noise makes it hard to pick up. It seems to come from the ground, and I definitely seem to hear it more often if I am near a geographical feature, like a deep terrace cut we made to level an area, an old outhouse, or our 4 foot utility trenches (when they were open). It can happen every 30 seconds, or it could happen once a day. I have since heard the same noise consistently on a small lake we kayak fish, when we are out on the water. Depending at where I am on the lake, the noise will sound like it comes from different compass directions. I also heard it once while hiking on a bench above a river that lies in a bit of a valley. If I plot these three points on a map, it makes a triangle with roughly 5-mile sides. At all three locations, the sound presents at the same "volume", meaning nowhere does it sound like the source is closer or further away.
My wife never hears noises that I hear, so the first year, I gave up trying to get her to hear it. This last spring, I got her to hear it at both our property and on the lake. Last year, my parents were with me when I heard it hiking by the river, and they heard it too.
I have been hearing about the so-called "worldwide hum" phenomenon for several years, so I began looking into that. What I found out is that the hum is sort of a catch-all for any environmental auditory phenomena that people experience. Most people that I read about experiencing it either hear a truck idling (kind of similar to mine) or a high-pitched whine. Unfortunately, with the decline of literacy you have a lot of people that are just incapable of describing what they hear, or even understanding what the words they use actually mean. Which is why there are people who hear what sounds like the bass rumble of a large engine idling and think of it as a "hum", kind of like people who think sour and bitter mean the same thing. I did read extensively about a college professor who has been running a study on the hum phenomenon for years. It seems like this professor come to the conclusion that the actual unidentified phenomenon is a higher-pitched hum that people hear that does not actually exist, and is possibly caused by some additive in sodas, with a huge percentage of people thinking that any unidentified noise they hear puts them in the hum club. So I ruled that out as what I was experiencing.
I also looked at industrial noise, which is the obvious answer. My area is mostly national forest, with no large quarrying or mining to speak of. This never seemed like the answer to me anyway, since the uniformity of the volume no matter where I hear it it is the same, and a sound from a pinpoint location like a quarry or mine would seem to diminish the further you get from it. Regardless, there are no operations like this within the triangle of where I hear the noise. We also have busy rail lines in the area. We can hear the train when it rolls through an area about 6 miles from us, but the mystery noise is nothing like the various noises that trains make.
What we also have in the area is a large natural gas pipeline that basically runs through the entire county from north to south. I have learned that these large gas lines need what is called a compressor station about every 50 miles because they have to constantly re-pressurize the gas to keep it moving. At this point, I think that this is the most likely source for the noise. I think because it runs the length of the county, it explains the uniform volume I hear. I don't fully understand how it can sound the same when I am 1/4 mile (the river spot) or 5 miles away (our property and the lake are both about 5 miles from the pipe), but I know that sound and vibration conducts strangely underground. The funny thing is that we lived less than a mile from one of the compressor stations, and about 100 yards from the actual pipeline for one winter and spring before we moved to this property, and I never heard the noise there.