PROBLEM 4–20 A mountain range can be represented as a periodic topography with a wavelength of 100 km and an amplitude of 1.2 km. Heat flow in a valley is measured to be 46 mW m−2. If the atmospheric gradi- ent is 6.5 K km−1 and k = 2.5 Wm−1 K−1, determine what the heat flow would have been without topog- raphy; that is, make a topographic correction.
PROBLEM 4–29 Estimate the effects of variations in bottom water temperature on measurements of oceanic heat flow by using the model of a semi-infinite half-space subjected to periodic surface temperature fluctuations. Such water temperature variations at a specific location on the ocean floor can be due to, for example, the transport of water with variable tem- perature past the site by deep ocean currents. Find the amplitude of water temperature variations that cause surface heat flux variations of 40 mW m−2 above and below the mean on a time scale of 1 day. As- sume that the thermal conductivity of sediments is 0.8 W m−1 K−1 and the sediment thermal diffusivity is 0.2 mm2 s−1.
PROBLEM 4–33 One way of determining the effects of erosion on subsurface temperatures is to consider the instantaneous removal of a thickness l of ground. Prior to the removal T = T0 + βy, where y is the depth, β is the geothermal gradient, and T0 is the surface temperature. After removal, the new surface is main- tained at temperature T0. Show that the subsurface temperature after the removal of the surface layer is given by
How is the surface heat flow affected by the removal of surface material?
PROBLEM 4–39 One of the estimates for the age of the Earth given by Lord Kelvin in the 1860s assumed that Earth was initially molten at a constant tem- perature Tm and that it subsequently cooled by con- duction with a constant surface temperature T0. The age of the Earth could then be determined from the present surface thermal gradient (dT/dy)0. Re- produce Kelvin’s result assuming Tm − T0 = 1700 K, c=1 kJ kg−1 K−1, L =400 kJ kg−1, κ =1 mm2 s−1, and (dT/dy)0 = 25 K km−1 . In addition, determine the thickness of the solidified lithosphere. Note: Since the solidified layer is thin compared with the Earth’s radius, the curvature of the surface may be neglected.
PROBLEM4–43 Themantlerocksoftheasthenosphere from which the lithosphere forms are expected to contain a small amount of magma. If the mass frac- tion of magma is 0.05, determine the depth of the lithosphere–asthenosphere boundary for oceanic li- thosphere with an age of 60 Ma. Assume L = 400 kJ kg−1,c=1kJkg−1 K−1,Tm =1600K,T0 =275K,and κ = 1 mm2 s−1.
PROBLEM 4–52 The ocean ridges are made up of a series of parallel segments connected by transform faults, as shown in Figure 1–13. Because of the dif- ference of age there is a vertical offset on the fracture zones. Assuming the theory just derived is applica- ble, what is the vertical offset (a) at the ridge crest and (b) 100 km from the ridge crest in Figure 4–46 (ρm = 3300kgm−3,κ=1mm2s−1,αv =3×10−5 K−1,T1− T0=1300K,u=50mmyr−1).
PROBLEM 5–7 What is the value of the acceleration of gravity at a distance b above the geoid at the equator (b ≪ a)?
PROBLEM 5–18 A volcanic plug of diameter 10 km has a gravity anomaly of 0.3 mm s−2. Estimate the depth of the plug assuming that it can be modeled by a verti- cal cylinder whose top is at the surface. Assume that the plug has density of 3000 kg m−3 and the rock it intrudes has a density of 2800 kg m−3.
PROBLEM 4–20 A mountain range can be represented as a periodic topography wit
Struggling with a similar assignment? Don’t know where to start? Don’t have time to work on this? Get a high-quality paper written for you from scratch – PLAGIARISM FREE, guaranteed to get you a good grade. To get started, please click on the Submit Your Instructions at the bottom of the page.
Need Writing Help? Our writing specialists are here 24/7, every day of the year, ready to support you! Instantly chat with an online tutor below or click here to submit your paper instructions to the writing team.
More than just an assignment.
Who is this homework service for?
* If you are having a really hard class and want to get through it, then this is for you.
* If you have a medical emergency or someone close to you has a medical emergency and you don’t think you’ll be able to turn your assignment on time, this is definitely a service you could use.
* You can use us if you are having a tough Professor who won’t give you the grades you deserve.
* If you have a tight work schedule and you are getting points deducted for not submitting assignments on time.
* English might not be your first language and you feel like you are being left behind in class because of it.
* If you have a large project coming up and don’t think you have enough time to get it done well, definitely reach out to us.
Hi there! My name is Anna.
Super stoked you are checking us out! We would like to help you with your assignment. We just need a few things from you:
* The full assignment instructions as they appear on your school account.
* If a Rubric is present, make sure to attach it.
* Any relevant weekly readings or learning resources.
* Include any special announcements or emails you might have gotten from your Professor regarding your assignment.
* Any templates or additional files required to complete the assignment.
If your assignment is somewhat complex and you need to explain it, please don’t hesitate to reach out to me via live chat.
Frequently asked questions
How soon can I get my paper done?
It depends with your deadline. If you need your paper completed in 3 hours, we will deliver it in that time. All you need to do is indicate your deadline in our custom order page here. Alternatively, if you are sending us your instructions via email, please be sure to indicate your deadline.
Will it be completely original? I don't want to be caught in a case of Academic Integrity Violation.
We are as paranoid as you are. Maybe even more! And we understand that the greatest sin you can commit in your academic journey is plagiarizing your academic work. To that end, we have made sure that we check and double-check our papers using high quality plagiarism detection tools such as SafeAssign and Turnitin before submitting the paper to you.
Who is my writer? Is he/she a native English Speaker?
All our writers are native English Speakers. That is not to say that ESL writers are not good, we just prefer hiring native writers because we want the very best people working on your paper. This might mean paying a little bit more for your paper as opposed to when you pay a foreign company whose writers are non-native English Speakers.
What if I need revisions? Will your charge additional for this?
Of course not! If you do happen to require a revision on your paper, our team will handle it for you free of charge. Matter of fact, we won’t rest till you are happy with your paper. So, ask for as many revisions as you need, it’s completely FREE!
Will you give me my money back if I don't like my paper?
We have very few instances where we delivered a paper that a client didn’t fall in love with. But if it so happens that you don’t like your paper for any reason whatsoever, we’ll refund your money back no questions asked.
I have more assignments after this, can you help me with those too?
Of course! And what’s even better is that we can reserve a writer permanently to work on your entire class. This comes in handy for projects which build up on each other and where you need just one writer, one writing style.
I got my order information wrong, can I change that?
Yes you can. Just reach out to our support team via email (email@example.com) or live chat here and they’ll help you change the instructions.
Can I place an order via email instead of going through the order page?
Yes you can. Email Anna at firstname.lastname@example.org, she’s in charge of our sales team. Alternatively, you can talk to our Live Chat team here and request to speak to Anna.