Donald V. Helmberger’s art and science of waveforms

Charles A. Langston

Center for Earthquake Research and Information, University of Memphis, Memphis, TN 38152, USA

I arrived at the Caltech Seismo Lab early in May 1972.The faculty and graduate students had the run of an old mansion (Donnelly Lab) that was slightly tattered around the edges but conducive to both all-night work sessions and goofing off since it still had well-kept grounds that included a tennis court. Most of the graduate students occupied the large dining room on the first floor and we hunted out our advisors, when needed, by trying their offices around the rest of the house, checking out the tennis courts, or visiting the coffee pot in the basement.

Since I arrived several months before the Fall 1972 semester, I was fortunate to be allowed to start working on graduate research. Don was assigned to be my advisor and I visited him in his second-floor office for a first encounter. He got down to business rather quickly by asking me point blank “why do you want to study geophysics?” I was totally unprepared for this question and, in fact, was probably unprepared for any other question as well. While an undergrad at Case Western Reserve, I had developed a burning hate for computer work but an intense love for geology. For some reason, I also did not like seismology, maybe because it was too esoteric, and vowed never to become a seismologist. So, I sat there stunned in front of this seismologist and finally mumbled something about wanting to study the Earth. I think Don just looked at me for a moment probably thinking that here was a guy without a whole lot of promise but that he would run me through some paces over the summer to see what would happen.

My first impression of Don was that here was a real scientist doing inscrutable things that I would really like to understand. He was very young, obviously confident and a bit stand-offish, but seemed to be a straight-ahead nice guy without a big ego. After that initial check-out question there was never a time where Don treated me (or any of his other students) other than an equal colleague. I think that this kind of behavior was what made the lab an incredible learning environment. To be treated as an equal meant that a student had to work hard to catch up with the faculty to earn that place of equality, at least in our own minds.

Don had me looking at seismograms that first summer.He had finished a short paper with an undergraduate intern on the arrival times of regional Pn and PL waves (York and Helmberger, 1973) and wanted to extend that project to determine crustal and upper mantle structure from the waveforms. Of course, I had no idea what to do but picked up some useful skills in digitizing analog seismograms that I used later in my thesis work. It would take another 7 years to complete this program of modeling PnL waves through his work with staff member Gladys Engen(Helmberger and Engen, 1980). Even so, that open-ended dive into seismological research from Don’s new perspective of using waveform shapes and amplitudes has stuck with me over my entire career. While staring at the wiggles on the paper that first summer I wondered if there were other ways of recording seismic data that would give an analyst direct knowledge of the properties of the seismic waves so they could be understood much more quickly. This question stewed for many years in my own research and has resulted in some very interesting new techniques in array seismology (e.g., Langston and Liang,2008; Langston, 2021). I fully attribute this to the questions that Don exposed me to that first summer.

Don was too young to be considered a father figure to his students at that time. Even so, as I look back to his mentoring, it struck me that he had one characteristic that my own father displayed. That characteristic was allowing freedom. Don allowed me and his other students freedom to pursue our work wherever it led. As graduate student life settled in, Don never dictated what should be done or when it should be done, we simply (and energetically)followed the science hunt to wherever it went. This was an incredible gift which the ensuing years have validated over and over seeing how faculty at other institutions treat (or mistreat) their students.

The curriculum at the Lab was unusual in that every course was “Advanced”. There was no preparation with lower-level courses that you often find in other university programs. That first year Don taught Advanced Seismology 261a and shared Advanced Seismology 261c with Dave Harkrider. There were no books, just notes which the students dutifully transcribed from the blackboard. Don’s lectures were quite thorough and addressed the theory behind his cutting-edge science.During that first quarter and continuing throughout the first year, I felt something shift in terms of my appreciation for seismology. Don’s lectures were pointed towards an end of developing ways to understanding the Earth by taking an almost absurdist viewpoint that every wiggle on the seismogram means something. Each feature of a waveform can say something about how seismic waves were produced by earthquakes or how they were affected by their propagation through the Earth.

As an example of how good these courses were, Don and I published a paper based on a homework problem from 261c. Working the material on using the Representation Theorem and resulting wave potentials from the Advanced Seismology course, I wanted to know what would be needed to compute synthetic seismograms from such a general source. Don was working on his seminal work on modeling teleseismic body waves from earthquakes using optic ray approximations of CagniarddeHoop solutions for sources in plane layered media(Helmberger, 1974). However, this paper did not include the full representation of an arbitrarily oriented dislocation source but only had two out of three major source terms. I was surprised when he came to my desk in the student area and asked for my derivation. I was floored when he suggested that we write it all up in a publication (Langston and Helmberger, 1975). This was a defining moment in my graduate career since it was the first time that I had done something that would prove to be useful in Don’s research and the research of many others afterward.

There is one story that I have told my students over the years on the magical wisdom of Don as a research advisor.My first project that developed into a publication involved using Don’s famous computer codes to make plots of synthetic seismograms to compare to the real seismogram data (Langston and Helmberger, 1974). I spent a week of late nights at the Caltech computer center on campus running the code and generated many sheets of Calcomp pen plots of seismograms. (A Calcomp plotter was the main way to make line drawings on the IBM mainframe computer. It consisted of a roll of graph paper and computer-controlled pen to draw each graph.) I had cut each seismogram from the large plots and taped them on other sheets of paper to make record sections of the synthetics to compare with our data. I brought my opus to Don in his office. His first comment was, “can you use more tape?” Obviously, he was amazed at how I had plastered all the cut-and-paste plots with tape; the sarcasm was noted. Ten seconds later he said, “it’s wrong”. It was matter of fact. I tried to argue. I told him how much time I had used sitting around the computer center and that I did everything right. “Nope, it’s wrong.” I was frustrated but we went over the program input and showed me a parameter that was not set correctly. It was then that I learned that “experience” was a very powerful tool when dealing with complicated problems. I have been in exactly the same position with many of my own students over the years when they bring in their work having to say, “Nope,it’s wrong”, and then explaining why. I usually tell this story to soften the blow.

One of Don’s quirks is that he might stare off into space at random times during a conversation. Some students found this unsettling but I was a bit amused by it since I sometimes do the same thing. I simply chalked it up to him trying to fit what he had just heard in the conversation with his intuition. Don was always heavily engaged in dreaming up reasons why a seismogram might look the way that it does. After a while, I came to the conclusion that Don did not do science in a “quantitative”way but did his best work with his intuition. Intuition, at least in my experience, needs some space and some time for a type of activity not too different from daydreaming.When faced with a statement, question, or observation that didn’t immediately fall into line with his thinking, Don’s internal intuition processor would kick in, he would turn his head to the right, and stare off for a while leaving the student to wonder what was going on.

Even though Don was at the forefront of computational seismology and had a deep grasp of the theoretical and mathematical bases of wave propagation, my view was that Don was more an artist than scientist. Perhaps more accurately, Don did excellent science by bringing his intuition to bear on the problem and then using the math to check it out. To me this was Don’s gift and it deepened the way I looked at the work of other scientists as well as how I did my own work.

Don also presented a strong message of academic honesty through his actions with his students. After the first two years of work with him, I was fortunate that my own work took off and that I basically operated independently. I could find a problem, solve the problem,and then write up the results for a publication (Langston,1976, 1977a, b, 1978; Langston and Butler, 1976; Burdick and Langston, 1977; Langston and Blum, 1977). I and my coauthors would show Don what we had accomplished,but he would not allow himself to be a coauthor on the publication because he felt that he hadn’t contributed to the work. Not only did this reinforce the feeling that students were equals to the faculty, but in years after, I got many uncomprehending looks from my peers when I told them that this was standard operating procedure at the Lab. Most faculty I know would never do this even under the same situation where the student did all of the work.

Working with Don in those 5 years at the Lab was among my most significant life experiences. He was a talented guide for turning graduate students into skilled,professional scientists. There is no doubt in my mind that his approach to science and his mentoring were the primary reasons that I have had success in my own career.I am grateful that I was one of his students.