are there any method that "Update" command not affect other unrelated indices?

Hi, I have the following table:
CREATE TABLE A
(
   a1 integer not null,
   a2 integer,
   a3 integer,
   a4 integer
)
and have the following four indices:
create index ind_a1 on A USING gist(a1);
create index ind_a2 on A USING gist(a2);
create index ind_a3 on A USING gist(a3);
create index ind_a4 on A USING gist(a4);

now we have 10,000 update command executions using spi_exeplan():
SPI_prepare(); // prepare the plan for "update A set a4 = $1;"
for(i=0;i<10000;i++ ){
   SPI_execute_plan();//   update A set a4 = i; 
}

the question is why all four indices updated in the execution of SPI_execute_plan()? 
I think there should only one index, that is ind_a4 be updated, how to avoid other three indices updated?
thanks!